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QUALITY IN FIVES

On the Analysis, Operationalization and Application ofNursing Schedule Quality

Johan H. Oldenkamp

Rijksuniversiteit Groningen

QUALITY IN FIVES

On the Analysis, Operationalizationand Application of Nursing Schedule Quality

Proefschrift

ter verkrijging van het doctoraat in deBedrijfskunde

aan de Rijksuniversiteit Groningenop gezag van de

Rector Magnificus Dr. F. van der Woudein het openbaar te verdedigen op

donderdag 10 oktober 1996des namiddags te 2.45 uur

door

Johannes Hendrik Oldenkampgeboren op 5 november 1966

te Groningen

Promotor

Prof. Dr. Ir. J.L. Simons

CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG

Oldenkamp, Johannes Hendrik

Quality in five; on the analysis, operationalization and application of nursingschedule quality / Johannes Hendrik Oldenkamp.Capelle a/d IJssel: Labyrint Publication. - Ill.Thesis Rijksuniversiteit Groningen. - With ref. - With summary in Dutch.ISBN Subject headings: nurse scheduling / decision support systems.

Layout: Henny Wever

Published by: LABYRINT PUBLICATIONP.O. Box 6622900 AR Capelle a/d IJsselThe Netherlandsfax 31 (0) 10-451 97 94

Printed by: Ridderprint, Ridderkerk

Copyright © 1996, J.H. Oldenkamp

All rights reserved. No part of this publication may be reprinted or utilized inany form or by any electronic, mechanical or other means, now known orhereafter invented, including photocopying and recording, or in anyinformation storage or retrieval system, without prior written permission fromthe copyright owner.

Promotiecommissie (Dissertation Committee)

Prof. Dr. A.F. CasparieProf. Dr. K.B. KosterProf. Dr. A.H. van der Zwaan

ACKNOWLEDGMENTS

This thesis describes the results of a study on nurse scheduling conducted atthe faculty of Management and Organization of the University of Groningen.Six health care organizations participated in this study, which are the univer-sity hospital of Groningen, the Groningen hospital ‘Martini’, the Zuidlaren psy-chiatric hospital ‘Dennenoord’, the Groningen nursing home ‘Heijmans-centrum’, the Winsum nursing home ‘De Twaalf Hoven’, and the Ermelo healthcare organization called ‘'s Heeren Loo-Lozenoord’. I would like to thankeveryone in one of these health care organizations who participated in thisresearch or made this research possible. Especially, I would like to mention thenurse schedulers who participated in more than one of this study's researchsteps. These nurse schedulers are Alberta de Jonge, Rewinga Wierenga,Geessiena Wildeman, Lizet van Leeuwen, Gerda Yntema, Alma Noppers, AnkeVreema, Ineke de Groot, Reinolt Mulder and Meindert Kamp.

The research described in this thesis was conducted by the QUINS project. Thisproject was supervised by my promotor John Simons. Without his efforts, thisthesis would not have been written.

Two students played in an important role in this project. Martha Lettengaassisted in the research step described in chapter 5, and Hein Zelle wrote theadditional software used in the final research step described in chapter 7. I amboth Martha and Hein grateful for their help.

This research used the ZKR scheduling support system to do several experi-ments. This system was supplied by IKS Produkten (see also Appendix C). Iwould like to thank Jacques Boersma and Erik Huisman for their cooperationwith the QUINS project.

Several others also contributed to this research. I would like to thank Rob deBruin for writing a computer program in FORTRAN for the analysis of a part ofthis study's research results and for commenting on the corresponding part ofchapter 6. I also would like to thank several of my former colleagues at theFaculty of Management and Organization for commenting on parts of this

study or previous publications based on this study. These former colleagues areDieta Mietus, Ad Breukel, Sven van der Zee, Henk Gazendam, Bert de Brock,Han Numan, Hans van den Broek, Vincent Homburg, Margriet Offereins, Henvan de Water and Derk Jan Kiewiet.

Furthermore, I am very grateful to Henny Wever. Without her tremendous help,the layout of this thesis would have been quite different.

Although most of their contribution is still to come, I would also like to thankmy paranymphs: Kees Tijs and Constantijn Heesen.

Also I would like to thank the members of my dissertation committee, professorVan der Zwaan, professor Koster and professor Casparie, for their comments onthis thesis.

Finally I would like thank my parents, Henk and Ria Oldenkamp, my wife,Monique Oldenkamp, and also Jan and Hil Bremer, my uncle and aunt. Withouttheir support and stimulation, I would not have been able to even start writingthis thesis.

Johan H. OldenkampGroningen, The NetherlandsJuly 1996

TABLE OF CONTENTS

List of figures and tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

PART I: INTRODUCTION

1 Quality of nursing schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 Nursing management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Policies and planning of nurses and patients . . . . . . . . . . . . . . . . 41.1.2 Levels of planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.3 Definitions of nurse scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.4 Consequences of nursing schedules . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 Pluriformity of nursing schedule quality . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.1 The nurses' view on nursing schedule quality . . . . . . . . . . . . . . . . 91.2.2 The patients' view on nursing schedule quality . . . . . . . . . . . . . 101.2.3 The management view on nursing schedule quality . . . . . . . . . 101.2.4 The nurse scheduler's view on nursing schedule quality . . . . . 11

1.3 Decision support for nurse scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.1 Influences on nurse scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.2 The quality chain of nurse scheduling support systems . . . . . . 121.3.3 Difficulty in solving the nurse scheduling problem . . . . . . . . . . 14

1.4 Preliminary research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.5 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

PART II: THEORETICAL BACKGROUND

2 Approaches to supporting nurse scheduling . . . . . . . . . . . . . . . . . . . . . . . 212.1 Theoretical quality aspects of nursing schedules . . . . . . . . . . . . . . . . . 21

2.1.1 Facilitation of high-quality nursing care . . . . . . . . . . . . . . . . . . . 222.1.2 Facilitation of efficient nursing care . . . . . . . . . . . . . . . . . . . . . . 232.1.3 Facilitation of job satisfaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Table of contentsii

2.1.4 Supporting multiple views on nursing schedule quality . . . . . . 242.2 Nurse scheduling support systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.1 Exhaustive search for optimal schedules . . . . . . . . . . . . . . . . . . . 272.2.2 Search for cyclic schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2.3 Heuristic search for feasible schedules . . . . . . . . . . . . . . . . . . . . 292.2.4 Knowledge-based search for good schedules . . . . . . . . . . . . . . . 302.2.5 Data management for nurse scheduling . . . . . . . . . . . . . . . . . . . . 312.2.6 Interactive scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.7 Self scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.8 Conclusions of the comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3 The approach of quality indication scheduling . . . . . . . . . . . . . . . . . . . 342.3.1 Assumption of formalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.2 Assumption of robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.3 Assumption of effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

PART III: METHODOLOGY

3 Methodological foundation of the research approach . . . . . . . . . . . . . . 393.1 Research question and hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.1 Hypothesis of formalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.1.2 Hypothesis of robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.1.3 Hypothesis of effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.1.4 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2 Research design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.1 Questionnaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2.2 Ranking experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2.3 Auditing experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2.4 Scheduling experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

PART IV: EMPIRICAL RESULTS

4 Quality factors of nursing schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.1 Candidates for quality factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 Analysis of the candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Table of contents iii

4.2.1 Analysis on perceivability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2.2 Analysis on independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2.3 Working set of quality factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3 Validation of the quality factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.3.1 Definition phrases referring to completeness . . . . . . . . . . . . . . . 594.3.2 Definition phrases referring to optimality . . . . . . . . . . . . . . . . . . 624.3.3 Definition phrases referring to proportionality . . . . . . . . . . . . . 624.3.4 Definition phrases referring to healthiness . . . . . . . . . . . . . . . . . 644.3.5 Definition phrases referring to continuity . . . . . . . . . . . . . . . . . . 654.3.6 Remaining phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.7 Conclusions of the qualitative factor analysis . . . . . . . . . . . . . . 66

4.4 Final set of quality factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5 Ranking of shift patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.1 Characteristics of a nursing unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.1.1 Levels of nursing expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.1.2 Length of schedule period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.1.3 Types of working days . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.1.4 Quantitative staffing demands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2 Design of the ranking experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.2.1 Decision aspects concerning completeness . . . . . . . . . . . . . . . . . 745.2.2 Decision aspects concerning optimality . . . . . . . . . . . . . . . . . . . 755.2.3 Decision aspects concerning proportionality . . . . . . . . . . . . . . . 755.2.4 Decision aspects concerning healthiness . . . . . . . . . . . . . . . . . . . 775.2.5 Decision aspects concerning continuity . . . . . . . . . . . . . . . . . . . 79

5.3 Results of the ranking experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.3.1 Rankings of shift patterns concerning completeness . . . . . . . . . 815.3.2 Rankings of shift patterns concerning optimality . . . . . . . . . . . 825.3.3 Rankings of shift patterns concerning proportionality . . . . . . . 825.3.4 Rankings of shift patterns concerning completeness . . . . . . . . . 835.3.5 Rankings of shift patterns concerning continuity . . . . . . . . . . . 84

5.4 Conclusions of the ranking experiment . . . . . . . . . . . . . . . . . . . . . . . . . 845.5 Operationalization of the quality factors . . . . . . . . . . . . . . . . . . . . . . . . 85

5.5.1 Indication of completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.5.2 Indication of optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.5.3 Indication of proportionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.5.4 Indication of healthiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Table of contentsiv

5.5.5 Indication of continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.5.6 Discussion of the operationalizations . . . . . . . . . . . . . . . . . . . . . 91

Table of contents v

6 Auditing of nursing schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.1 Design of the auditing experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.2 Results of the auditing experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.2.1 Determination of summation weights . . . . . . . . . . . . . . . . . . . . . . 976.2.2 Goodness of fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.2.3 Coping with differences in marking style . . . . . . . . . . . . . . . . . 102

6.3 Conclusions of the auditing experiment . . . . . . . . . . . . . . . . . . . . . . . . 104

7 Effective decision support for nurse scheduling . . . . . . . . . . . . . . . . . . 1077.1 Design of the scheduling experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.1.1 Steps of the sheduling experiment . . . . . . . . . . . . . . . . . . . . . . . 1087.1.2 Variables of the scheduling experiment . . . . . . . . . . . . . . . . . . . 1087.1.3 Characteristics of the East-5 nursing unit . . . . . . . . . . . . . . . . . 1107.1.4 Characteristics of the initial schedule . . . . . . . . . . . . . . . . . . . . 111

7.2 Results of the scheduling experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.2.1 Values of the original final schedules . . . . . . . . . . . . . . . . . . . . 1137.2.2 Values of the new final schedules . . . . . . . . . . . . . . . . . . . . . . . . 1197.2.3 Randomized pre-test post-test control group design . . . . . . . . 121

7.3 Conclusions of the scheduling experiment . . . . . . . . . . . . . . . . . . . . . 127

PART V: CONCLUSIONS

8 Analysis, operationalization, and application of nursingschedule quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1318.1 Analysis of nursing schedule quality . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.2 Operationalization of nursing schedule quality . . . . . . . . . . . . . . . . . 1328.3 Application of nursing schedule quality . . . . . . . . . . . . . . . . . . . . . . . . 1348.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1348.5 Generality of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1358.6 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

8.6.1 Nursing schedule quality in practice . . . . . . . . . . . . . . . . . . . . . 1368.6.2 Run-time quality indication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1378.6.3 Flexible support of nurse scheduling . . . . . . . . . . . . . . . . . . . . . 138

Table of contentsvi

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

AppendicesAppendix A Questionnaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Appendix B Rankings of the shift patterns . . . . . . . . . . . . . . . . . . . . . . . 153Appendix C The ZKR scheduling support system . . . . . . . . . . . . . . . . . 199Appendix D Reference case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Samenvatting (Summary in Dutch) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Curriculum vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

LIST OF FIGURES AND TABLES

Figure 1.1 Policies and planning of nurses and patients . . . . . . . . . . . . . . . . 4Figure 1.2 A nursing schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 1.3 Consequences of nursing schedules for the performance

of the nursing unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.4 Influences on nurse scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 1.5 The quality chain of nurse scheduling support systems . . . . . . 13Figure 1.6 Cycle of developing decision support . . . . . . . . . . . . . . . . . . . . . 14Figure 1.7 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 3.1 Four hierarchical layers of nursing schedule quality . . . . . . . . 40Figure 3.2 The first empirical cycle of the research design . . . . . . . . . . . . . 45Figure 3.3 The second empirical cycle of the research design . . . . . . . . . . 47Figure 3.4 The third empirical cycle of the research design . . . . . . . . . . . . 49Figure 3.5 The fourth empirical cycle of the research design . . . . . . . . . . . 50Figure 4.1 The working set of quality factors . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 4.2 Research steps taken to find the five factors of nursing

schedule quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 4.3 Final set of quality factors of nursing schedules . . . . . . . . . . . . 69Figure 7.1 Steps of the scheduling experiment . . . . . . . . . . . . . . . . . . . . . . 109Figure 7.2 The initial schedule used in the scheduling experiment . . . . . 112Figure 7.3 The original final schedule arranged by nurse scheduler

number five . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 7.4 The new final schedule rearranged by nurse scheduler

number five . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Figure C.1 Representation of a nursing schedule in the ZKRprogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

Figure D.1 The less flexible initial schedule used in the additionalcase study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Figure D.2 The arranged original final schedule . . . . . . . . . . . . . . . . . . . . . 204Figure D.3 The rearranged new final schedule . . . . . . . . . . . . . . . . . . . . . . . 205

List of figures and tablesviii

Table 2.1 Theoretical quality aspects of nursing schedules . . . . . . . . . . . . 22Table 2.2 Approaches to supporting nurse scheduling . . . . . . . . . . . . . . . . 25Table 2.3 Comparison of approaches to supporting nurse scheduling . . . 33Table 4.1 The eight goals of nurse scheduling . . . . . . . . . . . . . . . . . . . . . . . 54Table 4.2a The eighteen definitions of nursing schedule quality . . . . . . . . 60Table 4.2b The eighteen definitions of nursing schedule quality . . . . . . . . 61Table 4.3 Definition phrases referring to the completeness factor . . . . . . 62Table 4.4 Definition phrases referring to the optimality factor . . . . . . . . . 63Table 4.5 Definition phrases referring to the proportionality factor . . . . 63Table 4.6 Definition phrases referring to the healthiness factor . . . . . . . . 64Table 4.7 Definition phrases referring to the continuity factor . . . . . . . . . 65Table 4.8 Definition phrases referring to imperceivable aspects of

nursing schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table 5.1 Decision aspects of completeness . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 5.2 Decision aspects of optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 5.3 Decision aspects of proportionality . . . . . . . . . . . . . . . . . . . . . . . 77Table 5.4 Decision aspects of healthiness . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Table 5.5 Decision aspects of continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Table 5.6 Coefficients of concordance per quality factor per

decision aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Table 5.7 Required number of staff members per type of shift (n ) . . . . . 86ij

Table 5.8 Required number of registered nurses per type of shift (l ) . . . 88ij

Table 5.9 Unhealthy shift patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Table 5.10 Meaning of shift codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Table 6.1 Number of arranged nursing schedules per number of

unacceptable factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Table 6.2 Indication of the factor values of the fifteen fictitious

nursing schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Table 6.3 Correlation coefficients for the factor values . . . . . . . . . . . . . . . 96Table 6.4 Probabilities of non-correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 97Table 6.5 Quality marks given by the nurse schedulers (Q ) . . . . . . . . . . 98s,i

Table 6.6 Summation weights per nurse scheduler . . . . . . . . . . . . . . . . . . . 99Table 6.7 Predicted quality marks (QN ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 100s,i

Table 6.8 Mean marking scores and the standard deviation pernurse scheduler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Table 6.9 Linearly transformed quality marks (Q ) . . . . . . . . . . . . . . . . . 102 ns,i

Table 6.10 New summation weights per nurse scheduler . . . . . . . . . . . . . . 103Table 6.11 Predicted linearly transformed quality marks (QN ) . . . . . . . . 105n

s,i

List of figures and tables ix

Table 7.1 Characteristics of the East-5 nursing staff . . . . . . . . . . . . . . . . . 110Table 7.2 Average number of annual working days . . . . . . . . . . . . . . . . . 111Table 7.3 Factor values of the original final schedules . . . . . . . . . . . . . . 114Table 7.4 Total scheduling time in the traditional situation . . . . . . . . . . . 115Table 7.5a Numbers of occurrences of low-quality schedule patterns

in original final schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Table 7.5b Numbers of occurrences of low-quality schedule patterns

in original final schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Table 7.6 Summarized number of low-quality schedule patterns per

quality factor in original final schedules . . . . . . . . . . . . . . . . . . 119Table 7.7 Factor values of the new final schedules . . . . . . . . . . . . . . . . . . 120Table 7.8 Total scheduling time in the new situation . . . . . . . . . . . . . . . . 121Table 7.9a Numbers of occurrences of low-quality schedule patterns

in new final schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Table 7.9b Numbers of occurrences of low-quality schedule patterns

in new final schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Table 7.10 Summarized number of low-quality schedule patterns per

quality factor in new final schedules . . . . . . . . . . . . . . . . . . . . . 125Table 7.11 Results of the first pre-test post-test control group design . . . 125Table 7.12 Results of the second pre-test post-test control

group design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Table B.1 Combination decision about completeness on normalworking days (C-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Table B.2 Combination decision about completeness on specialworking days (C-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Table B.3 Combination decision about completeness per type ofworking day (C-3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Table B.4 Decision aspect of day shift optimality on normalworking days (O-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Table B.5 Decision aspect of evening shift optimality on normalworking days (O-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Table B.6 Decision aspect of night shift optimality on normalworking days (O-3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Table B.7 Combination decision about optimality on normalworking days per type of shift (O-4) . . . . . . . . . . . . . . . . . . . . . 172

List of figures and tablesx

Table B.8 Decision aspect of day shift optimality on specialworking days (O-5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Table B.9 Decision aspect of evening shift optimality on specialworking days (O-6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Table B.10 Decision aspect of night shift optimality on specialworking days (O-7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Table B.11 Combination decision about optimality on special workingdays per type of shift (O-8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Table B.12 Combination decision about optimality per type ofworking day (O-9) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Table B.13 Decision aspect of proportionality concerning thenumbers per type of shift (P-1) . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Table B.14 Decision aspect of proportionality concerning thedistribution of days off (P-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Table B.15 Decision aspect of proportionality concerning thedistribution of weekends off (P-3) . . . . . . . . . . . . . . . . . . . . . . . 180

Table B.16 Combination decision about the importance perdecision aspect concerning proportionality (P-4) . . . . . . . . . . 181

Table B.17 Decision aspect of healthiness concerning thenumber of consecutive night shifts (H-1) . . . . . . . . . . . . . . . . . 186

Table B.18a Decision aspect of healthiness concerning the numberof consecutive evening shifts (H-2) . . . . . . . . . . . . . . . . . . . . . . 182

Table B.18b Decision aspect of healthiness concerning the numberof consecutive evening shifts (H-2); re-interpretationof given rankings by clustering four items(g + h + i + j 6 g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Table B.19a Decision aspect of healthiness concerning the numberof consecutive day shifts (H-3) . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Table B.19b Decision aspect of healthiness concerning the numberof consecutive day shifts (H-3); re-interpretation of givenrankings by clustering four items (g + h + i + j 6 g) . . . . . . . . 185

Table B.20 Decision aspect of healthiness concerning the numberof consecutive working days (H-4) . . . . . . . . . . . . . . . . . . . . . . . 187

Table B.21 Combination decision about the importance per decisionaspect concerning healthiness of consecutive shifts (H-5) . . . 188

Table B.22 Decision aspect of healthiness concerning the amountof resting time after a period of night shifts (H-6) . . . . . . . . . . 189

Table B.23 Decision aspect of healthiness concerning the amount

List of figures and tables xi

of resting time between a change of shift without daysoff (H-7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Table B.24 Decision aspect of healthiness concerning the amountof resting time between a change of shift with daysoff (H-8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Table B.25 Combination decision about the importance per decisionaspect concerning healthiness of scheduled restingtime (H-9) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Table B.26 Combination decision about the importance of healthinessof consecutive shifts versus healthinesss scheduledresting time (H-10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Table B.27 Decision aspect of continuity during night shifts (T-1) . . . . . 194Table B.28 Decision aspect of continuity during evening shifts (T-2) . . . 195Table B.29 Decision aspect of continuity during day shifts (T-3) . . . . . . . 196Table B.30 Combination decision about the importance of continuity

per type of shift (T-4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Table D.1 Factor values of the original schedule . . . . . . . . . . . . . . . . . . . . 201Table D.2 Numbers of occurrences of low-quality patterns in the

orginal final schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

CHAPTER 1

QUALITY OF NURSING SCHEDULES

In most health care organizations, nursing care has to be provided continuously.This means that this process of providing nursing care goes on twenty-four hoursa day, seven days a week, and fifty-two weeks a year. Consequently, nurses haveto work during day shifts, evening shifts, and night shifts, and often on irregularworking days, such as holidays and weekends. The task of arranging these shiftsis generally called nurse scheduling.

This thesis describes a study which investigated the task of nurse scheduling.The present chapter introduces this subject of study. The first section describes thecontext of this task, which is nursing management, and deals with the relevanceof this study from a management point of view. The second section discusses thesocietal relevance of this study. This societal relevance is related to theconsequences of nursing schedules for both nurses and patients. The scientificrelevance of this study, which is the subject of the third section, is a new approachto supporting nurse scheduling. This chapter ends with preliminary researchquestions and an outline of this thesis.

1.1 NURSING MANAGEMENT

Health care organizations are mostly divided into a number of nursing units (seeLandman & Van den Boom, 1991, pp. 190-192). The director of a nursing unit iscalled a nurse administrator (see also Kedzierski & Vlemmix, 1992). One of thethe most important functions of the nurse administrators is to gear the deploymentof nurses to the patients admitted to the nursing unit (Gallagher, 1987). This sectiondiscusses the characteristics of this attunement. The next subsections describepolicies and planning related to this attunement, its levels of planning, definitions,and consequences.

Figure 1.1 POLICIES AND PLANNING OF NURSES AND PATIENTS

staffingpolicy

staffing

nursingstaff

nurse schedulingpolicy

nursescheduling

nursingschedule

admissionpolicy

admissionplanning

flow ofpatients

Chapter 14

1.1.1 Policies and planning of nurses and patients

The numbers of nurses working at a nursing unit is a result of the process ofnursing staff planning, mostly referred to as staffing. The staffing policy controlsthis process of staffing (see Louwies, 1984, pp. 81-91). This staffing policy deter-mines, for instance, the ratios per nurse category (e.g. registered nurses, licensedpractical nurses and nursing assistants) at each nursing unit.

On the other hand, the numbers of patients admitted to a nursing unit is a result ofthe process of admission planning (see also De Vries, 1984b). The admission policycontrols this process of admission planning (e.g. Hogewind, 1988; Kusters, 1988,pp. 71-72; Lettink, 1990, p. 394). This admission policy determines, for instance,the types of patients admitted to each nursing unit.

Nursing schedules attune the nurses working at the nursing unit to the patientsadmitted to this nursing unit. The process of nurse scheduling determines thefeatures of these nursing schedules (see Diekema, 1984, pp. 55-65). The nursescheduling policy controls this process of nurse scheduling (see Kedzierski, 1984,pp. 15-16). This nurse scheduling policy determines, for instance, the procedurefor assigning short time days (see also De Vries, 1984a).

Figure 1.1 shows these three management levels of the attunement of nursesand patients. The top levels are the policy levels. The intermediate levels concernsthe processes of planning. And the bottom levels represent the outcomes of theseplanning processes.

5

1.1.2 Levels of planning

Anthony (1965) distinguishes three different levels of planning: strategic, tactical,and operational planning. The three types of planning shown in figure 1.1 (i.e.nursing staff planning (or staffing), admission planning and nursing scheduleplanning (or nurse scheduling)) are divided on the basis of these three levels (seealso De Vries, 1988, pp. 43-44).

Strategic nursing staff planning involves the determination of the types ofpersonnel to be employed on a permanent basis. Tactical nursing staff planninginvolves determining the numbers of personnel assigned to a nursing unit. Thistactical nursing staff planning mostly involves a period of about a year. Thistactical staffing is mostly referred to as the ‘staffing problem’ (see Warner, 1976).Operational nursing staff planning involves the ‘allocation’ of the work tasks tothe nursing personnel. Operational nursing staff planning involves a period of oneday. This study will refer to operational nursing staff planning as the ‘taskallocation problem’.

Strategic admission planning involves the determination of the types ofpatients to be admitted to each nursing unit. Tactical admission planning involvesthe determination of the day and time of admission per patient. This tacticaladmission planning is also referred to as ‘inpatient admission scheduling’ (seeSmith-Daniels et al., 1988, pp. 897-899). Operational admission planning concernsthe assignment of each patient to a room and a bed.

Strategic nurse scheduling concerns scheduling decisions involving a periodof about a year, covering, for example, the planning of each nurse’s vacations.Tactical nurse scheduling involves determining those days and shifts when eachmember of the nursing staff is to report for work in the predetermined schedulinghorizon. In general, the length of this predetermined scheduling horizon variesfrom two to six weeks. This tactical nurse scheduling is mostly referred to as the‘nurse scheduling problem’ (see Ahuja & Sheppard, 1975; Warner, 1976). Opera-tional nurse scheduling concerns rescheduling caused by illness, on a daily basis.

1.1.3 Definitions of nurse scheduling

This study focuses on the nurse scheduling problem mentioned above. Thisproblem is primarily a tactical problem (see also Arthur & Ravindran, 1981, p. 55;Mietus, 1994, p. 18). Mostly, this tactical nurse scheduling is simply referred toas nurse scheduling, but ‘nurse shift scheduling’ (see Chen & Yeung, 1992) or

Chapter 16

‘nursing staff scheduling’ (see Okada & Okada, 1988) are also used. Nursescheduling is the procedure for providing nursing care by assigning shifts tonursing personnel (Rowland & Rowland, 1985). To be more specific, nursescheduling is the process of determining when each nurse of a nursing unit will beon or off duty, which shift will be worked, by whom, and how weekends, thenumber of consecutive days worked, requests, and vacations will be accounted for(Fluharty, 1988, p. 5).

Nurse scheduling involves three dimensions (see also Oldenkamp, 1992a, p.70; Oldenkamp & Simons, 1994, p. 2). The first dimension concerns the nursingstaff. Members of this nursing staff might differ concerning their professionalcategory (e.g. registered nurses, licensed practical nurses, nursing assistants, andstudent nurses or trainee nurses), or their labor contract (e.g. full time or part time).The second dimension concerns the days of the schedule period. These days canbe divided into two types: special working days (i.e. (public) holidays orweekends), and regular working days (i.e. all remaining days). The third dimensionof nurse scheduling concerns the shifts to be assigned to a member of the nursingstaff on a particular day of the schedule period. These shifts can be divided intotwo groups: ‘productive’ shifts (i.e. day shifts, evening shifts, and night shifts) and‘unproductive’ shifts (e.g. day off or special leave). In the case of the nursescheduling problem, each (productive) shift’s beginning and duration is fixed.

1.1.4 Consequences of nursing schedules

The outcome of the nurse scheduling task is the nursing schedule. Figure 1.2 showsthis type of nursing schedule.

Two of the three dimensions of nurse scheduling are explicitly representedin a nursing schedule. The horizontal dimension represents the days of the scheduleperiod, while the members of the nursing staff are represented vertically. The thirddimension of nurse scheduling is implicitly represented in the cells of the nursingschedule. The color (i.e. grey shade) of each cell represents the type of shiftassigned to the corresponding nurse on the corresponding day.

Nursing schedules have a number of consequences for the performance ofthe nursing unit. Fitzpatrick, Farrell and Richter-Zeunik (1987) found several ofthese types of (negative) consequences, such as unnecessary overtime, highcharges for agency nurses, frequent schedule changes and nurse dissatisfactionwith assignments that led to absenteeism and a high turnover rate (p. 10). For

7

Figure 1.2 A NURSING SCHEDULE

Figure 1.3 CONSEQUENCES OF NURSING SCHEDULES FOR THE PERFORMANCEOF THE NURSING UNIT

nursing schedule

nursing staff nursing care nursing unit

Chapter 18

with assignments that led to absenteeism and a high turnover rate (p. 10). Forexample, the nurse coded as ‘vm-11’ in figure 1.2 works nine days in a row startingin the third week. This type of working schedule might have negative consequencesfor this nurse (e.g. low job satisfaction).

Below, the consequences of nursing schedules are divided into three parts:the effectiveness in providing nursing care, the efficiency of a nursing unit and thejob satisfaction of the nursing staff. Figure 1.3 shows this division of theconsequences of nursing schedules for the performance of the nursing unit.

The main consequences of nursing schedules concern the effectiveness inproviding nursing care. The effectiveness is mostly specified as the continuity innursing care, because this continuity is an important requirement for the provisionof high-quality nursing care. Nursing schedules determine this continuity in thisnursing care (see Bisseling, 1993; Marquis & Huston, 1994).

Other consequences of nursing schedules concern the working hours of thenursing staff. A nursing schedule determines when each nurse will be on or off dutyand which shift will be worked. This determination of the nurses’ working hoursstrongly affects their social and family life (see Hung, 1992; Chen & Yeung, 1992;Oldenkamp, 1992b). As an impairment of social and family life decreases jobsatisfaction (see also Jansen et al., 1986; Jansen, 1987), nursing schedules affectthe job satisfaction of the nursing staff.

The remaining consequences of nursing schedules concern the nursing unit.Nursing schedules determine both the number of nurses and the amount of nursingexpertise present in the nursing unit at each time of day. These numbers of nursesand amounts of nursing expertise strongly influence the cost of providing the dailynursing care (see Gallagher, 1987; Fluharty, 1988). And because the salaries paidto nursing personnel constitute the largest single cost element in hospitals (e.g. Kao& Queyranne, 1985; Smith-Daniels et al., 1988; Ozkarahan & Bailey, 1988, p. 306),nursing schedules strongly affect the efficiency of a nursing unit. For example,there are too many nurses scheduled on the Monday and Tuesday of the fifth weekin figure 1.2, which decreases the efficiency of the presented nursing schedule.

Furthermore, both job satisfaction and the efficiency of a nursing unit willalso affect the quality of the nursing care, because an under-motivated nursing staff

9

or too few (registered) nurses per shift will reduce this quality. Figure 1.3 alsoshows these indirect consequences of nursing schedules.

1.2 PLURIFORMITY OF NURSING SCHEDULE QUALITY

Nurse scheduling involves three parties with different interests. These parties arethe nursing personnel working at the nursing unit, the patients admitted to thisnursing unit, and the (financial) management of the nursing unit. These parties canstrongly differ in their views on the intended quality of nursing schedules. Thefollowing subsections discuss these different views in more detail.

1.2.1 The nurses’ view on nursing schedule quality

Nurses have a strong interest in nurse scheduling because their social and familylife is highly restricted by the scheduled working hours. Also the health of nursesis strongly influenced by the irregularity in working hours (see Van Emmerik,1992a; 1992b). To reduce the health impairment for nurses, Dutch nurse schedulersare obliged to take into account a number of regulations (Grunveld, Van der Speld& Overbosch, 1993).

Furthermore, nurses in most nursing units can specify general preferencesand incidental requests. These preferences concern, for example, a fixed eveningoff (e.g. sports evening), while special requests mostly concern a day off (e.g. awedding). By means of these preferences and requests, nurses can influence theirown working schedules. The nurse scheduler decides which of these preferencesand requests can be granted.

Summarizing, the nurses’ view on nursing schedule quality concerns theimpairment of health and of social and family life. To stress this view, Bisseling(1993, p. 13) introduced the concept of ‘schedule contentment’, which he definednot only as the employee’s contentment concerning the scheduled shifts, but alsoas the contentment about several ‘schedule risk criteria’ (see also Jansen, 1987),the (in)convenience of the working hours, the potential for recovery and the em-ployee’s opinion about her or his health.

1.2.2 The patients’ view on nursing schedule quality

Because high-quality nursing care is strongly influenced by the continuity in thedaily scheduled nurses (see Marquis & Huston, 1994), a second party with aninterest in nurse scheduling is the patients. Furthermore, the numbers of nurses andtheir levels of nursing expertise also influence the quality of nursing care. Patientswill prefer health care organizations with nursing schedules that facilitate high-

Chapter 110

quality nursing care. Patient-centred health care organizations will therefore tryto provide patient care with high continuity. This means that a patient-centredmanagement view includes this patients’ view. Summarizing, the patients’ viewon nursing schedule quality concerns the continuity in the daily scheduled nurses,together with a sufficient amount of nursing expertise.

1.2.3 The management view on nursing schedule quality

A third party with an interest in nurse scheduling is the (financial) managementof the nursing unit. This interest is based on the fact that the efficiency of a nursingunit determines the costs to a large extent. This not only involves the total of themonthly salaries, but also a number of problems related to nurse scheduling. Highturnover, absenteeism and poor job performance are prevailing problems fornursing management in health care organizations (Richman, 1987; Hung, 1992).The stressful working environment, the uncompetitive salary, the lack of a positivecareer image and the irregular working schedules are factors which contribute tothese problems (Wagner, 1988). A management view on nursing schedule qualitywill therefore include these factors. Summarizing, the management view on nursingschedule quality concerns the effect of these working schedules on the efficiencyof the nursing unit.

1.2.4 The nurse scheduler’s view on nursing schedule quality

When arranging nursing schedules, nurse schedulers, as administrators of thenursing unit, take into account all the consequences nursing schedules have forthe performance of the nursing unit. These consequences are stressed by the inter-ests of the nursing unit’s nurses, patients or financial management. Mostly, theseinterests are conflicting, which makes it impossible to arrange a schedule whichis best according to all views. Therefore, a nurse scheduler tries to arrange anursing schedule which is as good as possible taking into account all theconsequences of this schedule for the parties involved. However, the prioritiesgiven to each of these consequences might very well differ per health care organiz-ation, nursing unit or nurse scheduler.

1.3 DECISION SUPPORT FOR NURSE SCHEDULING

The nursing schedule is an outcome of the process of nurse scheduling. An im-provement of nursing schedule quality will therefore require an improvement inthe process of nurse scheduling. The following subsection discusses four types ofinfluence on nurse scheduling that could facilitate an improvement. The rest of thissection will then discuss one of these influences in more detail.

Figure 1.4 INFLUENCES ON NURSE SCHEDULING

schedulingregulations

schedulingskill

nursescheduling

methodof scheduling

schedulingsupport

11

1.3.1 Influences on nurse scheduling

The actual process of nurse scheduling is influenced by the scheduling skill of thenurse scheduler, the method of scheduling applied to arrange nursing schedules,all kinds of scheduling regulations and all kinds of scheduling support. Figure 1.4shows these four influences on nurse scheduling.

Each of these four influences on nurse scheduling can be used to increase thequality of the resulting nursing schedules. Increasing the skill of nurse schedulersinvolves, for example, additional training programmes. Examples of increasingnursing schedule quality by means of improving the method of scheduling aregiven by Diekema (1994) and De Vries-Griever and colleagues (1994). Regulations(by Dutch law) designed to improve the quality of nursing schedules are describedby Grunveld, Van der Speld and Overbosch (1993). The fourth influence on nursescheduling concerns the support of this task by means of computer programs orother kind of tools.

For more than two decades, researchers have been trying to develop computerprograms in order to support the task of nurse scheduling (see Warner & Prawda,1972; Arthur & Ravindran, 1981; Ozkarahan & Bailey, 1988; Okada, 1992; Chen& Yeung, 1992; Mietus, 1994; Weil et al., 1995). The present study also followsthis management informatics approach. It focuses on the influence of the supportof computer programs on the task performance of nurse scheduling. The nextsubsection describes this influence as a link in a quality chain.

1.3.2 The quality chain of nurse scheduling support systems

During the last decades, many scientific studies have been conducted in order to

Figure 1.5 THE QUALITY CHAIN OF NURSE SCHEDULING SUPPORT SYSTEMS

NSSSdevelopment

NSSS

nursescheduling

nursingunit performance

nurseschedule

Chapter 112

support the task of nurse scheduling by means of a computer program (see Warner& Prawda, 1972; Arthur & Ravindran, 1981; Ozkarahan & Bailey, 1988; Okada,1992; Chen & Yeung, 1992; Weil et al., 1995). The idea behind these studies is thatthe performance of the task of nurse scheduling can be improved by using a nursescheduling support system (NSSS). Hofstede (1992, pp. 107-135) shows that thistype of intended improvement is one link of a quality chain (see also Simons &Verheijen, 1991, pp. 23-25). Figure 1.5 shows this quality chain applied to nursescheduling.

The final link in this quality chain of nurse scheduling support systems concernsthe consequences of nursing schedules for the performance of the nursing unit. Orto put it differently, the quality of nursing schedules affects the ‘quality’ of thenursing unit. Furthermore, the nursing schedule quality is affected by the ‘quality’of the nurse scheduling task performance. And as stated above, this quality of thenurse scheduling task performance is affected by the ‘quality’ of the nursescheduling support system. Finally, the quality chain of nurse scheduling supportsystems starts with the link between the ‘quality’ of the development of the nursescheduling support system and the resulting nurse scheduling support system.

The objective of this study is to increase the quality of nursing schedules byoperationalizing the quality concept in such a way that it positively influences allthree performance characteristics of a nursing unit discussed in the first section(i.e. the effectiveness in providing nursing care, the efficiency of a nursing unitand the job satisfaction of the nursing staff). The operational quality can be usedin the development of the nurse scheduling support system, the use of this system

Figure 1.6 CYCLE OF DEVELOPING DECISION SUPPORT

Sm

SrPr

Pm

13

and the task performance of nurse scheduling, and will therefore possibly resultin nursing schedules that positively influence the performance of a nursing unit.Research that operationalizes the quality concept of nursing schedules in such away has not yet been conducted, mainly because most research on nurse schedulingfocuses too much on solving the nurse scheduling problem according to one or twoviews on nurse scheduling quality discussed in the previous section. This limitedfocus is probably a result of the difficulty in solving the nurse scheduling problem.The following subsection describes why it is difficult to develop this type of nursescheduling support system.

1.3.3 Difficulty in solving the nurse scheduling problem

A nurse scheduling support system is a specific type of decision support system.An important part of a decision support system is its model base (Bonczek,Holsapple & Whinston, 1981). In general, a decision support system’s model baseis developed in four phases (see Sol, 1982; Verbraeck, 1991, p. 18; De Jong, 1992,p. 12). Firstly, the problem as perceived in reality (P ) is translated into a modelr

of this problem (P ). Next, a solution to this modelled problem is computed (S ).m m

Then, this solution to the model is translated into the real situation (S ). Finally,r

this solution in reality is applied to the problem as perceived in reality (P ). Figurer

1.6 shows these four phases.

However, in the case of a nurse scheduling support system, it is very difficult todevelop its model base (Smith & Wiggins, 1977). Nurse scheduling presents adifficult problem to model and solve (see Okada & Okada, 1988). This problem ishard to solve for three main reasons, which are the complex data structure, the largenumber of possible solutions and the large number of constraints. The first reasondisturbes the translation of the problem as perceived in reality into a model of thisproblem, while the last two reasons disturbe a computation of a solution of themodelled problem. Below, these three reason are discussed in more detail.

The nurse scheduling problem is hard to solve because of its complex datastructure containing all kinds of employee information and schedule data (Courbon& Esaki, 1992). Several skill categories (e.g. registered nurses, licensed practicalnurses and nursing assistants) are utilized to provide the blend of talents necessary

Chapter 114

for patient care. The blend of talents required can vary on a unit from shift to shift,depending upon the medical treatments typically provided (Smith & Wiggins,1977).

A second reason for the difficulty in solving the nurse scheduling problemis the very large number of possible nursing schedules combined with the lack ofan efficient search algorithm. This can be illustrated by calculating the number ofpossible nursing schedules for a fictitious nursing unit, called East-5. At the East-5nursing unit, a nursing schedule is arranged every four weeks. Each twenty-fourhours, East-5 needs two nurses on the night shift, three nurses on the evening shift,and five nurses on the day shift. On the basis of these daily staff requirements, thetotal number of possible shift assignments for one (natural) day of the scheduleperiod is 2.883×10 . The nursing schedule for the East-5 unit contains four weeks9

of seven days, which makes twenty-eight days. Therefore, the number of possiblenursing schedules for this nursing unit is (2.883×10 ) = 7.510×10 .9 28 264

A third reason for the difficulty in solving the nurse scheduling problemconcerns the large number of complicated constraints. For example, the laborcontract between the hospital and the nurse can place a variety of restrictions onthe types of schedules the nurse can perform (Rosenbloom & Goertzen, 1987, p.19). The large number of complicated constraints cannot easily be applied to limitthe space of acceptable solutions (Smith & Wiggins, 1977; Weil et al., 1995). Theseconstraints concern, for example, continuity in service, personnel policies, staffpreferences, operating budgets and labor constraints (see Rosenbloom & Goertzen,1987). Additionally, some of these considerations may be in conflict with others,such as employment requests and the need to balance the workload (Randhawa &Sitompul, 1993). Also Ozkarahan and Bailey (1988, p. 306) stress the conflictingobjectives and constraints of the nurse scheduling problem.

As described above, much research has been conducted to support the perfor-mance of the nurse scheduling task by means of a nurse scheduling support system.However, as the next chapter will describe, most of these systems (implicitly) focustoo much on one or two views on nursing schedule quality discussed in theprevious section. The quest for an operational quality concept remains unansweredso far.

1.4 PRELIMINARY RESEARCH QUESTIONS

This study aims to operationalize the concept of nursing schedule quality in sucha way that it can cope with the pluriform nature of nursing schedule quality. Thisoperationalization requires three steps. Firstly, the concept of nursing schedulequality needs to be (qualitatively) analyzed in such a way that all views on thisquality are taken into account. This type of an analysis results in a conceptualmodel of nursing schedule quality. The second step concerns the operationalizationof this conceptual model into a formal model of nursing schedule quality. This typeof formal model enables the measurement of this quality. The objective of the third

15

step is the application of this formal model in order to support the task of nursescheduling.

On the basis of these three steps, this study intends to investigate threepreliminary research questions:

1. How can the concept of nursing schedule quality be analyzed?

2. How can the conceptual model of nursing schedule quality be operation-alized?

3. How can the formal model of nursing schedule quality be applied in orderto effectively support the task of nurse scheduling?

If the first two research questions can be answered, this will result in formalizedquality criteria to assess nursing schedules. Answering the third question will resultin an application of these criteria.

1.5 THESIS OUTLINE

In short, this study tries to analyze, operationalize and apply nursing schedulequality. This thesis describes the design, empirical results and conclusions of thesethree steps. The next chapter describes the theoretical background of this study.It compares a number of approaches to supporting nurse scheduling. The resultsof this comparison will show the necessity of a new approach. The third chapterdescribes the methodological foundation of this study, which is designed to investi-gate this new approach. The research results of this study are described in chaptersfour to seven. The eighth and final chapter of this thesis describes the conclusionsof this study. Figure 1.7 shows this thesis outline.

Figure 1.7 STRUCTURE OF THIS THESIS

introduction of this study's topic(chapter 1)

theoretical background of this subject(chapter 2)

methodological foundation of the research approach(chapter 3)

research results of this approach(chapters 4, 5, 6, and 7)

conclusions of this study(chapter 8)

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CHAPTER 2

APPROACHES TO NURSE SCHEDULING SUPPORT

The present chapter compares studies on supporting nurse scheduling. Thiscomparison is based on theoretical quality aspects of nursing schedules. The firstsection discusses these theoretical quality aspects. The second section discussesthe application of these theoretical quality aspects in practice. This is done bycomparing seven distinct approaches to developing nurse scheduling supportsystems. This discussion shows that none of these approaches succeeds in applyingall quality aspects. This chapter ends by describing a new approach to supportingnurse scheduling, which aims to apply all theoretical quality aspects.

2.1 THEORETICAL QUALITY ASPECTS OF NURSING SCHEDULES

The previous chapter described several consequences of nursing schedules for theperformance of a nursing unit. The present section discusses theoretical guidelinesconcerning the effect of nursing schedules on the performance of nursing units byevaluating effectiveness, efficiency and job satisfaction (see also Haselhoff, 1987).For each of these three groups of consequences, a theoretical quality aspect isintroduced. Furthermore, the previous chapter also indicated that the prioritiesgiven to each of these three performance characteristics might differ per health careorganization, nursing unit or nurse scheduler. Therefore, a fourth theoreticalquality aspect is added which concerns the support of multiple views on nursingschedule quality.

Table 2.1 shows these four theoretical quality aspects and the abbreviations usedto identify each of these four. The following four subsections describe thesetheoretical quality aspects in more detail by discussing a number of studies on theconsequences of nursing schedules for the performance of a nursing unit.

Table 2.1 THEORETICAL QUALITY ASPECTS OF NURSING SCHEDULES

care

unit

staff

views

facilitation of high-quality nursing care

facilitation of efficient nursing care

facilitation of job satisfaction

supporting multiple views on nursing schedule quality

Chapter 222

2.1.1 Facilitation of high-quality nursing care

The effectiveness of a nursing unit depends on the quality of nursing care. Manystudies investigated the effects of nursing schedules on this quality of nursing care(Blau & Sears, 1983; Gallagher, 1987; Fluharty, 1988; Newman, 1991; Morrow,1994). Most of these studies stress the importance of continuity in the nursing stafffor high-quality nursing care. This continuity is defined by the number of differentnurses providing care for the same patient during the stay at the nursing unit.

Continuity also depends on the way the providing of nursing care is organ-ized. Marquis and Huston (1994, pp. 139-146) describe five different modes oforganizing patient care: case method nursing, functional nursing, team nursing,primary nursing and managed care. In case method nursing (or total patient care),one nurse is assigned to each patient. In functional nursing, several nurses areassigned to the same patient, each completing a different task or function. In teamnursing, a team of nurses is assigned to each patient. In primary nursing, eachpatient has a primary nurse who establishes the care plan and who is responsiblefor this planning. And finally, in managed care (or case management), a casemanager plans and coordinates the patient care, while case associates provide thiscare. The unit-oriented quality aspects are related to the fit between the character-istics of a particular nursing unit and one of the five modes of organizing patientcare. Selecting one of these modes should be based on this fit (Marquis & Huston,1994).

The influence of a nursing schedule on the quality of nursing care involvesthe assurance of continuity in the nursing staff. In other words, the quality ofnursing care could be improved by increasing the continuity in the scheduled shifts(Bisseling, 1993, p. 65). The relation between a nursing schedule and the qualityof nursing care is expressed by a theoretical quality aspect, abbreviated to ‘CARE ’.

Approaches to nurse scheduling support 23

This facilitation of high-quality nursing care is important because providingnursing care is the primary process of a nursing unit. This theoretical quality aspectis based on the causal relation between the nursing schedule and the consequencesof this schedule for providing nursing care as shown in figure 1.3.

2.1.2 Facilitation of efficient nursing care

Salaries paid to nursing personnel constitute the largest chunk of a hospital's bud-get. Therefore, this human resource must be utilized efficiently (Ozkarahan &Bailey, 1988, p. 306). This means that the total number of a nursing unit's nursesshould correspond with the daily staffing demands. The degree of this correspond-ence strongly determines the efficiency of a nursing unit.

The influence of a nursing schedule on the efficiency of a nursing unit takesinto account the daily staff requirements (see Excuro, 1993). For example, when-ever the number of daily scheduled nurses exceeds the required number, thisdecreases the nursing unit's efficiency. This is also true whenever more registerednurses are scheduled during a specific shift than is required. The causal relationbetween a nursing schedule and the efficiency of a nursing unit (as shown in figure1.3) is expressed by a theoretical quality aspect, abbreviated to ‘UNIT ’.

2.1.3 Facilitation of job satisfaction

The job satisfaction of the nursing unit's nurses is strongly based on the effects ofthe irregular working hours (Hung, 1992). This irregularity of their working hoursaffects the nurses, not only by restricting their family and social life, but also bydisturbing their circadian rhythm.

The circadian system requires a week or more to adjust to a change in routine(Knauth & Rutenfranz, 1982; Schwarzenau et al., 1986). Furthermore, theadjustment of the circadian rhythms to night work always remains incomplete.Possible effects of circadian rhythm disturbances are stomach-ache, indigestion,lack of appetite, headaches, nervousness and dizziness (Dirken, 1966; Hakkinen,1969). Therefore, the guidelines-based approach tries to minimize the disturbancesof circadian rhythms.

Many studies have focused on ergonomic criteria for nurse scheduling

Chapter 224

(Knauth & Rutenfranz, 1982; Akerstedt, 1985; Monk, 1986; Bosch & De Lange,1987; Wilkinson & Allison, 1989). These studies resulted in the following nursingschedule evaluation criteria: just a few night shifts in succession, alternate week-ends off, forward rotation of the shifts and no more than seven consecutive workingdays.

A third theoretical quality aspect is the facilitation of job satisfaction,abbreviated to ‘STAFF ’. This facilitation of job satisfaction is related to both theflexibility of nurse scheduling and the healthiness of nursing schedules. Theflexibility of nurse scheduling depends on the amount of influence the nurses haveon their own working schedules by means of personal preferences and specificrequests (see Ozkarahan & Bailey, 1988). And the healthiness of nursing schedulesis related to which of the ergonomic criteria mentioned above have been considered(see Chen & Yeung, 1992).

2.1.4 Supporting multiple views on nursing schedule quality

The objectives in nursing scheduling are multiple (see Randhawa & Sitompul,1993). The priorities given to these objectives may differ per health care organ-ization, nursing unit and even per nurse scheduler. This means that nurse sched-uling involves multiple views on nursing schedule quality. Therefore, it is impor-tant for nurse scheduling support systems to support these multiple views. A high-quality nurse scheduling support system will allow the nurse scheduler to givepriority to effectiveness, efficiency or job satisfaction. This supporting of multipleviews on nursing schedule quality is a fourth and last theoretical quality aspect andis abbreviated to ‘VIEWS ’.

2.2 NURSE SCHEDULING SUPPORT SYSTEMS

Research on supporting nurse scheduling has resulted in a large number of nursescheduling support systems (Smith & Wiggins, 1977; Choi et al., 1986; Chen &Yeung, 1992; Randhawa & Sitompul, 1993; Mietus, 1994, pp. 208-209). Most ofthese systems are decision support systems. A decision support system is an inter-active information system aimed at supporting decision-makers in solving semi-structured problems (Spraque & Carlson, 1982) and consists of three parts: a data

Table 2.2 APPROACHES TO SUPPORTING NURSE SCHEDULING

model-based data-based interface-based

exhaustive search

cyclic scheduling

heuristic search

knowledge-based search

data management interactive scheduling

self scheduling

Approaches to nurse scheduling support 25

base, a model base and a human-computer interface (Bonczek, Holsapple &Whinston, 1981).

This section compares seven approaches to supporting nurse scheduling. Onthe basis of the three parts of decision support systems, these eight approaches aredivided into three subgroups: model-based, data-based and interface-basedapproaches. Table 2.2 shows these three subgroups.

The first subgroup of studies on supporting nurse scheduling focuses on the modelbase of nurse scheduling support system. These approaches to supporting nursescheduling all provide a formal description of the nurse scheduling problem. Thisformal model is represented in a model base. There are many different ways todevelop the model base of a decision support system. As a result, there are differenttypes of model bases. The differences in type of model base are related to differentmethods for dealing with the very large number of possible nursing schedules. Thecollection of all these possible nursing schedules is referred to as the problemspace (see Luger & Stubblefield, 1989; Rich & Knight, 1991). The initial state ofthis nurse scheduling problem is a completely empty schedule. The nursescheduling problem is solved whenever this initial state has been changed into agoal state, which is a final schedule. The definition of these goal states dependson the type of model used and the intended nursing schedule quality.

Four different approaches to developing a model base for a nurse schedulingsupport system are discussed below. These approaches differ in the technique for‘navigating and pruning’ the state space search (i.e. investigating and narrowingthis search). The first model-based approach uses ‘brute force’ by evaluating allpossible nursing schedules. This means that the state space search covers the entireproblem space. In this way, the optimal nurse schedule will be found. This approachis called ‘exhaustive search’. The second model-based approach to supporting

Chapter 226

nurse scheduling is called ‘cyclic scheduling’. This approach only allows cyclicalschedules to be arranged. Therefore, cyclic scheduling adds an extra restrictionto the search for optimal schedules. The third model-based approach to supportingnurse scheduling uses heuristics. These heuristics are used to reduce the state spacesearch to the most promising part of the problem space. This approach is called‘heuristic search’. The fourth and last model-based approach to supporting nursescheduling is called ‘knowledge-based search’. The knowledge-based searchapproach uses domain-specific knowledge to reduce the large problem space ofthe nurse scheduling problem.

The second subgroup of studies on supporting nurse scheduling focuses onthe data base of nurse scheduling support system. This subgroup contains oneapproach, which is called ‘data management’. This data management approach aimsto reduce the complexity of the nurse scheduling data structure.

The third and last subgroup of studies on supporting nurse scheduling focuseson the human-computer interface of the nurse scheduling support system. Thissubgroup contains two approaches: ‘interactive scheduling’ and ‘self-scheduling’.Interactive scheduling aims to combine the strengths of both the human schedulerand the computer-based support system in order to solve the nurse schedulingproblem, while self-scheduling tries to solve this problem by allowing nurses toarrange their own working schedules.

Each of the following seven subsections discusses one of these approachesto supporting nurse scheduling. The approaches will be scored on a qualitativescale, consisting of the values ‘positive’ (+), ‘mediate’ (±) and ‘negative’ (-). Foran approach to supporting nurse scheduling, ‘CARE ’ has a positive value whenfollowing this approach results in nursing schedules that facilitate high-qualitynursing care. In the opposite case, when the arranged nursing schedules result inlow-quality nursing care, this criterion has a negative value. The mediate value willbe used for the remaining cases. In the same way, ‘UNIT ’ has a positive value whenfollowing this approach increases the efficiency of the nursing unit. In the case ofa decrease in efficiency, this criterion has a negative value. The mediate value willbe used for the cases in which the approach followed did not affect the efficiencyof the nursing unit. Thirdly, ‘STAFF ’ has a positive value when following thisapproach results in increasing the job satisfaction among the nurses. In theopposite case, this criterion has a negative value. The mediate value will be usedfor the remaining cases. Finally, ‘VIEWS ’ has a positive value when this approachis able to deal with different views on the quality of nursing schedules. If only oneview is supported, this criterion has a negative value. The mediate value will beused for the remaining cases.

Approaches to nurse scheduling support 27

2.2.1 Exhaustive search for optimal schedules

The first approach to supporting nurse scheduling applies an exhaustive search ofthe problem space. The objective of this exhaustive search approach is to obtainthe optimal nursing schedule (see Warner & Prawda, 1972). This approach makesuse of mathematical models to search for this optimal schedule. The exhaustivesearch approach is dominant within the field of Operations Research (see Miller,Pierskalla & Rath, 1976; Warner, 1976). However, this approach can also be foundin other fields (see Fitzpatrick et al., 1987, p. 10).

The standard method for obtaining an optimal nursing schedule is to convertthe nurse scheduling problem into a two-stage assignment problem (Arthur &Ravindran, 1981, p. 56). This two-stage assignment problem is also referred to asthe combination of the day-of-the-week problem and the time-of-day problem(Ozkarahan & Bailey, 1988, p. 308).

The objective in the first assignment stage — the day-of-the-week problem— is to find the optimal set of work patterns. For each day of the schedule period,these work patterns determine whether a nurse has a day on or a day off. Theoptimal work pattern is mostly found by using goal programming (see Arthur &Ravindran, 1981, p. 56) or linear integer programming (see Rosenbloom &Goertzen, 1987, pp. 19-22). The objective in the second stage — the time-of-dayproblem — is to find the optimal shift assignment for each working day in thesework patterns.

Another example of exhaustive search uses constraint programming forsolving the nurse scheduling problem. Constraint programming combines logicprogramming — an artificial intelligence technique — with operations researchtechniques (Weil et al., 1995). Constraint programming enables the problemmodelling to be dissociated from the algorithms used for the solution, whichprovides flexibility in adjusting the formal model of the nurse scheduling problem.Weil and others (1995) showed the efficiency of constraint programming in solvinga nurse scheduling problem with thirty nurses in a single-skill class, which theymodelled as a problem with 1470 constraints.

The main drawback of the exhaustive search approach is its rigidity con-cerning the priority structure of the optimization algorithm. Although both goalprogramming and constraint programming offer more flexibility in choosingpriorities, it still requires a fully specified hierarchy of priorities. Mostly, it is notpossible to provide this specification because the relative significance of variousrequirements may change depending on the situation during the period concerned(Okada & Okada, 1988, p. 54).

Chapter 228

In general, the exhaustive search approach cannot cope with individualdifferences among nurse schedulers concerning their view on nursing schedulequality, mainly because user interaction is almost impossible (see Ozkarahan &Bailey, 1988, p. 306). This drawback is mostly combined with rigidity in dealingwith personal requests and preferences by the nursing staff, although the studiesdescribed by Warner (1976) and Arthur and Ravindran (1981, p. 56) were able totake nurses' preferences and nurses' special requests into account. However, mostresearchers following the exhaustive search approach conclude that their systemshould not be considered as a rigid tool for schedule generation, but more as adecision-makers' aid in negotiations and decisions (see Weil et al., 1995). Thegenerated optimal schedule should be thought of as the first step in constructingthe final schedule (Arthur & Ravindran, 1981).

2.2.2 Search for cyclic schedules

The second approach to supporting nurse scheduling only searches for cyclicschedules. Many studies have described procedures for developing cyclic sched-uling patterns for the nursing staff (Howell, 1966; Frances, 1966; Smith, 1975;Rosenbloom & Goertzen, 1987). A cyclic schedule is a schedule which recurs aftera fixed cycle. Cyclic schedules have the advantage that they can be rotated amongemployees so that a new schedule (theoretically) only need be produced for anursing unit when changes occur in its average daily staff requirements.Predictable work patterns result which facilitate a staff member's planning ofpersonal activities around a shift schedule, and unpopular work stretches are sharedequally by the rotating staff.

However, there are a number of disadvantages of cyclic scheduling (see Smith& Wiggings, 1977, p. 196; Fluharty, 1988, p. 24). For example, individualpreferences for particular shifts are not taken into account. And also vacations,holidays and staff resignations create complications. Okada (1992, p. 417) con-cludes that, despite the merits of cyclic scheduling, its applicability is very limited.Mietus (1994, p. 37) comments that since nurse scheduling is mostly characterizedby a flexible alternating scheduling pattern which contrasts with the features ofa cyclic schedule, cyclic scheduling does not seem to be very useful in the dailypractice of nurse scheduling.

When comparing this second approach with the first approach, the mainadvantage of the cyclic scheduling is the resulting recurrence of the nursing

Approaches to nurse scheduling support 29

schedules. This recurrence enables the prediction of the type of shift in the future,which should have a positive effect on job satisfaction. However, cyclic schedulingdoes not allow changes in the work schedules, which partly reduces this positiveeffect.

2.2.3 Heuristic search for feasible schedules

Perhaps the most significant feature of the nurse scheduling exercise is a tendencyto start with an excessively tight set of specifications, and to relax certain con-straints when it becomes apparent that all specifications cannot be achieved.Furthermore, it seems almost impossible to define a simple hierarchy or set ofpriorities to enable a completely mechanical relaxation of the constraints. Thiscaused some researchers to adopt the heuristic search approach (see Smith &Wiggins, 1977, pp. 197-198).

Heuristic search uses heuristic models to find feasible schedules. A heuristicmodel is a set of rules that is constructed on the basis of some sources of expertise.A heuristic model does not guarantee an optimal solution. This heuristic search canbe found within the fields of both Operations Research and Artificial Intelligence.Its most important advantage compared with the exhaustive search approaches isthe increased efficiency in finding feasible schedules.

Smith and colleagues (1977; 1979) followed the heuristic search approachby using list processing. Others also adopted this approach (see Okada & Okada,1988; Okada, 1992). These studies aimed to solve the nurse scheduling problemby applying a state space search procedure similar to the manual method of thehuman scheduler.

Another example of the heuristic search approach to supporting nurse sched-uling is given by a nurse scheduling system developed by Randhawa and Sitompul(1993). In order to generate work patterns, the model base of this system consistsof a best-first search algorithm, which is a heuristic search technique.

Compared to the previously-discussed exhaustive search approaches, the heu-ristic search approach increases the efficiency of the state space search. However,this heuristic search approach does not do very well with regard to job satisfaction,because personal requests will only be granted whenever these requests do notconflict with other priorities. Furthermore, a heuristic approach is implicitly basedon a certain view on nursing schedule quality, which makes it less useful wheneveranother view is applied.

Chapter 230

2.2.4 Knowledge-based search for good schedules

The fourth approach to supporting nurse scheduling applies knowledge to searchthe problem space. This knowledge-based search approach tries to find goodschedules by using a knowledge base, a model base in which knowledge is repre-sented. A knowledge base contains expertise formalized into so-called ‘productionrules’ (see Newell & Simon, 1972; Newell, 1990). A production rule consists ofa condition part (the IF part) and an action part (the THEN part). An example of aproduction rule in the domain of nurse scheduling is given by Chen and Yeung(1992, p. 323) and is as follows:

IF previous shift is eveningTHEN assign day shift [cf = 70 percent]AND assign evening shift [cf = 90 percent]AND assign night shift [cf = 20 percent]

The shift assignment of the previous shift is tested. If it is true, all the three‘conclusion clauses’ will be considered. The ‘cf’ is the certainty factor which ex-presses how certain the conclusion is. In the nurse scheduling problem, it will bemore appropriate to interpret ‘cf’ as the preference for a particular shift (Chen &Yeung, 1992, p. 323).

The knowledge bases are developed by using knowledge acquisitiontechniques to elicit the domain knowledge of human experts and to formalize thisknowledge into production rules (e.g. Boose & Gaines, 1988; Roth & Woods,1989). These production rules guide the state space search. This approach isdominant within the field of Artificial Intelligence (e.g. Smith, 1976).

An example of the knowledge-based search approach is given by Chen andYeung (1992). They combined knowledge-based search with optimization algo-rithms. This resulted in a nurse scheduling system which uses linear zero-one goalprogramming to obtain an optimal work pattern and a knowledge base to assignthe particular shifts to these work patterns.

Compared to both the exhaustive search approaches and the heuristic searchapproach, the knowledge-based search approach produces the best result in termsof job satisfaction of the nursing staff. This is because all kinds of different rulesconcerning the granting of special requests can be incorporated into the knowledgebase. However, this method of dealing with requests and preferences of the nursingstaff is based on the view of the expert nurse scheduler who provides the

Approaches to nurse scheduling support 31

scheduling knowledge. Therefore, this knowledge-based search approach does notdo very well with regard to the support of multiple views on nursing schedulequality.

2.2.5 Data management for nurse scheduling

The search-based approaches discussed above uses a formal model to deal withthe complexity of the nurse scheduling problem. The fifth approach to supportingnurse scheduling focuses on managing the complex data structure involved innurse scheduling. This data management approach to supporting nurse schedulinguses data base management techniques to deal with the complexity of the nursescheduling data domain.

The data management approach has been (partially) followed by Smith andWiggins (1977) and Courbon and Esaki (1992). Difficulties in adapting purelymathematical structures to incorporate the complicated constraints involved innurse scheduling caused Smith and Wiggins (1977) to adopt problem-oriented datastructures, and Courbon and Esaki (1992) encountered this data management asthe first problem to be tackled in order to develop a nurse scheduling supportsystem. This problem is about taking care of a complex data structure containingemployee information — such as seniority, part-time or full-time, type of shifts,history of previous schedules and requests for the coming four weeks schedule —and schedule data — concerning past and present allocation of nurses to day shifts,evening shifts, night shifts or days off.

The advantage of the data management approach lies in the reduction of thehuman data management. This enables the nurse scheduler to spend more time onthe scheduling problem itself. This approach scores positively on the theoreticalquality aspect of supporting multiple views on nursing schedule quality becauseit does not restrict the nurse scheduler to applying one or a small set of views onnursing schedule quality. However, this approach has a mediate score on theremaining three theoretical quality aspects because it does not necessarilycontribute to a higher performance of the nursing unit.

2.2.6 Interactive scheduling

Chapter 232

The sixth approach to supporting nurse scheduling focuses on the human-computerinterface of the nurse scheduling support system. The interactive schedulingapproach stresses the human-computer interaction between the human schedulerand the nurse scheduling support system (see Ahuja & Sheppard, 1975). Accordingto this approach of interactive scheduling, the nurse scheduling problem ispotentially so complex that no single formulation or algorithm can provide aworkable solution for every possible variation of the problem (Bell, Hay & Liang,1986).

Support for the interactive scheduling approach is given by a survey of man-power planning models. Edwards (1983) reviewed several mathematical and statis-tical models and concluded that good representation of results and ease of use aremore important to users than theoretical sophistication.

Others followed the interactive scheduling approach in combination withanother approach (see also Hofstede, 1992, pp. 55-57). For example, Bell, Hay andLiang (1986) applied interactive scheduling in combination with combined searchto develop a nurse scheduling support system. They described the developedsystem's interface as a user-friendly interactive component which allows the userto run their model — which is a combination of an algorithm and a heuristic — anddisplay the results. Mietus (1994) described a research project that combined theinteractive scheduling approach with the knowledge-based search approach.

The main advantage of the interactive scheduling approach lies in thecombination of the scheduling expertise of the nurse scheduler and the representa-tional facilities of the decision support system. This allows nurse schedulers toapply their own views on nursing schedule quality (i.e. this provides a positivescore on the support of multiple views on nursing schedule quality). However,interactive scheduling has a mediate score on the remaining theoretical qualityaspects.

2.2.7 Self-scheduling

The most important feature of the seventh and last approach to supporting nursescheduling is that it enables the nursing unit's nurses to schedule their own workinghours. This approach is called self-scheduling (Miller, 1984; Hung, 1992, p. 6). Theessence of this scheduling method lies in the shared responsibility of all membersof the nursing staff to arrange good nursing schedules.

Several studies (see Hinshaw et al., 1987; Marquis, 1988) described the

Table 2.3 COMPARISON OF APPROACHES TO SUPPORTING NURSE SCHEDULING

care unit staff views + ± -

exhaustive search

cyclic scheduling

heuristic search

knowledge-based search

data management

interactive scheduling

self-scheduling

+

+

+

+

±

±

-

+

+

+

+

±

±

±

-

±

±

+

±

±

+

-

-

-

-

+

+

±

2

2

2

3

1

1

1

0

1

1

0

3

3

2

2

1

1

1

0

0

1

Approaches to nurse scheduling support 33

negative consequences of nurses perceiving a lack of control over their workinghours, such as increased attrition rates and burnout among nurses. On the basis ofthese studies, Marquis and Huston (1994) concluded that scheduling has becomea major factor in either fostering job satisfaction or in promoting job satisfactionand subsequent nurse retention. Therefore, managers who strive to develop aperception among staff that they do possess some control over scheduling canimprove job satisfaction (Marquis & Huston, 1994, p. 215).

The main advantage of self-scheduling is the resulting job satisfaction.Unfortunately, following this approach could result in a shift of the nursing unit'spriorities from patient-centred to staff-centred, which negatively affects the qualityof nursing care. Furthermore, this approach mostly supports the nurses' view onnursing schedule quality.

2.2.8 Conclusions of the comparison

Table 2.3 summarizes the comparison of the eight approaches to supporting nursescheduling discussed above. It shows the scores of these approaches on the fivequality aspects. It also shows the totals of positive, mediate and negative scores.

With regard to the facilitation of high-quality and efficient nursing care, onlythe four model-based approaches score positively. With regard to the facilitationof job satisfaction of the nursing staff, only self-scheduling and the knowledge-based search approach score positively. And with regard to the support of multiple

Chapter 234

views on nursing schedule quality, only data management and interactive sched-uling score positively. Therefore, the main conclusion of the comparisons of theseven approaches to supporting nurse scheduling is that none of the discussedapproaches scores positively on all comparison criteria.

2.3 THE APPROACH OF QUALITY INDICATION SCHEDULING

All theoretical quality aspects discussed in the second section are important foran effective approach to supporting nurse scheduling in practice. As none of theapproaches discussed in previous section has a positive score on all the theoreticalquality aspects, a new approach with positive scores on all four theoretical qualityaspects was researched. This new approach is called ‘Quality Indication Sched-uling’.

The Quality Indication Scheduling approach is based on three basic assump-tions. The first basic assumption is that nurse schedulers will have identical notionsabout the nursing unit's effectiveness, efficiency and job satisfaction. It is assumedthat this can be expressed in a formal way. This assumption is called theassumption of formalization. The formal expressions of these three notions willbe called quality factors of nursing schedules.

The second assumption is the assumption of robustness. This assumptionstates that nurse schedulers might differ in priorities given to the nursing unit's ef-fectiveness, efficiency and job satisfaction, respectively. For example, some nurseschedulers might give the highest priority to providing efficient nursing care, whileothers give the highest priority to maintaining job satisfaction.

The third assumption is the assumption of effectiveness. This assumptionstates that nurse scheduling can be effectively supported by informing nurse sched-ulers about the quality factors of nursing schedules. This assumption fits well withthe interactive scheduling approach.

The present chapter ends by discussing these three assumptions in moredetail. The following three subsections also discuss the resulting positive scoreson the four theoretical quality aspects.

2.3.1 Assumption of formalization

Approaches to nurse scheduling support 35

The first assumption of the Quality Indication Scheduling approach is the assump-tion of formalization. This assumption states that a formal representation of thequality of the nursing schedule can be constructed. Furthermore, it is assumed thatthis formal representation consists of several independent aspects of nursingschedules. These aspects will be called quality factors.

On the basis of the consequences of nursing schedules for the performanceof nursing units (see also figure 1.3), three possible quality factors have alreadybeen identified. The first one concerns the effectiveness of the nursing unit. Thisfactor refers to continuity in the daily staffing. The second quality factor of nursingschedules concerns the efficiency of the nursing unit. This factor refers to the dailystaffing demands. And the third quality factor of nursing schedules concerns thejob satisfaction of the nursing staff. This factor refers both to applying ergonomicscriteria and to allowing nurses to specify preferences and requests.

The approach of Quality Indication Scheduling aims to represent the overallquality of a nursing schedule as a combination of the quality factors of nursingschedules. If successfully implemented, this approach will score positively on thefacilitation of both high-quality and efficient nursing units and job satisfaction.

2.3.2 Assumption of robustness

The second assumption of the Quality Indication Scheduling approach is theassumption of robustness. As stated above, priorities given to each of the threeperformance characteristics may differ according to the health care organization,nursing unit or nurse scheduler. Therefore, it is expected that each nurse schedulermight give a different quality value to the same nursing schedule. This means thatthe Quality Indication Scheduling approach claims that the perfect or optimalnursing schedule does not exist. What is best depends on the view on nursingschedule quality (i.e. the priorities given to each of the three performance charac-teristics).

The assumption of robustness states that the quality of a particular nursingschedule according to a nurse scheduler can be computed as a weighted sum of thevalues of the quality factors. The quality factors are assumed to be generic andtherefore valid for all nurse schedulers, while the weights are expected to bespecific and therefore to vary according to the nurse scheduler. By introducingweights, the Quality Indication Scheduling approach scores positively on the com-parison criterion of supporting multiple views on nursing schedule quality.

Chapter 236

2.3.3 Assumption of effectiveness

The third assumption of the Quality Indication Scheduling approach is the assump-tion of effectiveness. This assumption states that informing nurse schedulers aboutthe current values of the quality factors will reduce the task complexity. Withoutthis additional information, the nurse schedulers ‘compute’ these valuesthemselves, which means that they have to do a lot of counting and checking. Byinforming them about these factor values, nurse schedulers will be able to put morecognitive effort into increasing the quality of nursing schedules.

The approach of Quality Indication Scheduling can be summarized as follows.Firstly, independent quality factors of nursing schedule quality are conceptuallymodelled. Then, these quality factors are operationalized in order to measure thevalues of these factors. Finally, the effectiveness of informing nurse schedulersabout the values of these quality factors will be investigated. These three steps willbe called the analysis, operationalization and application of nursing schedulequality.

The Quality Indication Scheduling approach combines aspects of the threedistinct approaches to supporting nurse scheduling discussed in the last section.This approach applies a formal way of modelling the performance characteristicsof the nursing unit, which is also done in the exhaustive search approach. Further-more, knowledge acquisition techniques will be used to attain these formalrepresentations, which is also done in the knowledge-based search approach. Athird approach of which certain aspects are also present in the Quality IndicationScheduling approach is interactive scheduling. The Quality Indication Schedulingapproach combines the computation powers of the nurse scheduling support systemwith the scheduling expertise of the nurse scheduler, which is also done in thisinteractive scheduling approach.

The next chapter will discuss the methodological foundation of this researchapproach. Then, chapters four to seven will describe the research results. Theeighth chapter will describe the conclusions based on these results.

CHAPTER 3

METHODOLOGICAL FOUNDATION OFTHE RESEARCH APPROACH

The last chapter discussed a comparison of approaches to supporting nurse sched-uling. This comparison revealed that none of the approaches discussed scorespositively on all comparison criteria. Therefore, a new approach was suggestedwhich would provide the required positive scores. This chapter discusses the meth-odological foundation of this approach.

The first section reformulates the assumptions on which this approach isbased, as discussed in the previous chapter, into testable hypotheses. This sectionalso describes the research questions that specify the testing of these hypotheses.

This chapter ends with discussing the research method designed to answerthe research questions. This research method consists of five phases. In the secondsection, the methodological foundation of this research approach will be describedfor each research phase.

3.1 RESEARCH QUESTIONS AND HYPOTHESES

The research objective of this study is to analyze, operationalize and apply theconcept of nursing schedule quality in order to support the task of nurse sched-uling. The approach to attain this objective is based on the assumption that a formalrepresentation of this concept of nursing schedule quality is essential for aneffective support of this task. The nature of this approach is empirical; it rests onthe belief that direct observation and experience provide the only firm basis forthis understanding. Therefore, as the next section will describe, this study'sresearch design is based on the empirical cycle of scientific research (De Groot,1969). This empirical cycle consists of five phases: observation (i.e. collection ofempirical data), induction (i.e. formulation of hypotheses), deduction (of testablepredictions), testing (of the predictions on the basis of new empirical data) and

Figure 3.1 FOUR HIERARCHICAL LAYERS OF NURSING SCHEDULE QUALITY

quality factors

decision aspects

shift patterns

nursingschedulequality

Chapter 340

evaluation (of the results of the testing). This study, therefore, is affiliated tomethodological pleas for a shift in research in the field of management and organ-ization, including the domain of planning and scheduling, towards an empiricalapproach (see Jansen, 1994).

This study aims to represent nursing schedule quality as a model consistingof hierarchical layers. The top layer contains the concept of nurse schedule qualityitself. The assumption of formalization, as described in the previous chapter, statesthat this concept of nursing schedule quality will consist of a number ofindependent quality factors. The second layer of the hierarchical model of nurseschedule quality contains these quality factors. The contents of the third and fourthlayers stress the empirical nature of this study's research approach. This approachassumes that each quality factor can be divided into a number of decision aspects.The third layer contains these decision aspects. Finally, the fourth and ‘bottom’layer of the hierarchical model of nurse schedule quality contains ‘shift patterns’(i.e. a shift pattern is a specific pattern (horizontal, vertical or diagonal) of severalshifts). This approach assumes that for each decision aspect the value for eachspecific pattern of shifts can be determined. Figure 3.1 shows these hierarchicallayers of nursing schedule quality.

As described below, three hypotheses can be formulated to specify the role of this

Methodological foundation of the research approach 41

hierarchical model for the analysis, operationalization and application of nursingschedule quality. These hypotheses are testable reformulations of the assumptionsdescribed in the previous chapter. This testability refers to the analysis of empiricaldata. Below, the next subsections discuss these three hypotheses in more detail.

3.1.1 Hypothesis of formalization

The hypothesis of formalization states that the concept of nursing schedule qualitycan be modelled as a concept consisting of quality factors. To be more precise, thishypothesis states that the second layer of the hierarchical model shown aboveconsists of a number of independent factors of nursing schedule quality. Thehypothesis of formalization claims that nurse schedulers will have the same notionof each of these independent factors of nursing schedule quality. This notionconcerns the values of specific shift patterns for each decision aspect per qualityaspect (i.e. the corresponding contents of the third and fourth layer). This meansthat, for a nursing schedule, the value for each quality factor can be determinedindependently of nurse schedulers' views on nursing schedule quality.

Summarizing, the hypothesis of formalization states that all layers of thehierarchical model of nursing schedule quality can be fully specified. This meansthat the concept of nursing schedule quality can be unravelled as number of in-dependent quality factors, that each quality factor consists of a number of decisionaspects, and that for each decision aspect the value of each relevant shift patterncan be determined. This unravelling facilitates a measurement of nursing schedulequality, which is a prerequisite for effective quality management (Besterfield, 1990,p. 408).

3.1.2 Hypothesis of robustness

The hypothesis of robustness asserts that the quality of a particular nursingschedule will not be assessed in the same way by all nurse schedulers. To be moreprecise, this hypothesis states that the total quality value given to a nursingschedule by a nurse scheduler equals a weighted sum of the factor values. In otherwords, this hypothesis states that a nurse scheduler weighs each quality factoraccording to an individual summation weight in order to determine the total quality

' j'

Chapter 342

value.Formula 3.1 expresses the hypotheses of robustness. In words, this formula

states that the total quality value (Q ) of a particular nursing schedule s, accordings,i

to the view of a nurse scheduler i, equals a weighted sum of several (the totalnumber is expressed by N) independent quality factors (F ). The summations,j

weights (T ) vary per quality factor j and nurse scheduler i.i,j

Formula 3.1: Specification of the hypothesis of robustness

In this formula, the factor values are generic (i.e. equal for all nurse schedulers),while the summation weights are specific.

3.1.3 Hypothesis of effectiveness

The hypothesis of effectiveness asserts that informing nurse schedulers on thevalues of the quality factors will improve the quality of nursing schedules. Thisscheduling using information about the quality factors will be called ‘quality indi-cation scheduling’. The hypothesis of effectiveness will be tested by comparingthe mean total quality value in a new situation (Q ), in which quality indicationn

scheduling is applied, with the mean total quality value in an old situation (Q ), ino

which quality indication scheduling is not applied. The null hypothesis states thatthis difference will be zero, while the alternative hypothesis states that thisdifference will be larger than zero:

H : Q - Q = 00n o

H : Q - Q > 01n o

In short, the hypothesis of effectiveness predicts that the null hypothesis will berejected and that the alternative hypothesis will be accepted.

Methodological foundation of the research approach 43

Qualitative research is defined as research that produces findings not arrived at by means1

of statistical procedures or other means of quantification (Strauss & Corbin, 1990, p. 17).

3.1.4 Research questions

In the first chapter, three preliminary research questions were formulated. On thebasis of the three hypotheses discussed above, these preliminary questions can berefined into four final research questions:

1. What are the independent factors of nursing schedule quality?

2. How can one operationalize each of these quality factors?

3. Can the total nursing schedule quality be explained on the basis of aweighted sum of factor values?

4. Does quality indication scheduling improve the quality of nursing schedu-les?

The first two research question are related to the hypothesis of formalization. Thelast two questions concern the correctness of the hypothesis of robustness and thehypothesis of effectiveness, respectively.

3.2 RESEARCH DESIGN

This section describes the research method designed to answer the research ques-tions discussed above. This research method can be identified as a mixture oftechniques, originating from ‘qualitative research ’ (see Glaser & Strauss, 1967;1

Strauss & Corbin, 1990; Patton, 1990), ‘quantitative analysis’ (see Lawson &Hanson, 1974; Neale & Liebert, 1986), and ‘knowledge engineering’ (see Burton& Shadbolt, 1987; Boose & Gaines, 1988; Parsaye & Chignell, 1988). The designedresearch method consists of four phases: a questionnaire, a ranking experiment,an auditing experiment and a scheduling experiment. Each of these four researchphases answers one of the final research questions stated above. The following foursubsections discuss these research phases.

Chapter 344

3.2.1 Questionnaire

The objective of the first research phase is to answer the first research question (i.e.“What are the independent factors of nursing schedule quality?”). This phase iscalled the questionnaire and it consists of four research steps. The first two stepsare designed to find the independent factors of nursing schedule quality, while thelast two research steps are designed to validate the factors found.

In the first research step of the questionnaire, all possible candidates for therequired quality factors described in literature on nurse scheduling will besummarized. This results in a set of candidate quality factors.

Secondly, each candidate quality factor will be qualitatively analyzed on bothindependence and perceivability. The independence analysis focuses on the deci-sion aspects underlying each candidate quality factor. Whenever two of thesecandidates include a similar decision aspect, then these candidates will be identi-fied as dependent. The perceivability analysis investigates the shift patterns relatedto the decision aspects underlying each candidate quality factor. Whenever thedetermination of the value of a candidate quality factor requires information otherthan perceivable shift patterns, then this candidate will be identified asimperceivable. This second step will result in a working set of quality factors. Thisworking set contains only perceivable and independent factors of nursing schedulequality.

In the third research step, a questionnaire will be designed and sent to severalnurse schedulers. This questionnaire will ask about a number of characteristics ofthe nurse scheduling task and for a definition of nursing schedule quality. Thefocus in this second phase is on these definitions of nursing schedule quality. Theresulting characteristics will be used in the following research phases, describedbelow.

In the fourth step of the questionnaire, the given definitions will bequalitatively analyzed. This analysis will try to relate the definitions to the perceiv-able and independent quality factors of nursing schedules found in the first phase.This step will be called the ‘qualitative factor analysis’. The result of this qualita-tive factor analysis will be a final set of quality factors. This final set contains onlyvalidated (perceivable and independent) factors of nursing schedule quality. Theresults of this and the previous research steps of the first phase are the subject ofthe fourth chapter.

The steps of this first research phase complete one empirical cycle. Figure3.2 shows the relation of the research steps described above to the five phases ofthe empirical cycle.

Figure 3.2 THE FIRST EMPIRICAL CYCLE OF THE RESEARCH DESIGN

observation

induction

deduction

testing

evaluation

selection of candidate quality factors

analysis on perceivability and independence

questionnaire

final set of quality factors

survey of literature

Methodological foundation of the research approach 45

3.2.2 Ranking experiment

In the second research phase, a ranking experiment will take place. The objectiveof this experiment is to operationalize each factor of the final set of quality factors.These operationalizations require the specification of each quality factor into anumber of decision aspects and the determination of the values of all relevant shiftpatterns per decision aspect. Five research steps are designed to attain theseoperationalizations.

Firstly, each (final) quality factor of nursing schedules will be further speci-fied into a number of possible decision aspects. These specifications will concerna fictitious nursing unit, which will be designed on the basis of ‘average’ nursingunit characteristics resulting from the questionnaire applied in the previous phase.This fictitious nursing unit will be called ‘East-5’.

Secondly, each of these possible decision aspects will be further specifiedinto a number of possible shift patterns. These shift patterns will also based on thecharacteristics of the fictitious nursing unit of East-5.

Then, in the third research step, a number of nurse schedulers will be asked

'j'

&

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Chapter 346

to rank the shift patterns per decision aspect. The nurse schedulers will be in-structed to rank according to each shift pattern's value for the relevant qualityfactor. This third step is based on a knowledge acquisition technique known as‘cart sort’ (see Burton & Shadbolt, 1987). The objective of both the ranking taskand the cart sort task is to reveal a ‘hidden’ dimension. In the case of the rankingof shift patterns, this dimension is the corresponding quality factor.

In the fourth step, the given rankings will be analyzed on the basis of thecommunality in these rankings. A statistical measure to determine the amount ofcommunality is the coefficient of concordance (Kendall, 1975, pp. 94-106). Thismeasure is based on the variance in the rank per object. Formula 3.2 shows thecomputation of this coefficient of concordance, represented as W.

Formula 3.2: Kendall's coefficient of concordance

This formula computes the coefficient of concordance per k rankings of N objects.Applying this formula to the ranking experiment, the variable of N represents thenumber of alternative shift patterns per decision aspect and þ stands for the meani

ranking of shift pattern i (i.e. the mean of all s per shift pattern). The position ofi

a shift pattern in a ranking is represented as s . In the case of tied ranks, these si i

have the value of the average of the positions these shift patterns would have hadif they had been distinguishable (see also Kendall, 1975, p. 34). Furthermore, þrepresents the mean of all shift pattern rankings per decision aspect.

In the fifth and final step of the ranking experiment, a number of conclusionswill follow from the rankings per decision aspect with a significant coefficient ofconcordance. These conclusions provide the basis for the operationalizations ofeach factor of the final set of quality factors. These conclusions provide an answerto the second research question (i.e. “How can one operationalize each of thesequality factors?”). This last step of the ranking experiment draws a conclusionabout the (in)correctness of the hypothesis of formalization. The results of this andthe previous research steps of the second phase are the subject of the fifth chapter.

The steps of this second research phase also complete one empirical cycle.Figure 3.3 shows the relation of the research steps described above to the fivephases of the empirical cycle.

Figure 3.3 THE SECOND EMPIRICAL CYCLE OF THE RESEARCH DESIGN

observation

induction

deduction

testing

evaluation final set of decision aspects(accept / reject hypothesis of formalization)

analysis of the rankings

alternative shift patterns per decision aspects

working set of decision aspects(hypothesis of formalization)

final set of quality factors

Methodological foundation of the research approach 47

3.2.3 Auditing experiment

In the third research phase, an auditing experiment will be conducted. Theobjective of this experiment is to test the hypothesis of robustness. To perform thistest, the auditing experiment consists of five research steps.

Firstly, the quality factors will be operationalized on the basis of the rankingsper significant decision aspect. This significance refers to the each decisionaspect's coefficient of concordance, which will result from the ranking experimentconducted in the previous phase. This step will result in so-called nursing schedulequality metrics.

In the second step, a number of nursing schedules for the ‘average’ nursingunit of East-5 will be arranged. These fictitious nursing schedules will stronglydiffer in the values of each quality factor.

Next, in the third step, a number of schedulers will be asked to audit thesefictitious nursing schedules. The nurse schedulers will be instructed to give eachnursing schedule a quality mark on a scale from one to ten.

In the fourth step, these audits will be analyzed by applying a least-squares

Chapter 348

algorithm (Lawson & Hanson, 1974). The objective of this analysis is to determineeach scheduler's individual weights per quality factor. In order to apply a least-squares algorithm, the results of the auditing experiment will be reformulated asan overdetermined set of linear equations in the form of Ax•b, where A representsthe m×n matrix (m$n) of factor values and b represents the quality marks givento a nursing schedules by a nurse scheduler. The values per nurse scheduler of thecolumn x, which minimizes the Euclidean norm of the residual vector r=b-Ax, willbe determined by using a standard algorithm for finding the minimal solution tothe overdetermined linear least-squares problem Ax•b (Lawson & Hanson, 1974,pp. 180-198). The resulting least-squares solutions (i.e. the column x) will showthe best estimations of the individual summation weights of the nurse schedulers.

Finally, the fifth step of the auditing experiment draws a conclusion aboutthe correctness of the hypothesis of robustness. This correctness concerns the vali-dity of the assumed weighted sum of quality factors. The required conclusion willbe based on the results of the analysis conducted in the previous step. This willanswer the third research question: “Can the total nursing schedule quality beexplained on the basis of a weighted sum of factor values?”. The results of this andthe previous research steps of the third research phase are the subject of the sixthchapter.

Again, the steps of this third research phase complete one empirical cycle.Figure 3.4 shows the relation of the research steps described above to the fivephases of the empirical cycle.

3.2.4 Scheduling experiment

In the fourth and final research phase, a scheduling experiment will take place. Theobjective of this experiment is to test the hypothesis of effectiveness. Four stepsare designed to perform this test.

Firstly, a software module will be developed, which can measure the valuesof each quality factor on the basis of the operationalization used in the auditingexperiment.

Subsequently, in the second step, two groups of nurse schedulers will beasked to arrange a nursing schedule for the fictitious East-5 nursing unit used inboth previous experiments. After arranging this nursing schedule, one group ofnurse schedulers — the experimental group — will receive additional information(i.e. quality indication) from the developed software module, while the other group

Figure 3.4 THE THIRD EMPIRICAL CYCLE OF THE RESEARCH DESIGN

observation

induction

deduction

testing

evaluation

fully specified hierarchical layers of nursing schedule quality

operationalization of nursing schedule quality(hypothesis of robustness)

test set of fictitious nursing schedules

least-squares analysis of given quality marks

validity of the operationalization(accept / reject hypothesis of robustness)

Methodological foundation of the research approach 49

of nurse schedulers — the control group — will not receive this quality indication.

The third step will focus on the resulting nursing schedules. The factor values ofeach arranged nursing schedule will be used to compute the estimated total qualityvalues. For practical reasons, these estimations will be based on average summationweights. Then, the difference in mean estimated total nursing schedule qualitybetween the informed (Q ) and the non-informed group (Q ) of nurse schedulersn o

will be analyzed. This difference will determine whether the null hypothesis (H 0

: Q - Q = 0) or the alternative hypothesis (H : Q - Q > 0) is correct.n o n o1

And in the fourth and final step of this scheduling experiment, the conclusionconcerning the effectiveness of the approach of quality indication scheduling willfollow from the results of the comparison of the estimated total quality valuesbetween the control group and the experimental group. This step will draw aconclusion about the (in)correctness of the hypothesis of effectiveness. This willanswer the fourth and final research question: “Does quality indication schedulingimprove the quality of nursing schedules?”. The results of this and the previoussteps of the fourth research phase are the subject of the seventh chapter.

Also, the steps of this fourth and last research phase complete one empirical

Figure 3.5 THE FOURTH EMPIRICAL CYCLE OF THE RESEARCH DESIGN

observation

induction

deduction

testing

evaluation

formal model of nursing schedule quality

quality indication scheduling(hypothesis of effectiveness)

nurse scheduling with / without quality indication

analysis of the difference between <with’ and <without’

effectiveness of <with’(accept / reject hypothesis of effectiveness)

Chapter 350

cycle. Figure 3.5 shows the relation of the research steps described above to thefive phases of the empirical cycle.

CHAPTER 4

QUALITY FACTORS OF NURSING SCHEDULES

The previous chapter described the research method designed to analyze,operationalize, and apply the concept of nursing schedule quality. This researchmethod consists of five phases. The present chapter describes the results of the firsttwo of these five research phases. These two research phases concern the qua-litative analysis of the concept of nursing schedule quality.

The first section of the present chapter describes the results of the survey ofstudies on the concept of nursing schedule quality. This survey resulted in anumber of nurse scheduling goals. These scheduling goals constitute the requiredset of candidate quality factors, as described in the previous chapter.

The second section discusses the analysis of these nurse scheduling goals onperceivability and independence. This resulted in a working set of quality factors.These first two sections deal with the results of the first research phase (i.e. thesurvey of literature).

The last two sections concern the results of the second research phase (i.e.the questionnaire). The third section describes the validation of the working setof quality factors. This validation is based on a questionnaire sent to a number ofnurse schedulers from different health care organizations. A so-called ‘qualitativefactor analysis’ was used to analyze the answers given by the nurse schedulers.

The last section of the present chapter draws conclusions from the results ofthe qualitative factor analysis of the answers on this questionnaire. Theseconclusions concern the validity of the working set of quality factors. This resultsin the final set of quality factors of nursing schedules.

4.1 CANDIDATES FOR QUALITY FACTORS

The second chapter described the results of a survey of studies on supporting nursescheduling. This survey was based on the comparison of the approaches followedin order to support this scheduling task. The present section describes the resultsof another survey of the same study material. The objective of this second survey

Table 4.1 THE EIGHT GOALS OF NURSE SCHEDULING

number ofthe goals description of the goals

to distribute the quantitative staffing proportionally

to distribute the qualitative staffing proportionally

to distribute shifts among personnel proportionally

to distribute shifts and days off

honoring wishes

a pleasant working atmosphere on the ward

continuity between and over days

taking into account the physiological aspects of human beings

1

2

3

4

5

6

7

8

Chapter 454

was to find independent factors of nursing schedule quality. This survey focusedon descriptions of possible quality factors of nursing schedules. These descriptionswill be called ‘candidates quality factors’ of nursing schedules.

The second survey of studies on supporting nurse scheduling resulted in eightcandidate quality factors of nursing schedules (Oldenkamp & Simons, 1995a;1995b). A cognitive task analysis for nurse scheduling (Mietus, 1994) identifiedthese eight candidates as ‘nurse scheduling goals’. Seven of these nurse schedulinggoals were identified explicitly (pp. 28-30), while the eighth nurse scheduling goal,namely ‘taking into account the physiological aspects of human beings’ (p. 30) wasidentified implicitly. Table 4.1 indicates these eight goals of nurse scheduling.Below, each of these candidate quality factors of nursing schedules is described.

The first nurse scheduling goal — to distribute the quantitative staffingproportionally — is related to the minimum number of nurses per shift. Thequantitative demands for occupation per shift are very strict and need to befollowed. All approaches to supporting nurse scheduling discussed in the secondchapter take this first nurse scheduling goal into account.

The second nurse scheduling goal — to distribute the qualitative staffingproportionally — is related to the different levels of expertise within the nursingstaff (i.e. registered nurses, licensed practical nurses, nursing assistants). In orderto provide a sufficient level of nursing care on a twenty-four hour day, seven days

Quality factors of nursing schedules 55

a week basis, the nursing expertise must be distributed over the different shifts.Especially, the data-based approach to supporting nurse scheduling — discussedin the second chapter — stresses this second nurse scheduling goal (see Courbon& Esaki, 1992), but a large number of other studies also take this aspect of nursescheduling into account (see Okada & Okada, 1988, p. 54).

The proportional distribution of shifts among personnel is a third nursescheduling goal. The purpose of this goal is to give each nurse about the samenumber of night shifts, evening shifts and weekends off. Several studies tosupporting nurse scheduling take this nurse scheduling goal into account (seeOkada, 1991).

The fourth nurse scheduling goal — to distribute shifts and days off — isrelated to the length of the working period and the period of days off. Both periodsshould not be too long or too short. Especially the optimization approach tosupporting nurse scheduling — discussed in the second chapter — puts muchweight on this nurse scheduling goal (see Rosenbloom & Goertzen, 1987).

Another important nurse scheduling goal concerns honoring wishes. A wishis a particular shift desired or not desired by a nurse on a particular day. By meansof these wishes nurses are able to influence their own schedule. Apart from thecyclic scheduling approach, all studies to supporting nurse scheduling — discussedin the second chapter — emphasize this nurse scheduling goal (see Weil et al.,1995).

Realizing a pleasant working atmosphere on the ward is also an importantnurse scheduling goal. An unpleasant working atmosphere will have a negativeimpact on the quality of the nursing care. A few other studies pay attention to thisnurse scheduling goal (see Hung, 1992).

The seventh nurse scheduling goal — the continuity between and over days— also involves the quality of the nursing care. Continuity in the nursing crew pershift is one of the conditions for providing good nursing care. Bisseling (1993)conducted research that focused on this nurse scheduling goal.

Taking into account the physiological aspects of human beings is the lastnurse scheduling goal mentioned in the results of the cognitive task analysis onnurse scheduling. This goal is directly related to the welfare and health of thenursing staff. Several studies aimed towards supporting nurse scheduling stressthe importance of this nurse scheduling goal (see De Vries-Griever, 1992; Chen& Yeung, 1993; De Vries-Griever et al., 1994).

Chapter 456

4.2 ANALYSIS OF THE CANDIDATES

The previous section described the results of a survey of literature on nurse sched-uling. This survey revealed eight nurse scheduling goals. The degree to which eachof these scheduling goals is attained in a nursing schedule constitutes a candidatequality factor. This section describes the analysis of this set of eight candidatequality factors (i.e. the eight nurse scheduling goals) on both perceivability andindependence. The objective of these analyses concerned a conversion of this setof candidate quality factors into perceivable and independent factors of nursingschedule quality (i.e. the required working set of quality factors).

4.2.1 Analysis on perceivability

A nursing schedule is a plan containing three-dimensional combinations of shifts,nurses and the days of a specific time period. This specific time period will becalled the schedule period. In a nursing schedule, only the scheduled shifts withinthis schedule period are perceivable.

When the eight nurse scheduling goals are analyzed on perceivability, it ap-pears that the realization of two goals cannot be perceived in a nursing schedule.These goals are ‘honoring wishes’ (nurse scheduling goal number 5) and ‘a pleas-ant working atmosphere on the ward’ (nurse scheduling goal number 6).

The degree in which the wishes are honored can only be determined when theoriginal list of wishes is compared with the actual shifts in a nursing schedule. Asthis information is not present in a nursing schedule, the number of honored wishesis not perceivable in a nursing schedule. Therefore the perceivability analysiseliminates this fifth nurse scheduling goal.

The same kind of argument applies to realizing a pleasant working atmos-phere on the ward. A nursing schedule contains no information from which thepleasantness on a ward can be deduced. Therefore, the perceivability analysis alsoeliminates this nurse scheduling goal.

4.2.2 Analysis on independence

When the six remaining nurse scheduling goals are analyzed on independence, it

Figure 4.1 THE WORKING SET OF QUALITY FACTORS

completeness

optimality

proportionality

healthiness

continuity

five factors

Quality factors of nursing schedules 57

appears that the realization of two goals has the same impact on a nursing schedule.When shifts and days off are distributed (nurse scheduling goal number 4), thephysiological aspects of human beings are indirectly also being taken into account(nurse scheduling goal number 8). Both goals can therefore be translated into oneunderlying quality factor. Therefore, the independence analysis reduces both nursescheduling goals to one quality factor. This means that the six remainingscheduling goals consist of five independent quality factors. The independenceof these five factors will be argued below.

4.2.3 Working set of quality factors

Submitting the eight candidate quality factors to a perceivability analysis and thento an independence analysis resulted in a working set of five perceivable and in-dependent factors of nursing schedule quality. Figure 4.1 shows the names givento these five quality factors.

Chapter 458

These five quality factors are described below. These descriptions will show thatthese five factors differ in their focus towards the nursing schedule. These differentfocuses make these quality factors independent of each other (i.e. the values of anursing schedule on each of these quality factors can be altered without changingthe values of the other factors).

The completeness factor represents the degree to which the quantitativedemands for occupation per shift are met. This factor concerns shortages of nursesper shift and per day of the schedule period. This means that the completenessfactor is a ‘vertical’ factor (i.e. it ‘scans’ the nursing schedule from top to bottomper shift and per day).

The optimality factor represents the degree to which nursing expertise isdistributed over the different shifts. This factor concerns the distribution of regi-stered nurses (and the other types of nurses) per shift and per day of the scheduleperiod. This means that the optimality factor is also a ‘vertical’ factor. However,the optimality factor focuses on the qualitative staffing demands, instead of thequantitative staffing demands, which is the focus of the completeness factor.

The proportionality factor represents the degree to which each nurse has beengiven about the same number of night shifts, evening shifts and weekends off. Thismeans that the proportionality factor is a ‘horizontal’ factor (i.e. it ‘scans’ thenursing schedule from left to right per nurse).

The healthiness factor represents the degree to which care has been taken ofthe welfare and health of the nursing staff. This means that the healthiness factoris also a ‘horizontal’ factor. However, the healthiness factor focuses on the lengthsof periods of days off or days on, while the proportionality factor focuses on eachnurse's proportion per type of shift.

And finally, the continuity factor represents the degree to which there iscontinuity in the nursing staff during the different shifts. This factor focuses onthe nurses who are scheduled for several consecutive shifts. This means that thiscontinuity factor is both a horizontal and a vertical factor (i.e. it ‘scans’ the nursingschedule from top to bottom for nurses with consecutive (left to right) shifts).

4.3 VALIDATION OF THE QUALITY FACTORS

In order to validate the working set of five factors of schedule quality, eighteennurse schedulers from six different health care organizations received a question-naire. This questionnaire consisted of six parts and contained sixty-nine questions

Quality factors of nursing schedules 59

(see Appendix A). Most questions dealth with characteristics of nurse scheduling.The analysis of the answers to these questions will be described in the followingchapters. This chapter only deals with the answers given to one of these questions,namely ‘How would you define nursing schedule quality?’.

Because each nurse scheduler answered this question differently, eighteendifferent definitions of schedule quality were collected. The tables 4.2a and 4.2bcontain the translations (into English) of these eighteen definitions of nursingschedule quality (originally given in Dutch). The numbers in front of eachdefinition refer to the nurse scheduler who provided the given definition.

In order to analyze these eighteen definitions of schedule quality, these definitionswere cut into definition phrases. A definition phrase is a part of definition whichrefers to one specific aspect of nursing schedules. In total, the eighteen definitionscontained forty-five of these definition phrases. Based on the meaning of thesephrases, a so called ‘qualitative factor analysis’ was performed. The objective ofthis qualitative factor analysis was a direct link between each of the forty-fivephrases and one of the quality factors.

The following subsections describe the results of the qualitative factoranalysis by enumerating the definition phrases per quality factor to which theyrefer. The numbers of each definition phrase are put in front of each phrase, whilethe numbers behind each phrase refer to the nurse scheduler who provided thedefinition which contained the given phrase.

4.3.1 Definition phrases referring to completeness

In total, seven of the forty-five phrases referred to the quality factor of com-pleteness. These seven phrases were mentioned by seven of the eighteen nurseschedulers. Five of them explicitly referred to this feature by mentioning ‘quantity’or ‘quantitative’. Table 4.3 shows these seven definition phrases referring to thecompleteness factor.

These seven defining phrases stress the quantitative staffing demands (i.e. suf-ficient numbers of nurses per shift). These phrases fit in very well with the givendescription of the completeness factor, namely the degree to which the quantitativedemands for occupation per shift are met.

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6 7 8 9

Table 4.2a THE EIGHTEEN DEFINITIONS OF NURSING SCHEDULE QUALITY

number description

planning sufficient numbers of nurses per shift and taking into account specific shifts desired by nurses on certain days

providing the right numbers of nurses and levels of expertise per shift and taking into account the satisfaction of the nursing staf

guaranteeing both the quantitative and the qualitative staffing demands and approaching the nurses individually

distributing the nursing expertise equally over the shifts; taking care of healthy working schedules for each nurse (which means amaximum of eight consecutive working days); trying to schedule the types of shift desired by each nurse on specific days

monitoring the continuity in nursing care concerning the quantitative and the qualitative staffing demands on the basis of fixedconstraints

arranging nursing schedules at least six weeks in advance; honoring as many as possible wishes of the nursing staff; regularity ishifts; at most eight consecutive working days; variation in day and evening shifts

quality of care and continuity in providing this care; quality of labor in combination with a social life and a sufficient amount of rerecovery time

a nursing schedule that guarantees in nursing care in combination with the least possible impairment of family and social life of tnurses

a nursing schedule which provides an optimal distribution of nursing expertise over the shifts and which takes into account the himpairment effects of irregular working hours

1

2

3

4

5

6

7

8

9

Chapter 460

Table 4.2b THE EIGHTEEN DEFINITIONS OF NURSING SCHEDULE QUALITY

number description

taking into account both the continuity of nursing care and the types of shift desired by each nurse on specific days

forward shift rotation; applying labor rules concerning working hours; the right combinations of nursing expertise

continuity over 24 hours a day provision of nursing care in accordance with the quantitative staffing demands

a good distribution of both the quantity and the quality in staffing per shift, in combination with the possibility for nurses to specifdesired shifts within the organizational constraints

well-balanced working schedules concerning the distribution of the days on and the days off and the distribution of irregular shifts(which means not a different shift on each working day and a sufficient amount of rest)

providing continuity in nursing care, while taking into account the personal interest of each nurse

continuity in the working schedules (e.g. a row of consecutive day shifts or evening shifts); making a good schedule according to tstaff's point of view (e.g. no series of a single evening shift between day shifts and no series of ten consecutive days on)

having the right amount of nursing expertise during each day, evening and night shift

guaranteeing the quantitative and the qualitative staffing demands

10

11

12

13

14

15

16

17

18

Quality factors of nursing schedules 61

Table 4.3 DEFINITION PHRASES REFERRING TO THE COMPLETENESS FACTOR

planning sufficient numbers of nurses per shift

providing the right numbers of nurses per shift

to guarantee the quantitative staffing demands

monitoring the quantitative staffing demands on the basis of fixedconstraints

... in accordance with the quantitative staffing demands

a good distribution of the quantity in staffing per shift

to guarantee the quantitative staffing demands

1

3

6

13

32

33

44

1

2

3

5

12

13

18

number definition phrases sched.

sched. = scheduler

Chapter 462

4.3.2 Definition phrases referring to optimality

Nine of the eighteen nurse schedulers mentioned optimality as a defining feature of schedule quality. Fourof these nine did this explicitly by mentioning ‘quality in staffing’ or ‘qualitative staffing demands’. Table4.4 shows these nine definition phrases referring to the optimality factor.

These nine definition phrases stress the qualitative staffing demands (i.e. the right levels of nursing expertiseper shift). These phrases fit in very well with the given description of the optimality factor, namely the degreeto which nursing expertise is distributed over the different shifts.

4.3.3 Definition phrases referring to proportionality

In total, seven definition phrases referred to the proportionality factor. This was done by six of the eighteennurse schedulers. They implicitly referred to proportionality by mentioning the distribution of the shifts orthe staff's satisfaction. Table 4.5 shows these seven phrases.

Table 4.4 DEFINITION PHRASES REFERRING TO THE OPTIMALITY FACTOR

providing the right levels of expertise per shift

guaranteeing the qualitative staffing demands

distributing the nursing expertise equally over the shifts

monitoring the qualitative staffing demands on the basis of fixedconstraints

a nursing schedule which provides an optimal distribution ofnursing expertise over the shifts

the right combinations of nursing expertise

a good distribution of the quality in staffing per shift

to have the right amount of nursing expertise during each day,evening and night shift

guaranteeing the qualitative staffing demands

4

7

9

14

24

30

34

43

45

2

3

4

5

9

12

13

17

18

number definition phrases sched.

sched. = scheduler

Quality factors of nursing schedules 63

Table 4.5 DEFINITION PHRASES REFERRING TO THE PROPORTIONALITY FACTOR

taking into account the satisfaction of the nursing staff

approaching the nurses individually

regularity in shifts

variation in day and evening shifts

well-balanced working schedules concerning the distribution of thedays on and the days off

... while taking into account the personal interest of each nurse

no rows of a single evening shift between day shifts

5

8

17

19

36

39

41

2

3

6

6

14

15

16

number definition phrases sched.

sched. = scheduler

Chapter 464

The last five of these seven definition phrases stress the distribution of the shifts and days off per nurse. Thefirst two refer to this distribution indirectly: this distribution will have its effect on the satisfaction of thenursing staff (definition phrase number 5), and can best be arranged on an individual basis (definition phrasenumber 8). Apart from this definition phrase number eight, which stresses an individual approach, all of thesephrases fit in well with the given description of the proportionality factor, which stresses a general approach,namely the degree to which each nurse has been given about the same number of night shifts, evening shiftsand weekends off.

4.3.4 Definition phrases referring to healthiness

Healthiness was mentioned by eight of the eighteen nurse schedulers. In total, nine definition phrases referredto healthiness. Table 4.6 shows these nine definition phrases referring to the healthiness factor.

Table 4.6 DEFINITION PHRASES REFERRING TO THE HEALTHINESS FACTOR

taking care of healthy working schedules for each nurse, whichmeans a maximum of eight consecutive working days

at most eight consecutive working days

quality of labour in combination with a social life and a sufficientamount of rest and recovery time

the least possible impairment of family and social life of the nurses

a nursing schedule which takes into account the health impairmenteffects of irregular working hours

forward shift rotation

applying labour rules concerning working hours

well-balanced working schedules concerning the distribution ofirregular shifts, which means not a different shift on each workingday and sufficient amount of rest

no series of ten consecutive days on

10

18

21

23

25

28

29

37

42

4

6

7

8

9

11

11

14

16

number definition phrases sched.

sched. = scheduler

Quality factors of nursing schedules 65

These nine definition phrases stress the importance of sufficient rest and recovery time (i.e. healthy workingschedules for each nurse). These phrases fit in very well with the given description of the healthiness factor,namely the degree to which care has been taken of the welfare and health of the nursing staff.

4.3.5 Definition phrases referring to continuity

Seven of the eighteen nurse schedulers mentioned continuity as an important feature of schedule quality.They all did this explicitly (i.e. they literally used the term ‘continuity’). Table 4.7 shows the definitionphrases in which these nurse schedulers referred to this continuity factor.

Table 4.7 DEFINITION PHRASES REFERRING TO THE CONTINUITY FACTOR

monitoring the continuity in nursing care

quality of care and continuity in providing this care

a nursing schedule that guarantees continuity in nursing care

taking into account the continuity of nursing care

continuity over 24 hours a day provision of nursing care

providing continuity in nursing care

continuity in the working schedules, e.g. a series of consecutiveday shifts or evening shifts

12

20

22

26

31

38

40

5

7

8

10

12

15

16

number definition phrases sched.

sched. = scheduler

Chapter 466

These seven definition phrases stress the importance of continuity for high-quality nursing schedules. Thesephrases fit in very well with the given description of the continuity factor, namely the degree to which thereis continuity in the nursing staff during the different shifts.

Table 4.8 DEFINITION PHRASES REFERRING TO IMPERCEIVABLE ASPECTS OFNURSING SCHEDULES

taking into account specific shifts desired by nurses on certain days

trying to schedule the types of shift desired by each nurse onspecific days

arranging nursing schedules at least six weeks in advance

honouring as many wishes of the nursing staff as possible

taking into account the types of shift desired by each nurse onspecific days

... in combination with the possibility for nurses to specify desiredshifts within the organizational constraints

2

11

15

16

27

35

1

4

6

6

10

13

number definition phrases sched.

sched. = scheduler

Quality factors of nursing schedules 67

4.3.6 Remaining phrases

The remaining six phrases concerned aspects of nurse scheduling which are not perceivable in a nursingschedule. Table 4.8 shows these definition phrases.

Apart from defining phrase number fifteen, all these remaining definition phrases refer to the honoring ofdesired shifts. As discussed above, this honoring is not perceivable in an arranged nursing schedule. Definingphrase number fifteen does not refer to the nursing schedule itself. Therefore, this defining phrase is alsonot perceivable in a nursing schedule.

4.3.7 Conclusions of the qualitative factor analysis

The previous part of this section can be summarized as follows. The questionnaire resulted in eighteendefinitions of nursing schedule quality. These definitions consisted of forty-five definition phrases. Theresults of a qualitative factor analysis showed that six of these forty-five definition phrases did not refer toone of the five quality factors of the working set. Furthermore, one definition phrase turned out to be

Chapter 468

inconsistent with the description given to the corresponding quality factor. This means that more than eightypercent of the given definition phrases (i.e. 38 out of 45) referred to one of the quality factors of the workingset. This validates the working set of five quality factors.

4.4 FINAL SET OF QUALITY FACTORS

The previous sections discussed the results of the first two research phases. These results consisted of areduction of eight candidate for quality factors of nursing schedules (i.e. eight nurse scheduling goals) intoa working set of five independent and perceivable quality factors. A qualitative factor analysis of the answersgiven to a questionnaire showed the validity of these five quality factors. Therefore, it can be concluded thatthe concept of nursing schedule quality can be modelled as a set of five independent and perceivable qualityfactors. These quality factors are called completeness, optimality, proportionality, healthiness and continuity.Figure 4.2 shows these research steps taken to find these factors of nursing schedule quality.

This provides an answer to the first research question described in the third chapter. Figure 4.3 shows theconcept of nursing schedule quality consisting of five independent factors.

Figure 4.2 RESEARCH STEPS TAKEN TO FIND THE FIVE FACTORS OFNURSING SCHEDULE QUALITY

qualitative factor analysis

18 definitions ofnursing schedule quality

final set of 5 quality factors

working set of 5 quality factors

questionnaire

8 candidate quality factors

survey of literature

analysis on perceivabilityand independence

Quality factors of nursing schedules 69

Figure 4.3 FINAL SET OF QUALITY FACTORS OF NURSING SCHEDULES

completeness

optimality proportionality

healthiness continuity

Chapter 470

CHAPTER 5

RANKING OF SHIFT PATTERNS

The previous chapter described a conceptual model of nursing schedule qualityconsisting of five independent quality factors. The present chapter describes anexperiment designed to answer the second research question (i.e. “How can oneoperationalize each factor of nursing schedule quality?”). In this experiment,nurse schedulers are asked to rank a number of alternative shift patterns. Thisexperiment is called the ‘ranking experiment’.

The ranking experiment is based on a fictitious nursing unit. The first sectiondescribes this fictitious nursing unit. The remaining three sections describe thedesign, the results and the conclusions of the ranking experiment.

5.1 CHARACTERISTICS OF A NURSING UNIT

In order to design a representative nursing unit, a questionnaire was used (seeAppendix A). This questionnaire was answered by eighteen nurse schedulers ofsix health care organizations. As described in the previous chapter, the answersto one of these questions are used to validate the five quality factors of nursingschedules. The remaining questions asked about unit characteristics — such as thenumber of nurses and levels of nursing expertise — and schedule characteristics— such as length of schedule period and types of shifts. The answers to thesequestions are used to design a fictitious ‘average’ nursing unit. This averagenursing unit is called ‘East-5’.

This section describes some of the remaining results of the questionnaire.These results concern the levels of nursing expertise, length of schedule period,types of working days and quantitative staffing demands. The following sub-sections discus these results and describe the corresponding average values for theEast-5 nursing unit.

Chapter 572

5.1.1 Levels of nursing expertise

There were two levels of nursing expertise at most nursing units involved in thequestionnaire. At the remaining nursing units, there was one. Therefore, two levelsof nursing expertise are present at the fictitious East-5 nursing unit. Registerednurses have the highest level of nursing expertise. In this study, nurses workingat the second level of nursing expertise are called ‘nursing assistants’, althoughothers identify this level as “nurses' aids” (see Arthur & Ravindran, 1981, p. 56;Bell, Hay & Liang, 1986, p. 134; Okada & Okada, 1988) or ‘nurse assistants’ (seeFluharty, 1988). Other levels of nursing expertise, such as ‘licensed practicalnurses’, are not present at the fictitious East-5 nursing unit. In total, the nursingstaff of East-5 consists of nine registered nurses and thirteen nursing assistants.

5.1.2 Length of schedule period

The results of the questionnaire showed that the length of the schedule period canvary from fourteen days to eight weeks. Mostly, this period is between four andsix weeks. For practical reasons (i.e. it takes less time to arrange), a schedule periodlength of four weeks will be used at the fictitious East-5 nursing unit.

5.1.3 Types of working days

The results of the questionnaire showed that most nursing units distinguishbetween three types of working days: normal working days (i.e. Mondays,Tuesdays, Wednesdays, Thursdays and Fridays), weekends (i.e. Saturdays andSundays), and holidays (e.g. New Year's day, Christmas). Again for practicalreasons, two types of working days will be used at the fictitious East-5 nursing unit:normal working days and special working days. These special working daysinclude holidays and weekends.

Ranking of shift patterns 73

5.1.4 Quantitative staffing demands

The results of the questionnaire showed a wide variety in types of shifts (e.g.different starting times and different shift lengths) and in the correspondingquantitative staffing demands. Only the standard types of shift are used at thefictitious East-5 nursing unit: day shifts, evening shifts and night shifts. At East-5,the corresponding quantitative staffing demands vary per type of working day. Oneach normal working day of the schedule period, two night shifts, three eveningshifts, and five day shifts need to be scheduled, while on special working days ofthe schedule period, the quantitative staffing demands are two night shifts, threeevening shifts and four day shifts.

5.2 DESIGN OF THE RANKING EXPERIMENT

The previous chapter described the modelling of nursing schedule quality as aconcept consisting of five independent quality factors. The research objective ofthe ranking experiment is to operationalize each of these quality factors. Asdescribed in the third chapter, five steps are designed to attain these operationaliza-tions. The first two research steps constitute the preparation part of the rankingexperiment. This section discusses the results of these two preparation steps. Thenext two sections discuss the results of the remaining three research steps.

In the first research step of the ranking experiment, each quality factor wasspecified by a number of aspects which could be both uniquely identified and un-ambiguously detected. These aspects are called ‘decision aspects’ (see also figure3.1). In the second step, each of these decision aspects was translated intoalternative shift patterns (i.e. the bottom layer in the hierarchical model of nursingschedule quality).

The following five subsections describe both specifications. Firstly, eachquality factor will be specified by means of several decision aspects. The totalnumber of decision aspects per quality factor depends on the theoretical possiblevariation. For each quality factor, as many decision aspects as possible were formu-lated. And for each of these decision aspects, all (reasonable) alternative shiftpatterns were identified.

The nurse schedulers who participated in the ranking experiment were askedto rank these alternative shift patterns per decision aspect according to eachpattern's value for the corresponding quality factor on the basis of their own view

Chapter 574

on nursing schedule quality. This means that the best shift pattern according to anurse scheduler will be ranked first, while the worst shift pattern according to thisnurse scheduler's opinion will be ranked as last.

Furthermore, related decision aspects are combined into one (extra) decisionaspect. This type of decision aspect will be called a ‘combination decision’. Thesecombination decisions contain several decision aspects. The participating nurseschedulers were asked to rank these decision aspects according to their importancefor the corresponding quality factor. In other words, the decision aspects are theranking objects of the combination decisions. These combination decisions arenecessary for the determination of the importance of each decision aspect for thecorresponding quality factor. On the basis of each decision aspect's importance (i.e.its position in the ranking) the rankings given to these combination decisions canbe used to integrate the decision aspects into a single quality factor.

Below, the decision aspects, the corresponding shift patterns and the combin-ation decisions are discussed per quality factor. Appendix B contains a full descrip-tion of these shift patterns. Below, the decision aspects are identified by a factorcode (i.e. ‘C’, ‘O’, ‘P’, ‘H’ or ‘T’) and a number (i.e. 1 up to the maximum of 10),while the shift patterns are identified by a factor code, the number of the decisionaspect and a letter (i.e. ‘a’ up to the maximum of ‘j’).

5.2.1 Decision aspects concerning completeness

The completeness factor represents the degree in which the quantitative demandsfor occupation per shift are met. Because these quantitative staffing demands differper type of working day, one decision aspect of the quality factor completenessconcerns incompleteness during normal working days (C-1), while anotherconcerns incompleteness during special working days (C-3). Furthermore, theresults of the questionnaire also shows that a surplus, which is quantitativeoverstaffing, does not influence completeness. Therefore, both decision aspectshave three alternative shift patterns, which can be described as an incompletenesscaused by a daily shortage of one day shift (C-1a and C-2a), one evening shift (C-1b and C-2b) or one night shift (C-1c and C-2c). A third decision aspect related tothe completeness factor (C-3) is a combination decision, and has to do with theimportance of completeness during normal working days (C-3a) compared to

Table 5.1 DECISION ASPECTS OF COMPLETENESS

incompleteness on normal working days

incompleteness on special working days

incompleteness per type of working day

C-1

C-2

C-3

3

3

2

code decision aspect sp

sp = number of shift patterns

Ranking of shift patterns 75

special working days (C-3b). Table 5.1 mentions the three decision aspects relatedto the completeness factor. The number of alternative shift patterns are mentionedin parentheses.

5.2.2 Decision aspects concerning optimality

The optimality factor represents the degree to which nursing expertise isdistributed over the different shifts. This nursing expertise per shift can be ex-pressed by the proportion of registered nurses scheduled. This proportion dependson the total number of nurses, and can thus differ per type of shift and per type ofworking day. Therefore, the optimality factor can be specified in six decisionaspects (O-1, O-2, O-3, O-5, O-6 and O-7) and three combination decisions O-4,O-8 and O-9). Each decision aspect has three corresponding shift patterns: onepattern representing about forty percent of registered nurses per shift, one with anextra registered nurse and one with a registered nurse less. The first twocombination decisions (O-4 and O-8) combine the importance of the proportionof registered nurses scheduled per type of working day, while the third combin-ation decision (O-9) combines these two combination decisions. Table 5.2 indicatesthese nine decision aspects related to the optimality factor.

5.2.3 Decision aspects concerning proportionality

The proportionality factor represents the degree to which each nurse has beengiven about the same number of night shifts, evening shifts and weekends off. This

Table 5.2 DECISION ASPECTS OF OPTIMALITY

day shift optimality on normal working days

evening shift optimality on normal working days

night shift optimality on normal working days

optimality on normal working days per type of shift

day shift optimality on special working days

evening shift optimality on special working days

night shift optimality on special working days

optimality on special working days per type of shift

optimality per type of working day

O-1

O-2

O-3

O-4

O-5

O-6

O-7

O-8

O-9

3

3

3

3

3

3

3

3

3

code decision aspect sp

sp = number of shift patterns

Chapter 576

factor has been specified by three decision aspects and one combination decision.Table 5.3 indicates these four decision aspects related to the proportionality factor.

The first decision aspect of proportionality (P-1) concerns the proportion of dayshifts to evening shifts to night shifts. This decision aspect has been translated intoseven shift patterns. Each of these shift patterns represents a total of twenty-fourshifts. The first pattern (P-1a) has fourteen day shifts, six evening shifts and fournight shifts, while, for example, the last one (P-1g) has ten day shifts, eight eveningshifts and six night shifts.

The second decision aspect of proportionality (P-2) concerns the distribution ofdays off. This decision aspect has also been translated into seven shift patterns.These patterns differ in length and number of periods of days off. For example, oneof these patterns (P-2d) represents four periods of days off, while another (P-2f)contains six periods of days off.

The third decision aspect of proportionality (P-3) concerns the distributionof weekends off. This decision aspects has been translated into four shift patterns.These patterns differ in number of consecutive weekends on. This number is onefor the first shift pattern (P-3a), and it increases per pattern to four for the last shiftpattern related to this decision aspect of distribution of weekends off (P-3d).

Table 5.3 DECISION ASPECTS OF PROPORTIONALITY

proportionality concerning the numbers per type of shift

proportionality concerning the distribution of days off

proportionality concerning the distribution of weekends off

importance per decision aspect concerning proportionality

P-1

P-2

P-3

P-4

7

7

4

3

code decision aspect sp

sp = number of shift patterns

Ranking of shift patterns 77

The fourth and last decision aspect of proportionality (P-4) is a combination deci-sion. It concerns the importance per decision aspect concerning proportionality.These decision aspects P-1, P-2 and P-3 are represented as the ‘ranking objects’P-4a, P-4b and P-4c, respectively.

5.2.4 Decision aspects concerning healthiness

The healthiness factor represents the degree to which care has been taken of thewelfare and health of the nursing staff. This factor has been specified by sevendecision aspects and three combination decisions. Table 5.4 mentions these tendecision aspects related to the healthiness factor.

The first decision aspect of healthiness (H-1) concerns the number of consecutivenight shifts. This decision aspect has been translated into seven shift patterns.These shift patterns differ from a single night shift for the shortest pattern (H-1a)to seven consecutive night shifts for the longest shift pattern (H-1g).

The second decision aspect of healthiness (H-2) concerns the number of con-secutive evening shifts. This decision aspect has been translated into ten shift pat-terns. These shift patterns differ from a single evening shift for the shortest pattern(H-2a) to ten consecutive evening shifts for the longest shift pattern (H-2j).

The third decision aspect of healthiness (H-3) concerns the number of con-secutive day shifts. This decision aspect has also been translated into ten shiftpatterns. These shift patterns differ from a single day shift for the shortest pattern

Table 5.4 DECISION ASPECTS OF HEALTHINESS

healthiness in relation to the number of consecutive night shifts

healthiness in relation to the number of consecutive evening shifts

healthiness in relation to the number of consecutive day shifts

healthiness in relation to the number of consecutive working days

importance per decision aspect in relation to healthiness ofconsecutive shifts

healthiness in relation to the amount of resting-time after a nightshift period

healthiness in relation to rest during a shift change without daysoff

healthiness in relation to the amount of rest during a shift changewith days off

importance per decision aspect in relation to healthiness ofscheduled rest

importance of healthiness of consecutive shifts versus scheduledrest

7

10

10

7

4

6

4

6

3

2

H-1

H-2

H-3

H-4

H-5

H-6

H-7

H-8

H-9

H-10

code decision aspect sp

Chapter 578

(H-3a) to ten consecutive day shifts for the longest shift pattern (H-3j).The fourth decision aspect of healthiness (H-4) concerns the number of con-

secutive working days. This decision aspect has been translated into seven shiftpatterns. These shift patterns differ in the length of the period of consecutiveworking days. The longest pattern (H-4g) consists of ten consecutive working days,while the shortest pattern (H-4a) consists of four consecutive working days.

The fifth decision aspect of healthiness (H-5) is a combination decision. This com-bination decision concerns the importance per decision aspect concerning healthi-ness of consecutive shifts. It combines the first four decision aspects of healthiness.These decision aspects, H-1, H-2, H-3 and H-4, are represented as H-5a, H-5b, H-5cand H-5d, respectively.

The sixth decision aspect of healthiness (H-6) concerns the amount of restafter a night shift period. This decision aspect has been translated into six shift pat-terns. These patterns vary from 47.5 hours of rest after a night shift period for the‘shortest’ pattern (H-6a) to 103.5 hours of night shift recovery time for the‘longest’ shift pattern (H-6f).

Table 5.5 DECISION ASPECTS OF CONTINUITY

T-1

T-2

T-3

T-4

continuity during night shifts

continuity during evening shifts

continuity during day shifts

continuity per type of shift

4

4

4

3

code decision aspect sp

sp = number of shift patterns

Ranking of shift patterns 79

The seventh decision aspect of healthiness (H-7) concerns the amount of restduring a shift change without days off. It has been translated into four shiftpatterns. These patterns vary from eight hours of rest for the ‘shortest’ pattern (H-7c) to thirty-two hours for the ‘longest’ shift pattern (H-7b).The eighth decision aspect of healthiness (H-8) concerns the amount of rest duringa shift change with days off. It has been translated into six shift patterns. Thesepatterns vary from thirty-two hours of rest for the ‘shortest’ pattern (H-8d) to fifty-six hours for the ‘longest’ shift pattern (H-8c).

The ninth decision aspect of healthiness (H-9) is a combination decision. Thiscombination decision concerns the importance per decision aspect concerninghealthiness of scheduled rest. It combines the three decision aspects H-6, H-7 andH-8. These decision aspects are represented as H-9a, H-9b and H-9c, respectively.

The tenth decision aspect of healthiness (H-10) is again a combination deci-sion. It concerns the importance of healthiness of consecutive shifts (H-10a) versushealthiness of scheduled rest (H-10b). It thus combines the two combinationdecisions H-5 and H-9.

5.2.5 Decision aspects concerning continuity

And finally, the continuity factor represents the degree to which there is continuityin the nursing staff during the different shifts. This factor has been specified bythree decision aspects and one combination decision. Table 5.5 mentions these fourdecision aspects related to the continuity factor.

Chapter 580

The first decision aspect of continuity (T-1) concerns the continuity during nightshifts. This decision aspect has been translated into four shift patterns. Thesepatterns differ in the distribution of the fourteen night shifts a week over thenursing staff. As a consequence of this distribution, the pattern with the highestcontinuity (T-1d) involves the scheduling of two nurses a week, while the patternwith the lowest continuity (T-1c) involves the scheduling of six nurses a week.

The second decision aspect of continuity (T-2) concerns the continuity duringevening shifts. This decision aspect has also been translated into four shift patterns.These patterns differ in the distribution of the twenty-one evening shifts a weekover the nursing staff. As a consequence of this distribution, the pattern with thehighest continuity (T-2d) involves the scheduling of seven nurses a week, whilethe pattern with the lowest continuity (T-2e) involves the scheduling of nine nursesa week.

The third decision aspect of continuity (T-3) concerns the continuity duringday shifts. This decision aspect has alos been translated into four shift patterns.These patterns differ in the distribution of the thirty-three day shifts a week overthe nursing staff. As a consequence of this distribution, the pattern with the highestcontinuity (T-3a) involves the scheduling of ten nurses a week, while the patternwith the lowest continuity (T-3e) involves the scheduling of fourteen nurses aweek.

The fourth decision aspect of continuity (T-4) is a combination decision. Thiscombination decision concerns the continuity per type of shift. It combines the firstthree decision aspects of continuity. These decision aspects T-1, T-2 and T-3 arerepresented as the ranking objects T-4a, T-4b and T-4c, respectively.

5.3 RESULTS OF THE RANKING EXPERIMENT

Ten nurse schedulers from five different health care organizations ranked thediscussed alternative shift patterns per decision aspect on the basis of the corre-sponding quality factor. As described in the third chapter, the agreement amongthe nurse schedulers with respect to these rankings can be computed on the basisof Kendall's coefficient of concordance (Kendall, 1979, pp. 94-106). These coef-ficients of concordance determine whether nurse schedulers agree on the relative‘quality’ of each shift pattern. Table 5.6 shows these resulting coefficients of con-cordance per quality factor and per decision aspect. Appendix A shows the corres-ponding rankings per decision aspect.

Table 5.6 COEFFICIENTS OF CONCORDANCE PER QUALITY FACTORPER DECISION ASPECT

number C O P H T

1

2

3

4

5

6

7

8

9

10

0.52 *

0.57 *

0.11

0.23

0.77 *

0.86 *

0.53

0.48 *

0.70 *

0.73 *

0.05

0.35

0.64 *

0.87 *

0.83 *

0.46 *

0.49 *

0.29 *

0.54 *

0.23 *

0.36 *

0.04

0.57 *

0.01

0.68 *

0.49 *

0.16

0.36 *

1.00 *

0.08

* p < 0.01

Ranking of shift patterns 81

In this table, the coefficients of concordance marked with an asterisk (*) aresignificant when using an error tolerance of one percent. For these marked coef-ficients of concordance, the probability that the rankings of the ten nurse sched-ulers are similar is ninety-nine percent certain. Below, these coefficients of con-cordance are discussed per quality factor.

5.3.1 Rankings of shift patterns concerning completeness

The ten nurse schedulers agreed about the relative importance of incompletenessfor each type of shift. According to this agreement, a shortage of a night shift isworse than a shortage of an evening shift or a day shift, and a shortage of anevening shift is worse than a shortage of a day shift. On the other hand, the resultsdid not show that shortages during special working days are worse than shortagesduring normal working days.

Chapter 582

5.3.2 Rankings of shift patterns concerning optimality

The rankings of shift patterns related to optimality showed a significant com-munality on five of the six decision aspects. These results show that qualitativeunderstaffing is worse than qualitative overstaffing. Furthermore, the nurse sched-ulers agreed that qualitative understaffing during evening shifts or night shifts isworse than qualitative understaffing during day shifts, and that qualitative under-staffing during day shifts on special working days is worse than on normal workingdays. On the other hand, the results did not show that qualitative understaffing (orqualitative overstaffing) during special working days is worse than qualitativeunderstaffing (or qualitative overstaffing) during normal working days.

In order to interpret the coefficient of concordance for the final combinationdecision (O-9), a coefficient of concordance was computed with a virtual thirddecision aspect. This gave a coefficient of concordance of 0.07, which was notsignificant using an error tolerance of one percent.

5.3.3 Rankings of shift patterns concerning proportionality

The results of the rankings on the first decision aspect of proportionality (P-1)showed that the ten nurse schedulers did not agree about the best proportion of dayshifts to evening shifts to night shifts. On the other hand, the ten nurse schedulersagreed about the best distribution of both days off and weekends on. Thesignificant coefficient of concordance in the shift patterns concerning thedistribution of days off (decision aspect P-2) can be explained on the basis of thenumbers of single days off. This type of single day off is a sequence of shifts withone day off between two days on. The significant coefficient of concordance in theshift patterns concerning the distribution of weekends off (decision aspect P-3)can be explained on the basis of the number of consecutive weekends on. Finally,the insignificant coefficient of concordance for the combination decision ofhealthiness (P-4) was caused by the disagreement on this first decision aspect ofproportionality. Analyzing the relative rankings on this combination decision ofthe other two decision aspects showed that the occurrence of a shift patternconsisting of one day off between two days on was significantly worse than theoccurrence of two consecutive weekends on.

Ranking of shift patterns 83

5.3.4 Rankings of shift patterns concerning healthiness

The rankings of shift patterns related to healthiness showed a significant commun-ality on all decision aspects and on two of the three combination decisions. Below,these results are discussed per decision aspect or combination decision.

Blocks of consecutive night shifts with a length of three or four are thehealthiest (decision aspect H-1). Both shorter and longer night shifts periods weresignificantly unhealthier.

Blocks of consecutive evening shifts with a length of two, three or four arethe healthiest (decision aspect H-2). These resulting rankings showed that the nurseschedulers mostly agreed about the three most unhealthy shift patterns, whichconsisted of eight, nine and ten consecutive evening shifts. Even when these threeshift patterns were replaced by a single shift pattern, the coefficient of concordancefor this decision aspect slightly decreased to 0.76 , but still remained significant,*

using an error tolerance of one percent.Blocks of consecutive day shifts with a length of two, three, four, or five are

the healthiest (decision aspect H-3). These resulting rankings showed that the nurseschedulers mostly agreed about the three most unhealthy shift patterns, whichconsisted of eight, nine and ten consecutive day shifts. Even when these three shiftpatterns were replaced by a single shift pattern, the coefficient of concordance forthis decision aspect slightly decreased to 0.57 , but still remained significant, using*

an error tolerance of one percent.Analyzing the rankings given by the ten nurse schedulers for decision aspect

H-4 showed a significant concordance, which means that these rankings werestatistically similar. The ‘average’ ranking expressed in consecutive working dayswas 7, 6, 5, 4, 8, 9 and 10. This can be summarized by stating that blocks of con-secutive days on with a length of more then seven are unhealthy.

The ten nurse schedulers agreed about the first combination decision ofhealthiness (H-5). This agreement concerns the fact that the occurrence of a blockof consecutive days on, with a length of more than seven, is worse than an un-healthy block of consecutive shifts.

The nurse schedulers also agreed about the decision aspect of healthiness thatconcerns the amount of rest after a night shift period (H-6). This agreementconcerns the fact that, after a block of consecutive night shifts, at least three daysmust follow.

Furthermore, the results also show communality in the rankings concerningthe decision aspects H-7 and H-8, and concerning the combination aspect H-9. Thiscommunality can be summarized by stating that the occurrence of an evening shift

Chapter 584

followed by a day shift is unhealthy.The only insignificant coefficient of concordance concerning the healthiness

factor concerns the importance of healthiness of consecutive shifts compared tohealthiness scheduled rest. On the basis on the ten rankings on this combinationdecision, it cannot be concluded that the former aspect is more (or less) importantthan the latter.

5.3.5 Rankings of shift patterns concerning continuity

The rankings of shift patterns related to continuity showed a significant commun-ality on two of the three decision aspects (T-1 and T-3) and on the only combina-tion decision (T-4). The first two significant coefficients of concordance can beexplained on the basis of the number of corresponding nurses scheduled for thesame shift the day before. Furthermore, the communality in the rankings on thecombination decision showed that continuity is most important during the dayshifts.

5.4 CONCLUSIONS OF THE RANKING EXPERIMENT

The objective of the ranking experiment was to provide specifications for theoperationalization of each quality factor. The previous section described the resultsof the ranking experiment. Concluding from these results, this final sectiondescribes the specifications for the operationalization of each quality factor.

The completeness factor can be specified as a function which decreasesaccording to the relative number of shortages. This relative quantitative shortagedepends on the ratio between the number of ‘missing’ nurses and the required num-ber of nurses.

The optimality factor can be specified as a function which decreases ac-cording to the relative deviation from the qualitative staffing demands. This rela-tive qualitative deviation depends on the ratio between the number of ‘missing’registered nurses and the required number of registered nurses.

The proportionality factor can be specified as a function which decreases witheach occurrence of either a single day off or a sequence of two weekends on. Itshould be noted that this means that the occurrence of a sequence of three

Ranking of shift patterns 85

weekends on decreases proportionality twice as much as the occurrence of a se-quence of two weekends on.The healthiness factor can be specified as a function which decreases with eachoccurrence of an unhealthy shift pattern. These unhealthy shift patterns concernsequences of too many days on or too few days off.

And finally, the continuity factor can be specified as a function which de-creases with each absence of continuity. This discontinuity occurs whenever thenumber of nurses scheduled for a day shift, who are also scheduled for a day shifton the previous day, is less then the required number.

These specifications of the five quality factors provide guidelines for ananswer to the second research question described in the third chapter: “How canone operationalize each quality factor?”. The following section describes howthese specifications are used to develop nursing schedule quality metrics. Thesemetrics are represented as formulas. These formulas provide the required answerto the second research question (i.e. they describe how to operationalize eachquality factor).

5.5 OPERATIONALIZATION OF NURSING SCHEDULE QUALITY

This section describes the operationalization of the quality factors based on thespecifications described above. In this description, the term quality indicator willbe used for an operationalized quality factor. These quality indicators will indicatethe value of the corresponding quality factors on a scale from zero to one.

The following five subsections discuss the formulas used to compute thevalue of these indicators. These computations should, one way or another, integrateover the length of the schedule period (N), the number of types of shift (D), andthe staff size (M). Furthermore, a calibration factor " will be used to make sure thatprecisely sufficient quality will reflect a value of 0.55.

5.5.1 Indication of completeness

The results of the ranking experiment showed that the completeness factor can bespecified as a function which decreases according to the relative amount ofshortages. This relative quantitative shortage depends on the ratio between the

Chapter 586

number of ‘missing’ nurses and the required number of nurses. On the basis of thisspecification, the completeness factor is operationalized into a completenessindicator. The value of this completeness indicator is represented as C.

' &j'

j'

& )

% )

Table 5.7 REQUIRED NUMBER OF STAFF MEMBERS PER TYPE OF SHIFT (n )ij

ji 1 2 3 4 5 6 7

1

2

3

5

3

2

5

3

2

5

3

2

5

3

2

5

3

2

4

3

2

4

3

2

Ranking of shift patterns 87

Formula 5.1: Indication of the value of the completeness factor (C)

The value of the completeness indicator depends on the planned number of staffmembers per type of shift, represented as nN , in relation to the required numberi,j

of staff members per type of shift, represented as n . The value of the latter variablei,j

varies per number of the day of each week (i) and type of shift (j). Table 5.7 showsthese values. In this table, i=1 represents a Monday and i=7 a Sunday. Furthermore,j=1 stands for day shifts, j=2 for evening shifts, and j=3 represents night shifts.

An acceptable shift pattern for the completeness factor turned out to be a shortageof one nurse on a day shift. A shortage of one nurse on an evening shift was stillacceptable. The least acceptable shift pattern for the completeness factor was ashortage of two nurses on a day shift. Further more, a shortage on the night shiftwas unacceptable. Therefore, an " of 0.1373 is used. For example, thisoperationalization results in a value for C of 0.60 for a shortage of one nurse duringthe day shift on a normal working day, a value of 0.56 for a shortage of one nurseduring the evening shift, and a value of 0.53 for a shortage of one nurse during thenight shift.

' &j'

j'

* & ) *

% )

Chapter 588

5.5.2 Indication of optimality

The results of the ranking experiment showed the optimality factor can be specifiedas a function which decreases according to the relative deviation from thequalitative staffing demands. This relative qualitative deviation depends on theratio per type of shift between the number of ‘missing’ registered nurses and therequired number of registered nurses. On the basis of this specification, the opti-mality factor is operationalized into an optimality indicator. The value of this opti-mality indicator is represented as O.

Formula 5.2: Indication of the value of the optimality factor (O)

The value of the optimality indicator depends on the planned number of registerednurses per type of shift, represented as lN , in relation to the required number ofi,j

registered nurses per type of shift, represented as l . The value of the latter variablei,j

varies per number of the day of the week (i) and type of shift (j). Table 5.8 showsthese values.

Acceptable shift patterns for the optimality factor turned out to be a surplus of oneregistered nurse on a day shift, an evening shift or a night shift. A shortage of oneregistered nurse on a day shift on a normal working day was still acceptable. Theleast acceptable combination of shift patterns for the optimality factor was twicea surplus of registered nurses on a day shift on a special working day. Furthermore,shortages of registered nurses on the evening shift or the night shift wereunacceptable. Therefore, an " of 0.1651 is used. For example, this operation-alization results in a value for O of 0.63 for a surplus of one registered nurse ona normal working day during the day shift, and a value of 0.60 for a shortage ofone registered nurse in the same situation. Furthermore, this operationalizationresults in a value for O of 0.60 for a surplus of one registered nurse during anevening or a night shift, and a value of 0.53 for a shortage of one registered nurseduring both types of shift.

ji 1 2 3 4 5 6 7

1

2

3

2

1

1

2

1

1

2

1

1

2

1

1

2

1

1

1

1

1

1

1

1

Table 5.8 REQUIRED NUMBER OF REGISTERED NURSES PER TYPE OF SHIFT (l )ij

' &j'

%

%

Ranking of shift patterns 89

5.5.3 Indication of proportionality

The results of the ranking experiment showed that the proportionality factor canbe specified as a function which decreases for each occurrence of either a singleday off or a sequence of two weekends on. On the basis of this specification, theproportionality factor is operationalized into a proportionality indicator. The valueof this proportionality indicator is represented as P. Formula 6.3 represents the wayin which this value is computed.

Formula 5.3: Indication of the value of the proportionality factor (P)

The value of this quality indicator depends on the number of occurrences of singledays off, represented as v , and the number of occurrences of sequences of twoj

weekends on, represented as w .jAn acceptable shift pattern for the proportionality factor turned out to be the

occurrence of one sequence of two weekends on. The occurrence of one single dayoff was still acceptable. The least acceptable combination of shift patterns for theproportionality factor was the occurrence of one single day off combined with asequence of two weekends on. Therefore, an " of 0.1468 is used. For example, thisoperationalization results in a value for P of 0.62 for one occurrence of a sequenceof two weekends on in the four-week nursing schedule, and a value of 0.58 for theoccurrence of a single day off for one nurse in the arranged schedule.

' &j'

j'

Chapter 590

5.5.4 Indication of healthiness

The results of the ranking experiment showed the healthiness factor can be speci-fied as a function which decreases with each occurrence of an unhealthy shift pat-tern. These unhealthy shift patterns concern sequences of too many days on or toofew days off. On the basis of this specification, the healthiness factor is opera-tionalized into a healthiness indicator. The value of this healthiness indicator isrepresented as H.

Formula 5.4: Indication of the value of the healthiness factor (H)

The value of this quality indicator depends on the independent variable o . Thei,j

default value for this variable is 0. The value of 1 is used for unhealthy shift pat-terns. Table 5.9 shows these unhealthy patterns.

These unhealthy shift patterns are represented as sequences of codes. Table5.10 explains these codes.

The unhealthy shift patterns presented above are consistent with theergonomics criteria for nurse scheduling discussed in the second chapter. Forexample, three of these criteria are no more than seven consecutive working days,just a few night shifts in succession and forward rotation of the shifts. Thesecriteria correspond to the first, fourth and last unhealthy shift pattern presented intable 5.9, respectively.

The least acceptable combination of shift patterns for the healthiness factorwas the occurrence of two unhealthy shift patterns. Three or more unhealthy shiftpatterns per nursing schedule turned out to be unacceptable. Therefore, an " of0.1383 is used. For example, this operationalization results in a value for H of 0.59for the occurrence of one unhealthy shift pattern in the arranged four-week nursingschedule, and three of these patterns result in a value of 0.52.

Table 5.9 UNHEALTHY SHIFT PATTERNS

shift pattern description

S S S S S S S S

D D D D D D

E E E E E

N N N N N

N N O O S

O S O

E D

8 consecutive days on

6 consecutive day shifts

5 consecutive evening shifts

5 consecutive night shifts

only 2 days off after a series of night shifts

only 1 consecutive day on

a day shift directly following an evening shift

Table 5.10 MEANING OF SHIFT CODES

code description

D

E

N

S

O

day shift

evening shift

night shift

day on

day off

Ranking of shift patterns 91

5.5.5 Indication of continuity

The results of the ranking experiment showed the continuity factor can be specifiedas a function which decreases with each absence of daily continuity. This dailycontinuity depends on the number of nurses scheduled for a day shift, who are alsoscheduled for a day shift on the previous day. An absence of daily continuityoccurs whenever this number of ‘overlapping’ nurses is less than the requirednumber. On the basis of this specification, the continuity factor is operationalizedinto a continuity indicator. The value of this continuity indicator is represented as

Chapter 592

T (the C already represents completeness).

' &j'

& )

% )

Ranking of shift patterns 93

Formula 5.5: Indication of the value of the continuity factor (T)

The value of this indicator depends on the planned continuity per day, representedas t' , in relation to the required continuity per day, represented as t . On the basisi i

of the results of the ranking experiment, the value of the latter variable is set at two.This means that, each day, two overlapping nurses need to be scheduled.

Three absences of continuity in a schedule turned out to be the least accept-able combination of shift patterns for the continuity factor. More absences of conti-nuity were unacceptable. Therefore, an " of 0.2397 is used. For example, thisoperationalization results in a value for T of 0.66 for one absence of continuity,a value of 0.60 for two such absences, and a value of 0.52 for four absences of con-tinuity in the arranged four-week nursing schedule.

5.5.6 Discussion of the operationalizations

The described quality indicators differ in orientation to the schedule. These orien-tations will be called vertical, horizontal and diagonal.

Both the completeness and the optimality indicator are vertically oriented.This means that they ‘scan’ a nursing schedule per daily column (top-down). Theyintegrate over the vertical dimension and are scaled with the length of the scheduleperiod (N) and the number of types of shift (D). These indicators are independentof the staff size (M).

The proportionality and the healthiness indicators are horizontally oriented.This means that they ‘scan’ a nursing schedule per row (left-right). They integrateover the horizontal dimension and are scaled with the staff size (M) and the lengthof the schedule period (N). These indicators are independent of the number of typesof shift (D).

Finally, the continuity factor is both vertically and horizontally oriented. Itwill therefore be called ‘diagonally’ oriented (down-left-right). It integrates overboth the vertical and the horizontal dimension and is related to a vertical require-ment (i.e. t = 2) and scaled with the (horizontal) length of the schedule period (N).i

Chapter 594

This indicator is independent of both the number of types of shift (D) and the staffsize (M).

The described operationalizations of the five quality factors all ground onthe specifications concluded from results of the ranking experiment. One plausibleinterpretation of these specifications resulted in the five quality indicators de-scribed above. Other interpretations of these specifications are also possible.However, this is of little importance for the auditing experiment described below.The main purpose of these operationalizations is to provide an indication of the‘goodness’ of a nursing schedule for each quality factor. Furthermore, these indica-tions must be in the same order of magnitude, which is the case for the describedquality indicators.

' % % % %

CHAPTER 6

AUDITING OF NURSING SCHEDULES

The previous chapter described the results of the ranking experiment. The con-clusions of this ranking experiment consisted of five quality indicators. Each ofthese quality indicators measured the value of the corresponding factor of nursingschedule quality. On the basis of these conclusions, a second experiment wasdesigned. The objective of this second experiment was to test the hypothesis ofrobustness, discussed in the third chapter. This hypothesis states that the totalquality value of a nursing schedule according to a nurse scheduler can be explainedon the basis of a weighted sum of the generic factor values.

The present chapter discusses this follow-up experiment. In this experiment,nurse schedulers were asked to audit several nursing schedules. This experimentis called the ‘auditing experiment’. The following sections describe the design,results and conclusions of this auditing experiment.

6.1 DESIGN OF THE AUDITING EXPERIMENT

The objective of the auditing experiment is to test the hypothesis of robustness,which states that the total quality value of a nursing schedule s according to nursescheduler i (Q ) can be explained on the basis of a weighted sum of the values ofs,i

the quality factors (i.e. completeness (C), optimality (O), proportionality (P),healthiness (H) and continuity (T)).

Formula 6.1: The audit value as a weighted sum of the factor values

To test this hypothesis, an auditing experiment was designed. In the design of thisexperiment, Q was treated as the dependent variable. Furthermore, the factors,i

values (C , O , P , H , and T ) were designed to be the instrumental variables, ands s s s s

the summation weights (T , T , T , T , and T ) were designed to be the explanatoryi i i i ic o p h t

Table 6.1 NUMBER OF ARRANGED NURSING SCHEDULES PER NUMBER OFUNACCEPTABLE FACTOR

totalUFV /sched

Psched / UFV

Asched / UFV

0

1

1

1

5

2

2

10

4

3

10

6

4

5

2

5

1

0

32

15

Chapter 694

variables.In this auditing experiment, five nurse schedulers were asked to give a quality

mark on a scale from one to ten according to their own view on nursing schedulequality. These nurse schedulers were instructed to give unacceptable schedules aquality mark below 5.5, and acceptable ones a quality mark above 5.5.

The expected accuracy in giving these quality marks can be expressed as thestandard error (F) (see Lawson & Hanson, 1974). In this auditing experiment, thevalue of 0.5 is assumed to be realistic. This means that when a quality mark m isgiven to a nursing schedule by a nurse scheduler, the ‘real’ quality mark m of thisr

nursing schedule for this nurse scheduler will have a value above m-2F and belowm+2F in ninety-five percent of all cases. For example, when a mark of seven isgiven, there is a five percent chance that the really intended mark is below six orabove eight.

In total, the nurse schedulers were asked to give quality marks to fifteen nursingschedules for the fictitious nursing unit of East-5. For this nursing unit, the threeindependent variables — the length of the schedule period (N), the number of typesof shift (D) and the staff size (M) — have the values of twenty-eight, three andtwenty-three, respectively. Of these twenty-three nurses, nine are registered nursesand fourteen are nursing aids.

These fifteen fictitious nursing schedules differed in the number of qualityfactors with an unacceptable value, which is a value below 0.55. In total, thirty-sixunacceptable factor values were distributed equally over the five quality factors.With an average of 7.2 times an unacceptable value per quality factor, four of thefive quality factors have an unacceptable value in seven of the fifteen nursingschedules, while the remaining one — optimality — has an unacceptable value ineight of the fifteen nursing schedules. This equal distribution is important becausethe hypothesis of robustness, discussed in the third chapter, assumes that nurse

Table 6.2 INDICATION OF THE FACTOR VALUES OF THE FIFTEENFICTITIOUS NURSING SCHEDULES

schedules

name number C O P H T

factor values (x 10 )-1

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

6

8

3

12

5

14

1

10

7

2

11

15

4

13

9

6.0

5.6

9.9

4.4

6.0

4.3

6.0

9.9

5.6

4.9

4.8

9.9

4.0

4.0

4.4

5.5

4.2

6.3

3.7

6.0

9.9

4.2

4.6

4.1

4.2

9.9

4.2

6.3

6.3

3.7

6.2

5.5

5.8

9.9

4.5

5.5

6.2

4.5

4.8

9.9

4.8

6.2

4.6

4.6

4.8

5.9

9.9

4.8

5.9

4.8

5.9

4.9

5.9

9.9

5.0

5.9

4.8

4.9

4.9

5.9

6.6

6.0

6.6

6.0

6.6

3.7

9.9

4.5

4.7

6.6

4.5

4.0

9.9

4.1

3.1

Auditing of nursing schedules 95

schedulers will differ in the summation weights per quality factor. An unbalancedset could therefore affect the determination of the summation weights.

Furthermore, the thirty-six unacceptable factor values were distributed ‘nor-mally’ over the fifteen fictitious nursing schedules. As there are five quality fac-tors, a nursing schedule has five or less unacceptable factor values. This numberof unacceptable factor values per nursing schedule is abbreviated to ‘UFV/sched’in table 6.1.

In total, there are thirty-two different nursing schedules possible consideringonly the acceptable and unacceptable values for the five quality factors. The theor-

Table 6.3 CORRELATION COEFFICIENTS FOR THE FACTOR VALUES

O P H T

- 0.22 - 0.11

- 0.35

- 0.13

- 0.21

- 0.14

- 0.08

- 0.16

0.17

- 0.22

C

O

P

H

Chapter 696

etically possible number of different nursing schedules per number of unacceptablefactor values is abbreviated to ‘Psched/UFV’ in table 6.1.

Fifteen of these thirty-two possible combinations of acceptable and unaccept-able factor values were used as a design for arranging the fictitious nursingschedules. The number of arranged nursing schedules per number of unacceptablefactor values is abbreviated to ‘Asched/UFV’ in table 6.1.

Table 6.1 shows the ‘normal’ distribution of the thirty-six unacceptable factorvalues over the fifteen fictitious nursing schedules. This table shows that this distri-bution for the arranged nursing schedules (Asched/UFV) is similar to the normaldistribution for the theoretically possible number of different nursing schedulesper number of unacceptable factor values (Psched/UFV).

The fifteen nursing schedules were arranged according to both distributions.Table 6.2 shows the factor values for each of these fifteen nursing schedules.

The requirement of a balanced set of nursing schedules can also be tested on thebasis of the correlation coefficients between the values of the five quality factors.Table 6.3 shows these correlation coefficients for the arranged fifteen nursingschedules.

Table 6.4 shows the probability that a pair of quality factors for these fifteennursing schedules do not correlate. As all probabilities are above an error toleranceof five percent (0.05), the values of the five quality factors are not significantlycorrelated.

Summarizing, the set of fifteen fictitious nursing schedules is balanced withrespect to the distribution of the unacceptable factor values over both the qualityfactors and the nursing schedules. Furthermore, no pair of quality factors iscorrelated.

Table 6.4 PROBABILITIES OF NON-CORRELATION

O P H T

C

O

P

H

0.44 0.69

0.20

0.63

0.45

0.61

0.77

0.58

0.54

0.43

Auditing of nursing schedules 97

6.2 RESULTS OF THE AUDITING EXPERIMENT

Five nurse schedulers were asked to give a total quality mark (Q ), on a scale froms,i

one to ten, to each of the fifteen fictitious nursing schedules of the test setdiscussed above. The nurse schedulers were instructed to a give an unacceptablenursing schedule a mark below 5.5. Furthermore, the nurse schedulers were askedto clock the amount of time needed for the audit of each of these fifteen nursingschedules. Table 6.5 shows the quality marks given to the fifteen nursing schedulesby the five nurse schedulers (i.e. the results of the auditing experiment).

6.2.1 Determination of summation weights

The given quality marks were used to validate the hypothesis of robustness. To testthis hypothesis, the results of the auditing experiment were reformulated as anoverdetermined set of linear equations in the form of Ax•b, where A represents them×n matrix (m$n) of factor values (table 6.2) and b represents the quality marksgiven to each of the fifteen nursing schedules by one of the five nurse schedulers(each column from table 6.5). The values per nurse scheduler of the column x,which minimizes the Euclidean norm of the residual vector r=b-Ax, are determinedby using a NAG FORTRAN Library Routine, called F04JAE, for finding theminimal solution to the overdetermined linear least-squares problem Ax•b (Lawson& Hanson, 1974, pp. 180-198). Table 6.6 gives the resulting least-squares solutionper nurse scheduler. For each of these solutions, a rank of five was computed.

Table 6.5 QUALITY MARKS GIVEN BY THE NURSE SCHEDULERS (Q )s,i

nursingsched-

ules

nurse schedulers

1 2 3 4 5

7.5

5.4

6.5

4.5

5.4

3.5

5.4

5.0

4.0

5.4

6.0

5.4

3.0

3.5

4.0

7.5

5.5

7.0

1.0

5.0

2.0

7.0

3.0

4.5

5.0

3.0

5.0

1.0

4.0

5.0

9.8

8.8

9.4

7.8

8.6

8.0

9.2

7.8

8.8

9.0

7.0

8.4

8.2

6.6

6.8

7.5

7.5

6.5

6.0

6.0

6.5

7.8

6.5

6.2

7.0

5.5

6.0

5.4

5.4

5.4

6.2

4.5

6.0

4.3

5.0

5.8

7.5

4.3

4.5

4.5

5.5

3.8

4.5

5.2

4.0

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

Chapter 698

The resulting least-squares solutions show that nurse schedulers strongly differconcerning their personal summation weights. Nurse scheduler number two putmost of the weight on completeness, while two other nurse schedulers (i.e. numbersthree and four) distributed these weights more equally over all five quality factors.And nurse scheduler number five considered optimality and continuity to be themost important quality factors, while for nurse scheduler number one, the mostimportant quality factors turned out to be completeness and proportionality.

Furthermore, these results show one negative weight value. An investigationof this negative summation weight of the second scheduler for the optimality factorshowed that this nurse scheduler ‘rewarded’ qualitative overstaffing. This was

Table 6.6 SUMMATION WEIGHTS PER NURSE SCHEDULER

schedulersummation weights

TTc TTo TT p TTh TTt FF

1

2

3

4

5

2+

3.3

4.2

3.0

2.0

1.0

3.9

1.3

- 1.1

1.6

1.2

3.1

0.0

2.1

0.0

2.6

2.4

0.8

0.0

0.8

1.9

3.3

3.0

0.8

2.0

1.0

2.3

3.6

2.3

3.0

1.5

1.1

2.2

0.7

0.7

0.9

Auditing of nursing schedules 99

probably due to the fact that this nurse scheduler's own nursing unit only consistedof nurses with the same level of nursing expertise. This nurse scheduler wastherefore unfamiliar with differences in optimality. As this factor was unknown tothis second nurse scheduler, the results of this nurse scheduler were analyzed withthe requirement that all solution components must be non-negative. This was doneby using another NAG FORTRAN Library Routine, called E04NCE. Table 6.6 alsoshows the resulting non-negative least-squares solution for this second nursescheduler (2 ). This solution also shows the weight nurse scheduler number two+

puts on the completeness factor.

6.2.2 Goodness of fit

Table 6.6 also shows the standard error (F) for each least-squares solution. Thisstandard error has the value %(r r/(m-k)) when m>k, and the value zero when m=k.T

The r r in this computation expresses the residual sum of squares. Furthermore,T

m represents the number of rows of the matrix A, which is 15 in this case, and kstands for the rank of matrix A, which turned out to be 5 for all solutions.Therefore, in this case, the standard error F has the value of %(r r/10).T

These standard errors provide a measure for the quality of the least-squaressolutions. With a probability of ninety-five percent, the quality mark a nurse sched-uler will give (or has given) to a nursing schedule (Q ) will be above QN -2Fs,i s,i

Table 6.7 PREDICTED QUALITY MARKS (Q' )s,i

nursingsched-ules

nurse schedulers

1 2 3 4 5 2+

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

out ofrange 4 7 0 0 2 8

total outof range 13 14

5.1

4.9

6.3

5.1

4.7

4.7

5.2

5.7

4.7

4.6

5.2

5.9

3.9

4.3

2.7

5.3

5.8

4.9

8.6

9.2

9.4

8.6

7.9

7.6

9.3

8.4

8.5

6.6

7.3

7.1

6.9

6.0

6.0

6.9

6.4

6.8

5.3

4.9

5.8

4.7

5.2

5.5

5.8

4.6

4.4

4.5

4.9

5.9

3.8

4.4

3.3

5.1

5.6

4.6

5.3

4.8

5.9

4.5

3.9

3.7

4.1

3.1

5.5

4.2

2.9

3.3

8.7

7.8

8.3

8.6

6.5

6.2

6.9

6.1

6.3

6.4

5.1

5.0

5.0

5.8

4.3

6.1

4.3

3.4

4.0

3.7

5.4

4.3

3.1

3.2

- - -

-

- -

--

-

- -

-

-

-

- -

-

-

- -

-

- p > 0.05

Chapter 6100

and below QN +2F. This QN is the predicted quality mark on the basis of the sum-s,i s,i

mation of the factor values multiplied by the nurse scheduler's personal weightvalues. For example, on the basis of the weight values of the fifth nurse scheduler,

Table 6.8 MEAN MARKING SCORES AND THE STANDARD DEVIATION PER NURSESCHEDULER

nurse schedulers

1 2 3 4 5mean

Q

sd

ms,i

i

5.0

1.2

4.4

2.0

8.3

0.9

6.4

0.8

5.0

1.0

5.8

1.2

Auditing of nursing schedules 101

a quality mark of 6.1 ± 1.0 (i.e. two times the tolerable standard error of 0.5) ispredicted for schedule m with a probability of ninety-five percent. The actualquality mark given to this schedule by this nurse scheduler was 4.5, which is notwithin the predicted range.

For all the fictitious nursing schedules, table 6.7 shows the predicted qualitymarks for each of the five nurse schedulers. When applying a tolerable standarderror of 0.5 for all schedulers, which has been assumed to be realistic for a markingscale from one to ten, not all the predicted quality marks fall within the ninety-fivepercent probability range. Those that do not fall within this range are marked witha negative sign ( ).-

These predicted quality marks illustrate the values of the standard errors shownin table 6.10. The hypothetical modelling of nursing schedule quality as a weightedsum of the factor values is strongly supported by the quality marks given by twoof the five nurse schedulers (nurse schedulers numbers three and four). All qualitymarks given by these two nurse schedulers are explained by the hypothetical modelas represented in formula 6.1. The quality marks given by another two of the fivenurse schedulers (nurse schedulers numbers one and five) still support thepresented model, although not very strongly. However, the model is not supportedby one of the five nurse schedulers (nurse scheduler number two). In total, sixty-two of the seventy-five quality marks given by the five nurse schedulers to thefifteen nursing schedules support the hypothetical model. This means that eighty-three percent of these quality marks can be explained on the basis of a weightedsum of the factor values. The restriction that all summation weights must be non-negative resulted in a total of fourteen out-of-range predictions, which slightlyreduces this percentage to eighty-one.

Table 6.9 LINEARLY TRANSFORMED QUALITY MARKS (Q )ns,i

nursingsched-

ules

nurse schedulers

1 2 3 4 5

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

7.6

5.9

6.7

5.3

5.9

4.4

5.9

5.5

4.7

5.9

6.3

5.9

3.9

4.3

4.7

7.0

6.1

6.8

3.9

5.8

4.3

6.8

4.8

5.6

5.8

4.8

5.8

3.9

5.3

5.8

7.1

6.1

6.7

5.0

5.8

5.2

6.5

5.0

6.0

6.3

4.1

5.6

5.4

3.9

3.9

6.9

6.9

5.7

5.1

5.1

5.7

7.3

5.7

5.3

6.3

4.4

5.1

4.3

4.3

4.3

6.7

5.0

6.5

4.8

5.5

6.3

8.0

4.8

5.0

5.0

6.0

4.3

5.0

5.7

4.5

Chapter 6102

6.2.3 Coping with differences in marking style

Nurse schedulers might differ with respect to their marking style. This means thatboth the mean marking score (Q ) and the standard deviation (sd ) can differ pers,i i

m

nurse scheduler i. The five nurse schedulers who participated in the ranking experi-ment did strongly differ with respect to both the mean marking score and thestandard deviation of these scores. Table 6.8 shows these differences.

By applying a standard transformation, these differences in marking style canbe eliminated. This standard transformation results in a standard distribution for

'&

%

schedulersummation weights

TTc TTo TT p TTh TTt FF

Table 6.10 NEW SUMMATION WEIGHTS PER NURSE SCHEDULER

1

2

3

4

5

3.1

3.0

2.3

1.8

1.2

1.6

0.7

0.4

0.5

3.3

2.3

1.2

1.6

2.1

0.9

1.3

2.5

2.1

2.7

1.0

1.2

2.0

3.1

2.3

3.1

0.9

1.2

0.7

0.8

0.9

Auditing of nursing schedules 103

each nurse scheduler. A standard distribution has a mean of zero and a standarddeviation of one. The computation of the original marking values (Q ) intos,i

standard marking values (Q ) is based on the equation of Q =Q +sd ×Q . Ins,i s,i s,i i s,is m s

order to achieve new marking values (Q ) with a mean of 5.5, which is the means,in

of the range from one to ten, and a standard deviation of one, the following lineartransformation was performed.

Formula 6.2: Linear transformation of the original marking values into newmarking values

By applying this formula, the original marking values (Q ) were linearly trans-s,i

formed into the new marking values (Q ). Table 6.9 shows these linearly trans-s,in

formed quality marks.Table 6.10 gives the resulting least-squares solution per nurse scheduler. Also

for each of these solutions, a rank of 5 was computed (i.e. A is of full rank).For all the fictitious nursing schedules, table 6.11 shows the predicted new

quality marks (QN ) for each of the five nurse schedulers. When applying ain

tolerable standard error of 0.5 for all schedulers, not all the predicted quality marksfall within the ninety-five percent probability range. Those that do not fall withinthis range are marked with a negative sign ( ).-

Chapter 6104

Table 6.11 shows that in fourteen of the seventy-five cases the predicted newquality marks are out of range. In thirteen of the seventy-five cases, the predictedoriginal quality marks are out of range. Although the linear transformation did havea small effect on the goodness of fit per nurse scheduler, these results show thatdifferences in marking style do not affect the overall results of the auditingexperiment. These overall results show that more than eighty percent of the qualitymarks given to fifteen fictitious nursing schedules by five nurse schedulers fallwithin the predicted range.

6.3 CONCLUSIONS OF THE AUDITING EXPERIMENT

The results of the auditing experiment show that more than eighty percent of thequality marks given to fifteen fictitious nursing schedules by five nurse schedulerscan be explained on the basis of a weighted sum of factor values. These results sup-port the hypothesis of robustness. Furthermore, these results are not affected bydifferences in marking style. Therefore, the auditing experiment shows that nursingschedule quality can be modelled as a weighted sum of factor values, where thefactor definitions are generic and the summation weights are specific. This providesa positive answer to the third research question asked in the third chapter (i.e. “Canthe total nursing schedule quality be explained on the basis of a weighted sum offactor values?”). The next chapter describes the investigation of the applicationof this operational model of nursing schedule quality.

nursingsched-

ules

nurse schedulers

1 2 3 4 5

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

Table 6.11PREDICTED LINEARLY TRANSFORMED QUALITYMARKS (Q )' n

s,i

out ofrange

total outof range

2 6 1 3 2

14

5.7

5.7

6.8

5.7

5.3

5.4

5.9

6.1

5.3

5.9

5.5

5.3

5.1

4.4

4.2

5.7

6.3

6.6

5.4

5.3

4.9

6.0

6.2

6.0

5.5

5.1

6.0

5.4

4.2

4.3

5.9

6.3

6.5

5.8

5.4

4.7

6.6

5.8

5.8

6.0

4.9

5.7

6.0

4.2

4.1

5.8

6.4

6.1

6.0

5.1

4.9

6.2

5.6

6.0

6.0

5.0

5.5

5.6

4.3

4.3

5.7

5.4

6.3

5.1

5.6

6.0

6.2

5.1

4.9

5.4

6.3

4.9

6.5

4.7

3.7

-

-

-

-

-

-

-

-

- -

-

-

-

-

- p > 0.05

Auditing of nursing schedules 105

CHAPTER 7

EFFECTIVE DECISION SUPPORTFOR NURSE SCHEDULING

The third chapter described three hypotheses. Two of these hypotheses — the hyp-othesis of formalization and the hypothesis of robustness — have been confirmed.This chapter describes the scheduling experiment, an experiment which wasdesigned to test the third and last hypothesis: the hypothesis of effectiveness. Thishypothesis states that the task of nurse scheduling can be effectively supported bymeans of quality indication.

In the scheduling experiment, nurse schedulers were asked to arrange anursing schedule for a fictitious nursing unit. This experiment investigates theeffect of supporting the nurse schedule with information about the factor valueson the quality of the arranged nursing schedules. The following sections discussthe design, results and conclusions of this scheduling experiment.

7.1 DESIGN OF THE SCHEDULING EXPERIMENT

The objective of the scheduling experiment is to test the hypothesis of effective-ness. This hypothesis states that quality indication can be effectively used to sup-port the task of nurse scheduling. To attain this objective, the scheduling experi-ment was based on a pre-test post-test design. In this design, the pre-test conditionconcerns the old situation, while the post-test measures the new situation. Bothsituations are separate steps in the scheduling experiment. Below, the firstsubsection describes these steps. The second subsection discusses the variablesused in this experiment. And the third subsection describes additional charac-teristics of the East-5 nursing unit, essential for the scheduling experiment.

Chapter 7108

7.1.1 Steps of the scheduling experiment

In the second step of the scheduling experiment, a number of nurse schedulers weregiven an initial four-week schedule for the fictitious nursing unit of East-5. Thisinitial schedule resulted from the initialization. In the scheduling experiment, thisinitialization has already been completed.

In the second step of the scheduling experiment, the nurse schedulers wereasked to arrange a high-quality nursing schedule for this nursing unit on the basisof this initial schedule with the assistance of a nurse scheduling support system(i.e. the ZKR system; see also Appendix C). This step is called ‘traditional sched-uling’, and the results of this step are called the ‘original final schedule’.

Normally, nurse scheduling only involves the two steps mentioned above.In the scheduling experiment, a third step is added. In this third step, each nursescheduler was informed about the factor values of the arranged nursing scheduleas computed by an additional software module which computes the values of thequality indicators according to the formulas described in the fifth chapter. Then,the nurse schedulers decided if and how they would use this information to re-arrange the original final schedule into a new final schedule. Figure 7.1 showsthese three steps of the scheduling experiment and the resulting ‘status’ of theschedule.

7.1.2 Variables of the scheduling experiment

The objective of the scheduling experiment is to determine the effectiveness of‘quality indication scheduling’, the third step discussed above. This effectivenessconcerns the quality of the new final schedules compared to the quality of the orig-inal final schedules. Therefore, the nursing schedule quality is the dependentvariable. This variable will be estimated as a non-weighted sum of the factor values.This estimation does not need the determination of the individual summationweights, which requires an analysis like the one discussed in the previous chapter.An average (i.e. non-weighted) sum of the factor values will provide a valid estima-tion of the required average value of nursing schedule quality.

Receiving additional quality indication is the independent variable. In thesecond step of the scheduling experiment, the nurse schedulers did not receivequality indication, whereas they did receive this quality indication in the third stepof the scheduling experiment.

Figure 7.1 STEPS OF THE SCHEDULING EXPERIMENT

initial schedule

initialization

traditional scheduling

original final schedule

quality indication scheduling

new final schedule

Effective decision support for nurse scheduling 109

The difference in nursing schedule quality between the original final schedule (Q )o

and the new final schedule (Q ) will determine the effectiveness of qualityn

indication. The null hypothesis is that this difference will be zero (H : Q - Q =0n o

0), while the alternative hypothesis is that this difference will be greater than zero(H : Q - Q > 0).1

n o

Table 7.1 CHARACTERISTICS OF THE EAST-5 NURSING STAFF

full-time equivalent

1.0 0.9 0.8 0.7 0.6 0.5

total fte

registered nurses

nursing assistants

total

2

3

5

2

2

4

1

2

3

2

2

3

2

2

4

1

3

4

9

14

23

7.0

10.5

17.5

Chapter 7110

17.5 fte × 203/365 yield/fte × 28 days = 272.5 shifts1

7.1.3 Characteristics of the East-5 nursing unit

The nursing staff of the East-5 nursing unit consists of nine registered nurses andfourteen nursing assistants. Some of these twenty-three nurses work full-time. Inthis study, this means that these nurses have a so-called full-time equivalent of 0.8or higher. The remaining nurses work part-time, which means that they have a full-time equivalent below 0.8. Table 7.1 shows this division into registered nurses andnursing assistants per full-time equivalent (fte).

The required total of full-time equivalents of a nursing staff can be computedaccording to a standard calculation (Excuro, 1993). In this calculation, normal daysoff, festive days, short-time days, special leaves and educational days aresubtracted from the total number of days in a year. Furthermore, this calculationis based on an average illness ratio of five percent. Finally, the holidays are sub-tracted from this subtotal. Table 7.2 shows this calculation for a nurse with a full-time equivalent of 1.0. This nurse has an average of 203 working days a year. Thisequals a ‘yield’ of 203/365 per fte. As table 7.1 shows, the East-5 nursing unit hasa total of 17.5 fte. This means that the East-5 nursing unit can provide 272.5 shiftsper schedule period of four weeks . And, as described in the last chapter, the East-51

nursing unit requires the assignment of 272 shifts per schedule period of fourweeks. Therefore, the East-5 nursing unit has just the size to meet its quantitativestaffing demands.

Table 7.2 AVERAGE NUMBER OF ANNUAL WORKING DAYS

total

total number of days within a year

minus number of normal days off

minus number of festive days

minus number of short-time days

minus average number of special leave days a year

minus average number of educational days a year

minus average number of sick-leave days a year (5% of the above)

minus number of holidays a year

average number of working days a year

365

104

7

12

1

3

12

23

203

Effective decision support for nurse scheduling 111

7.1.4 Characteristics of the initial schedule

The quantitative staffing demands of the East-5 nursing unit, as described in theprevious chapter, require that a total of 272 shifts are scheduled in a four-weekschedule period. This total consists of 56 night shifts, 84 evening shifts and 132day shifts.

The total of full-time equivalents of the East-5 nursing staff determines themaximum number of shifts that can be scheduled at 350. This maximum is com-puted by multiplying the total number of full-time equivalents by five shifts a weekduring four weeks.

In the initial schedule used in the scheduling experiment, five nurses had aweek of holidays in the four-week schedule period. Furthermore, on eight occa-sions a nurse was not available for a day on. These holidays and ‘not available’days could not be exchanged for a day on (i.e. a day, evening or night shift). Thismeans that there were 340 shifts available, while there were 272 shifts required.This provides some flexibility in arranging the required nursing schedules, whichensures that this experiment would not be too time-consuming to perform.

Chapter 7112

Figure 7.2

Effective decision support for nurse scheduling 113

Figure 7.2 shows the initial schedule (as represented by the user interface of theZKR scheduling support system; see also Appendix C). This initial schedule coversthe weeks numbered as 2, 3, 4 and 5. Week number one is the last week of theprevious schedule. In this initial schedule, five blocks of five consecutive holidaysare represented by dotted rectangles, and the eight crosses represent the ‘notavailable’ days. The nursing staff is represented vertically.

7.2 RESULTS OF THE SCHEDULING EXPERIMENT

In total, eight nurse schedulers agreed to participate in the scheduling experiment.This experiment consisted of two parts. In the first part, each of these eight nurseschedulers arranged a nursing schedule. This resulted in eight original finalschedules. In the second part, the nurse schedulers received quality indication. Thisinformation could be used to rearrange these original final schedules into new finalschedules. The section below discusses the resulting factor values of both theoriginal final schedules and the new final schedules.

7.2.1 Values of the original final schedules

In the first part of the scheduling experiment, each of these eight nurse schedulersarranged a nursing schedule in the traditional situation. Table 7.3 shows the factorvalues of the resulting original final schedules. The five quality factors, com-pleteness, optimality, proportionality, healthiness and continuity, are representedas C, O, P, H and T, respectively.

As described in the previous chapter, the auditing experiment showed anaverage summation weight of approximately two. Therefore, summation weightsof two were used for all quality factors to compute an estimation of the total qualityvalue of a nursing schedule. Table 7.2 also shows these estimated total qualityvalues of the original final schedules, represented as Q . Furthermore, table 7.3o

shows the mean values (m) and the standard deviations (F) for each quality factorand for the estimation of the total quality value.

The mean estimated total quality value for these original nursing scheduleswas nearly five on a scale from one to ten. These values range from 4.4 to 6.2. Thearranged original final schedules show that the nurse schedulers differed consider-

Table 7.3 FACTOR VALUES OF THE ORIGINAL FINAL SCHEDULES

C O P H T Q

1

2

3

4

5

6

7

8

0.60

0.46

0.56

1.00

1.00

0.56

0.56

1.00

0.41

0.22

0.45

0.35

0.60

0.55

0.36

0.36

0.45

0.48

0.49

0.46

0.62

0.46

0.49

0.41

0.41

0.37

0.45

0.35

0.40

0.28

0.40

0.28

0.37

0.65

0.47

0.49

0.49

0.59

0.40

0.35

mean

F

0.72

0.24

0.41

0.12

0.48

0.06

0.37

0.06

0.48

0.11

4.5

4.4

4.8

5.3

6.2

4.7

4.4

4.8

4.9

0.6

Chapter 7114

ably in the values per quality factor. However, most nurse schedulers scored highon completeness. The scores on continuity and proportionality are mostly secondor third in rank. And for half of the arranged original nursing schedules, the scoreson optimality are low (i.e. below 0.4). The most remarkable result is the fact thatall arranged final schedules scored low on healthiness (i.e. 0.45 or lower).

The eight nurse schedulers differed significantly in the amount of time needed toarrange these original final schedules. The fastest nurse scheduler completed theschedule in slightly more than one hour, whereas the slowest nurse schedulerneeded almost two hours to arrange the original final schedule. For this traditionalsituation, table 7.4 shows the total scheduling time expressed in minutes. This tablealso shows the mean total scheduling time and its standard deviation, which isrepresented between rounds.

The computation of the values of each of the quality factors, as described inthe previous chapter, is based on the occurrences of a number of low-quality sched-ule patterns. In total, twenty-one different low-quality schedule patterns are identi-fied. In order to enable a more detailed analysis of the arranged original finalschedules, the tables 7.5a and 7.5b show the numbers of occurrences for each ofthese patterns per arranged nursing schedule. This table also shows the totals per

Table 7.4 TOTAL SCHEDULING TIME IN MINUTES IN THE TRADITIONAL SITUATION

schedulermean

time

1 2 3 4 5 6 7 8

62 110 89 68 95 107 108 63 88 21

FF

Effective decision support for nurse scheduling 115

low-quality schedule pattern and the totals per nurse scheduler. Low-qualityschedule patterns with most occurrences are ‘day over-qualification’ (O4) and‘evening shift followed by day shift’ (H7). These results also show that none of thenurse schedulers scheduled more night shifts than required (O6), and just onces,too many consecutive evening shifts (H3) were scheduled. Also only one nursescheduler scheduled (twice) a single day on (H6).

The eight nurse schedulers differed strongly concerning the number of low-qualityschedule patterns that occurred in the original final schedules. These numbersranged from about twenty to just over hundred.

Table 7.6 shows the summarized number of low-quality schedule patterns perquality factor.

The results of this summarization show that the total number of scheduledlow-healthiness schedule patterns was nearly as high as the total of the remaininglow-quality schedule patterns. On average, the arranged original final schedulesscore worst on healthiness and best on completeness.

Figure 7.3 shows one of the arranged original final schedules. The blackrectangles represent night shifts. The day shifts are represented by the lightly-dotted rectangles. And the remaining, grey-dotted rectangles represented eveningshifts. The scheduled holidays and days off were removed for ease of survey.

The original final schedule shown in figure 7.3 has the highest total qualityvalue compared with the other original final schedules. However, this schedule hasa low value on healthiness. This can be illustrated by the seven occurrences of anevening shift followed by a day shift, which strongly decreases the healthiness ofthis schedule.

Table 7.5a NUMBERS OF OCCURRENCES OF LOW-QUALITY SCHEDULE PATTERNS IN ORIGINAL FINAL SCHEDULES

schedules

1 2 3 4 5 6 7 8

completeness:

day incompleteness

evening incompleteness

night incompleteness

optimality:

day under-qualification

evening under-qualification

night under-qualification

day over-qualification

evening over-qualification

night over-qualification

proportionality:

single day off

double weekend on

triple weekend on

12

1

0

0

0

0

0

0

0

2

6

1

0

0

3

6

3

3

23

13

0

2

4

0

0

1

0

0

0

0

10

0

0

3

1

0

0

0

0

2

0

0

15

8

0

1

5

1

0

0

0

1

0

0

0

0

0

0

1

0

1

1

0

1

0

0

0

1

0

4

2

0

0

1

0

2

1

0

17

0

0

1

3

1

0

0

0

3

0

0

16

4

0

7

4

0

total

93

2

3

3

15

4

3

26

0

20

26

3

Chapter 7116

Table 7.5b NUMBERS OF OCCURRENCES OF LOW-QUALITY SCHEDULE PATTERNS IN ORIGINAL FINAL SCHEDULES

schedules

1 2 3 4 5 6 7 8

healthiness:

too many consecutive days on

too many consecutive day shifts

too many consecutive evening shifts

too many consecutive night shifts

too few days off after night shifts

single day on

evening shift followed by day shift

continuity:

semi-discontinuity

full-discontinuity

total (table 7.5a + table 7.5b)

total

0

2

0

0

5

0

7

6

2

44

0

9

0

12

3

0

0

1

0

82

0

1

0

4

3

0

1

3

1

28

4

7

0

0

4

0

15

4

1

67

1

1

0

0

3

0

11

5

0

23

10

0

1

24

0

0

26

2

0

73

1

0

0

0

7

0

9

4

2

49

2

3

0

0

14

2

40

2

4

101

18

23

1

40

39

2

109

27

10

467

Effective decision support for nurse scheduling 117

Chapter 7118

Table 7.6 SUMMARIZED NUMBER OF LOW-QUALITY SCHEDULE PATTERNS PERQUALITY FACTOR IN ORIGINAL FINAL SCHEDULES

schedules

total1 2 3 4 5 6 7 8

C

O

P

H

T

1

12

9

14

8

3

48

6

24

1

1

10

4

9

4

0

17

7

30

5

0

1

1

16

5

2

2

6

61

2

1

20

5

17

6

0

23

11

61

6

8

141

49

232

37

Effective decision support for nurse scheduling 119

7.2.2 Values of the new final schedules

In the following stage of the scheduling experiment, each nurse scheduler wasinformed about the values of the five quality factors of the arranged nursing sched-ule. On the basis of the quality indication, each of the eight nurse schedulersrearranged the original final schedule into a new final schedule. Table 7.7 showsthe factor values and estimations of the total quality values of these new finalschedules. Table 7.7 also shows the differences in the estimation of the total qualityvalue per nurse schedule between the original final schedule and the new finalschedule ()). Furthermore, this difference is also represented as the relativeindividual gain score (%).

The results of a one-sided t-test for paired samples showed that the meanestimated total quality value for the original final schedules (Q ) was lower (t-o

value=6.81, df=7, p<0.0005) than this mean for the new final schedules (Q ). Thisn

means that quality indication scheduling significantly increased the quality of thefinal schedules. These results reject the null hypothesis, which stated that thisdifference would be zero (i.e. H : Q - Q = 0), and confirm the alternative0

n o

hypothesis, which stated that this difference would be greater than zero (i.e. H :1Q -Q > 0). These findings clearly support the effectiveness of the qualityn o

indication scheduling approach.However, it could be argued that the significant results of the scheduling

experiment are (partially) caused by the large number of available shifts in the

Table 7.7 FACTOR VALUES OF THE NEW FINAL SCHEDULES

C O P H T Q )) %

mean

F

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.00

0.41

0.24

0.44

0.37

1.00

0.60

0.38

0.38

0.48

0.23

1

2

3

4

5

6

7

8

0.49

0.62

0.55

0.50

0.62

0.50

0.51

0.53

0.54

0.05

1.00

0.39

0.55

0.46

0.55

0.34

0.46

0.36

0.51

0.21

0.55

1.00

0.49

0.55

0.55

0.65

0.65

0.65

0.64

0.16

6.9

6.5

6.1

5.8

7.4

6.2

6.0

5.8

6.3

0.6

2.4

2.1

1.3

0.5

1.2

1.5

1.6

1.0

1.5

0.6

53

48

27

9

19

32

36

21

31

15

Chapter 7120

initial schedule compared with the number of required shifts. To deal with thiscriticism, one nurse scheduler arranged a nursing schedule on the basis of a lessflexible initial schedule. Also in this case, quality indication scheduling could beused to increase the estimated total nursing schedule quality. Appendix C showsthese results.

The rearranging of the original final schedules into the new final schedules tookmost nurse schedulers about twenty minutes. Table 7.8 shows the total schedulingtime in the new situation.

Table 7.9 shows the numbers of occurrences for each of the low-qualityschedule patterns per rearranged nursing schedule. In this new situation, thenumber of occurrences of most low-quality schedule patterns shows a largedecrease compared to the original situation. The low-healthiness schedule patternof ‘an evening shift followed by a day shift’ (H7) shows the largest decrease innumber of occurrences. Also in the new situation, the low-quality schedule patternof ‘day over-qualification’ (O4) still has the most occurrences. Furthermore, thenumber of occurrences of two low-quality schedule patterns (O1 and H3) increasedby one or two as a result of the re-arrangement.

In total, the number of occurrences of the low-quality schedule pattern

Table 7.8 TOTAL SCHEDULING TIME IN MINUTES IN THE NEW SITUATION

schedulermean

time

1 2 3 4 5 6 7 8

78 129 114 80 114 127 125 77 106

FF

23

Effective decision support for nurse scheduling 121

decreased from 467 to 256, which is a decrease of forty-five percent. This meansthat, on average, a nurse scheduler was able to reduce the number of low-qualityschedule patterns to almost half the original number on the basis of the informationon quality factor values.

Table 7.10 shows the summarized number of low-quality schedule patterns perquality factor for the new final schedules. The summarizations show a very largedecrease in low-healthiness schedule patterns. Apparently, the application ofquality indication scheduling enables nurse schedulers to increase the healthinessof nursing schedules. Another demonstrated advantage of quality indication sched-uling is the resulting absence of incompleteness.

Figure 7.4 shows one of the new final schedules. This new final schedule onlycontains six low-quality schedule patterns, while the original final schedulecontains twenty-three of these patterns.

The new final schedule shown in figure 7.4 has the highest total quality valuecompared with the other new final schedules. This schedule has acceptable valueson all quality indicators, including healthiness. This can be illustrated by the factthat all seven occurrences of an evening shift followed by a day shift in the originalfinal schedule (see figure 7.3) are successfully removed in this new final schedule.

7.2.3 Randomized pre-test post-test control group design

As described in the previous subsection, the results of the scheduling experimentshowed that the approach of quality indication scheduling is effective. However,this conclusion could be criticized for the lack of a control group (Neale & Liebert,1986, pp. 134-147). Therefore, the data presented above were reanalyzed in such

Table 7.9a NUMBERS OF OCCURRENCES OF LOW-QUALITY SCHEDULE PATTERNS IN NEW FINAL SCHEDULES

schedules

1 2 3 4 5 6 7 8 total %

completeness:

day incompleteness

evening incompleteness

night incompleteness

optimality:

day under-qualification

evening under-qualification

night under-qualification

day over-qualification

evening over-qualification

night over-qualification

proportionality:

single day off

double weekend on

triple weekend on

0

0

0

17

4

0

78

22

0

5

19

2

- 2

- 3

- 3

+2

0

- 3

- 15

- 4

0

- 15

- 7

- 1

- 100

- 100

- 100

+ 13

0

- 100

- 16

- 15

0

- 75

- 27

- 33

0

0

0

6

3

0

23

13

0

0

1

0

0

0

0

2

0

0

9

0

0

1

1

0

0

0

0

3

0

0

10

7

0

1

2

1

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

1

0

0

0

0

0

2

2

0

0

0

0

2

1

0

12

0

0

1

3

0

0

0

0

3

0

0

13

2

0

0

4

0

11

0

0

0

0

0

0

0

0

5

1

0

Chapter 7122

a way that the scheduling experiment fulfilled this requirement of a control group.This was done by using (ad hoc) a randomized pre-test post-test control

Table 7.9b NUMBERS OF OCCURRENCES OF LOW-QUALITY SCHEDULE PATTERNS IN NEW FINAL SCHEDULES

schedules

1 2 3 4 5 6 7 8

healthiness:

too many consecutive days on

too many consecutive day shifts

too many consecutive evening shifts

too many consecutive night shifts

too few days off after night shifts

single day on

evening shift followed by day shift

continuity:

semi-discontinuity

full-discontinuity

total

%

total %

0

0

0

0

0

0

0

3

0

20

- 24

- 55

0

5

0

12

2

0

0

0

0

65

- 17

- 21

0

0

0

0

2

0

0

2

1

18

- 10

- 36

1

0

1

0

4

0

1

0

1

32

- 35

- 52

0

0

0

0

2

0

0

3

0

6

- 17

- 74

3

0

1

24

0

0

5

1

0

39

- 34

- 47

0

0

0

0

2

0

5

1

0

27

- 22

- 45

0

4

0

0

6

2

16

1

0

49

- 52

- 51

4

9

2

36

18

0

27

11

2

256

- 14

- 14

+ 1

- 4

- 21

- 2

- 82

- 16

- 8

- 211

- 78

- 61

+ 100

- 8

- 54

- 100

- 75

- 60

- 80

- 45

Effective decision support for nurse scheduling 123

Chapter 7124

n

Table 7.10 SUMMARIZED NUMBER OF LOW-QUALITY SCHEDULE PATTERNS PERQUALITY FACTOR IN NEW FINAL SCHEDULES

schedules

1 2 3 4 5 6 7 8

total )) %qualityfactor

C

O

P

H

T

0

11

6

0

3

0

45

1

19

0

0

11

2

2

3

0

20

4

7

1

0

0

1

2

3

0

1

4

33

1

0

15

4

7

1

0

18

4

26

1

0

121

26

96

13

- 8

- 20

- 23

- 136

- 24

- 100

- 14

- 47

- 59

- 65

Table 7.11 RESULTS OF THE FIRST PRE-TEST—POST-TEST CONTROL GROUP DESIGN

mean value of Q mean scheduling time

C E

original situation

new situation

C E

mean FF mean FF mean FF mean FF

CE

==

control groupexperimental group

4.8

4.8

0.4

0.4

5.0

6.6

0.8

0.7

98

98

20

20

89

108

19

21

Effective decision support for nurse scheduling 125

group design (Neale & Liebert, 1986, pp. 147-149). This design was applied twice.In the first pre-test post-test control group design, all schedulers with an evennumber were assigned to the control group (C), while all schedulers with an oddnumber were assigned to the experimental group (E). In this design, only theexperimental group received quality indication in the post-test condition. In thepre-test condition, neither group received quality indication. And for the controlgroup, the post-test condition and the pre-test condition were identical. Table 7.11shows the results of this first pre-test post-test control group design.

mean value of Q mean scheduling time

C E

original situation

new situation

C E

mean FF mean FF mean FF mean FF

CE

==

control groupexperimental group

5.0

5.0

0.8

0.8

4.8

6.1

0.4

0.3

89

89

19

19

98

103

20

29

Table 7.12 RESULTS OF THE SECOND PRE-TEST—POST-TEST CONTROL GROUPDESIGN

Chapter 7126

The results of a one-sided t-test for paired samples showed that, in the new situa-tion, the mean estimated total quality value for the experimental group significantlyexceeds this mean for control group (t-value=3.82, df=3, p=0.016). The amountof time required in the new situation did not differ significantly (t-value=0.59,df=3, p=0.299).

In the second pre-test post-test control group design, the situation wasreversed. Now, all schedulers with an odd number were assigned to the controlgroup (C), while all schedulers with an even number were assigned to the experi-mental group (E). Table 7.12 shows the results of this second pre-test post-testcontrol group design.

Again, the results of a one-side t-test for paired samples showed that, in the newsituation, the mean estimated total quality value for the experimental groupexceeds this mean for control group (t-value=2.62, df=3, p=0.040). The amountof time required in the new situation did not differ significantly (t-value=0.68,df=3, p=0.274).

The reanalysis of the results of the scheduling experiment emulating arandomized pre-test post-test control group design also showed an improvementof nursing schedule quality caused by the use of quality indication. This improve-ment is significant when an error tolerance of five percent is used. The results ofthis reanalysis show the validity of the results of the scheduling experiment, andit refutes criticism based on the lack of a control group.

Effective decision support for nurse scheduling 127

7.3 CONCLUSIONS OF THE SCHEDULING EXPERIMENT

The objective of the scheduling experiment is to test the hypothesis of effective-ness. This hypothesis states that the task of nurse scheduling can be effectivelysupported by means of quality indication. The results of the scheduling experimentshowed a significantly higher quality value for nursing schedules arranged on thebasis of quality indication, compared to nursing schedules arranged without thisadditional information. To be more specific, all nurse schedulers involved in thisexperiment used the quality indication, which resulted in an improvement ofnursing schedule quality value of about thirty percent and an average decrease oflow-quality schedule patterns of forty-five percent. Therefore, the results of thescheduling experiment clearly support the hypothesis of effectiveness. Thisprovides a positive answer to the fourth and last research question described in thethird chapter: “Does quality indication improve the quality of nursing schedules?”.

Chapter 8132

8.1 ANALYSIS OF NURSING SCHEDULE QUALITY

The analysis of the concept of nursing schedule quality was guided by the firstresearch question. This question asked about the independent factors of nursingschedule quality. Three steps were taken to answer this question.

Firstly, a survey of literature was conducted in order acquire candidates forthese quality factors. This resulted in eight candidates (i.e. possible quality factors).

Subsequently, these candidates were analyzed on independence and perceiv-ability. Three candidates did not survive this analysis. Therefore, this step resultedin a working set of five independent and perceivable quality factors of nursingschedules.

The third step involved a questionnaire. The answers given by eighteen nurseschedulers to the question “How would you define nursing schedule quality?” werethen qualitatively analyzed (by means of a so-called ‘qualitative factor analysis’)in order to validate the working set of five quality factors. The results of thisanalysis supported each of the five quality factors of this working set.

The results of the analysis of the concept of nursing schedule quality showthat this concept consists of five independent quality factors (i.e. ‘Quality inFives’). These factors were identified as completeness, optimality, proportionality,healthiness and continuity. The completeness factor represents the degree to whichthe quantitative demands for occupation per shift are met. The optimality factorrepresents the degree to which nursing expertise is distributed over the differentshifts. The proportionality factor represents the degree to which each nurse hasbeen given about the same number of night shifts, evening shifts and weekends off.The healthiness factor represents the degree to which care has been taken of thewelfare and health of the nursing staff. And finally, the continuity factor representsthe degree to which there is continuity in the nursing staff during the differentshifts.

8.2 OPERATIONALIZATION OF NURSING SCHEDULE QUALITY

The operationalization of the concept of nursing schedule quality was guided bythe second and third research question. The second research question asked howto operationalize each of the five quality factors, while the third research questionasked if the total nursing schedule quality can be explained on the basis of aweighted sum of factor values. The ranking experiment and the auditing experiment

' % % % %

Analysis, operationalization, and application of nursing schedule quality133

were designed to answer these two questions, respectively.In the ranking experiment, ten nurse schedulers were asked to rank several

alternative shift patterns according to the schedulers own view on nursing schedulequality. In total, each nurse scheduler was asked to make thirty rankings of amaximum of ten ranking objects (i.e. alternative shift patterns).

The results of the ranking experiments showed that nurse schedulers have thesame notion about the values of (most) alternative shift patterns per correspondingquality factor. Those decision aspects, of which the rankings of alternative shiftpatterns showed a significant coefficient of concordance, were included in thespecification of each of the five quality factors. On the basis of these specifications,each quality factor was operationalized into a so-called ‘quality indicator’. Thesequality indicators measure the value of the corresponding quality factor on a scalefrom zero to one. These quality indicators provide an answer to the second researchquestion. Therefore, the results of the ranking experiment support the hypothesisof formalization.

In the auditing experiment, nurse schedulers were asked to audit severalnursing schedules by giving each nursing schedule a quality mark on a scale fromone to ten. The results of this auditing experiment showed that the total quality val-ues of nursing schedules (i.e. the given quality marks) can be explained on thebasis of a weighted sum of factor values. In this explanation, the factor values aregeneric (i.e. vary per nursing schedule), while the summation weights are specific(i.e. vary per nurse scheduler).

The results of the auditing experiment can be summarized by a formula:

Formula 8.1: The operationalization of nursing schedule quality

Formula 8.1 shows the total quality value (Q ) of a nursing schedule s accordings,i

to nurse scheduler i as a weighted sum of the values of the quality factors. In thisformula, the factors values are represented as C , O , P , H and T , while the sum-s s s s s

mation weights are represented as T , T , T , T and T . The sixth chapter de-i i i i ic o p h t

scribes the formulas for the computation of the generic factor values, and alsoshows the determination of the individual summation weights.

The research results of the auditing experiment answer the third researchquestion positively. Therefore, these results support the hypothesis of robustness.

Chapter 8134

8.3 APPLICATION OF NURSING SCHEDULE QUALITY

The application of the concept of nursing schedule quality in order to effectivelysupport the task of nurse scheduling is guided by the fourth and last researchquestion. This research question asked whether ‘quality indication scheduling’ im-proves the quality of nursing schedules. This quality indication scheduling informsnurse schedulers about the factor values of the arranged nursing schedule. This ap-plication of the operationalized concept of nursing schedule quality is based onthe hypothesis that this information will enable the nurse scheduler to improve thenursing schedule's quality (i.e. the hypothesis of effectiveness). The schedulingexperiment was designed to test this hypothesis and thus to answer the fourth andfinal research question.

The results of the scheduling experiment showed an improvement of thirtypercent in nursing schedule quality caused by quality indication scheduling. Thisimprovement consisted of a decrease in low-quality patterns by forty-five percent.This provides a positive answer to the fourth and final research question. Therefore,the results of the scheduling experiment support the hypothesis of effectiveness.

8.4 CONCLUSIONS

This study showed how to analyze, operationalize and apply of the concept ofnursing schedule quality. The analysis was based on the search for independentfactors. The operationalization used the communality among nurse schedulersabout the interpretation of these factors. And finally, the application showed theeffectiveness of informing nurse schedulers about the values of these factors.Therefore, this study showed that task of nurse scheduling can be effectively sup-ported by means of quality indication scheduling. This approach supports the nursescheduler by providing quality indicators that measure the schedule's value foreach of the five quality factors.

The focus of this study was the nurse scheduling problem, which was definedas a tactical problem. However, the results of this study also have strategic andoperational implications. For example, this study's research results give groundsfor a conclusion about the healthiness of nursing schedules. The results of thescheduling experiment, as described in the seventh chapter, showed that all nurseschedulers arranged original final schedules that scored low on the healthiness

Analysis, operationalization, and application of nursing schedule quality135

factor. This conclusion is consistent with the findings of other research on thehealthiness of nursing schedules (see De Vries-Griever et al., 1994).

8.5 GENERALITY OF THE RESULTS

Our society is increasingly becoming a twenty-four-hour economy. Worldwide,the numbers of employees who have to work on special working days (i.e. week-ends or holidays) or special working hours (i.e. in the evening or at night) increaseannually. This study has focused on a small part within this group of employees,namely the nurses who work at continuously operational health care organizations.

The nurse scheduling problem is an instance of a more general type of prob-lem, which can be identified as the ‘general employee scheduling problem’. Thegenerality of the five factors of schedule quality, found in the present study, canbe hypothesized on the basis of a description of this general employee schedulingproblem given by Glover and McMillan (1986). This generality is described belowper quality factor.

The completeness factor is present in all cases of staff scheduling with mini-mum staffing requirements. This is the case in all staff scheduling problems. Theoptimality factor is present in all cases of staff scheduling with a non-homogeneousemployee pool. This is true for most staff scheduling problems (Glover &McMillan, 1986, p. 565). The proportionality factor plays a role whenever theemployees have to work during weekends. Most staff scheduling problems meetthis requirement. The healthiness factor is an essential part of schedule qualitywhenever the employees have to work at both during the day and at night. Again,this is true for most organizations with staff schedules. Finally, the continuity fac-tor is present whenever the employees provide services (i.e. work with clients). Thisis true for a large portion of organizations with staff schedules. Therefore, the fiveidentified quality factors of nursing schedules are likely to be relevant to othertypes of staff schedules as well. This suggests the possibility of applying thisstudy's research results to other staff scheduling domains.

Another way to hypothesize the generality of this study's research results in-volves the five conditions for effective control (De Leeuw, 1990, pp. 112-116).Effective control requires an objective, a model of the controlled system, informa-tion about the system's environment and state, a sufficient number of controllingmeasures and sufficient information-processing capacity. This study showed anincreased effectiveness of nurse scheduling by choosing an operational approach

Chapter 8136

to modeling the controlled system. This not only resulted in more informationabout the system's state, it also increases the nurse scheduler's information-processing capacity. This type of operational approach therefore seems likely tobe applicable to other (scheduling) situations as well.

8.6 FUTURE RESEARCH

This section describes several suggestions for further research. These suggestionsconcern the evaluation of nursing schedule in practice, run-time quality indicationand flexible support of nurse scheduling. Each of these suggestions for furtherresearch is based on this study's operationalization of nursing schedule quality.

8.6.1 Nursing schedule quality in practice

The results of a follow-up research, which was based on the results of the rankingexperiment, showed a low quality of nursing schedules in practice (Lettenga, 1995,p. 28; see also Oldenkamp, Lettenga & Simons, 1996). This follow-up researchcompared the theoretical rankings of shift patterns (i.e. the rankings given duringthe ranking experiment) with these rankings in practice (i.e. the rankings based onthe number of occurrences per shift pattern in arranged nursing schedules). Thesecomparisons were made per scheduler (Lettenga, 1995, pp. 9-14). In total, fiveschedulers participated in this follow-up research, called ‘ranking evaluation’. Asdescribed in the fifth chapter, the ranking experiment showed the rankings of theshifts patterns in theory. In the ranking validation, twenty-three of these rankingswere compared with rankings of the same shift patterns in practice. These rankingsin practice are based on the occurrence of each shift pattern in a schedule arrangedby one of five schedulers who also participated in the ranking experiment.Subsequently, both rankings were analyzed on similarity by computing the rankcorrelation of both rankings. In total, nine out of ninety-five rankings (i.e. ninepercent) showed a significant rank correlation when an error tolerance of fivepercent is applied (Lettenga, 1995, pp. 15-20). This shows that the quality of thearranged nursing schedules in practice is not as high as it theorectically could havebeen. This finding also provides justification for this study's subject of research.

It would be interesting, in future research, to investigate to what extent the

Analysis, operationalization, and application of nursing schedule quality137

quality of nursing schedules in practice can be improved by applying quality in-dication scheduling. This can be investigated by using the research designdescribed in the seventh chapter. Furthermore, this type of study can also includemeasurements based on nursing schedules after the schedule period has beencompleted. These measurements could include variables such as illness rates andnumbers of shifts changed after the final schedule was completed.

8.6.2 Run-time quality indication

It would also be interesting, in future research, to investigate the effectiveness ofrun-time information about the values of the quality indicators. This run-timequality indication scheduling can be compared with an instrument landing system(Kendal, 1993). These instrument landing systems highly improve the quality ofaircraft landing under bad weather conditions. The basic principle is that the pilotsees the aircraft as a point in a two-dimensional coordination system. This is anenormous decrease in information, compared with conventional instruments. Thepilot's job is to keep the point inside a safe box, indicating the area of quality (i.e.high safety).

The nurse scheduler arranging a nursing schedule can be compared with apilot flying an airplane. By means of run-time quality indication scheduling, thenurse scheduler can monitor the quality indicator(s). This monitoring might enablethe nurse scheduler to arrange nursing schedules with quality values that are evenhigher than the ones described in the seventh chapter. This expectation issupported by the findings described in the third appendix (C). These findings arebased on an additional case study. The nurse scheduler who participated in thiscase study was constantly aware of the low-quality patterns that were measuredby the quality indicators (i.e. this nurse scheduler received virtual run-time qualityindication). This enabled this nurse scheduler to arrange an original final nursingschedule with just six low-quality patterns. And after receiving quality indication,the nurse scheduler was even able to rearrange this schedule in such a way that nolow-quality shift pattern occurred in the new final schedule. The findings of thiscase study suggests that run-time quality indication will be very effective.

CHAPTER 8

ANALYSIS, OPERATIONALIZATION, ANDAPPLICATION OF NURSING SCHEDULE QUALITY

The research objective of this study is to analyze, operationalize, and apply theconcept of nursing schedule quality in order to support the task of nurse sched-uling. The approach followed to attain this objective was based on the assumptionthat an understanding of the concept of nursing schedule quality is essential foran effective support of this task. As described in the first chapter, this study startedby investigating three preliminary research questions: “How can one analyze theconcept of nursing schedule quality?”, “How can one operationalize the concep-tual model of nursing schedule quality?” and “How can one apply the operation-alized concept of nursing schedule quality in order to effectively support the taskof nurse scheduling?”.

A survey of literature on supporting nurse scheduling, as described in thesecond chapter, showed than none of the discussed approaches to supporting nursescheduling scored positively on all theoretical quality aspects. Therefore, a newapproach was suggested which was based on three assumptions: the assumptionof formalization, the assumption of robustness and the assumption of effectiveness.

In the third chapter, which dealt with this study's methodological foundation,these assumptions were reformulated as testable hypotheses: the hypotheses offormalization, robustness and effectiveness. To test these three hypotheses, thepreliminary research questions were refined into four final research questions.These four final research questions are “What are the independent factors ofnursing schedule quality?”, “How can one operationalize each of these qualityfactors?”, “Can the total nursing schedule quality be explained on the basis of aweighted sum of factor values?” and “Does quality indication scheduling improvethe quality of nursing schedules?”.

The first four sections of this chapter summarize the answers obtained by thisstudy to the research questions asked in the third chapter. The fifth sectiongeneralizes these answers towards staff scheduling in general. The sixth and lastsection describes indications for future research.

Chapter 8138

8.6.3 Flexible support of nurse scheduling

Many researchers stress the importance of flexibility in the case of nurse sched-uling (see Rosenbloom & Goertzen, 1987, p. 23; Ozkarahan & Bailey, 1988, p.315). It would be interesting to combine the approach of quality indication sched-uling with flexible scheduling algorithms. Rosenbloom and Goertzen (1987) con-clude that such flexible scheduling algorithms allow both the hospital administra-tion and the nurses to consider the effect of various labor constraints on the qualityof the schedules (p. 23). By means of quality indication scheduling, these effectsof scheduling regulations can be measured quantitatively.

A combination of a flexible ‘scheduling engine’ and quality indicators alsoallows nurse schedulers to gain more insight into the nurse scheduling problem (i.e.increase scheduling skill). This provides nurse schedulers, and also the hospitaladministration, with a tool for knowledge management (see Simons & Spijkervet,1994, p. 14).

Finally, a number of studies have argued that ‘requests scheduling’ (i.e.scheduling based on special requests) causes working schedules with low heal-thiness (see Bisseling, 1993; De Vries-Griever et al., 1994). Quality indicationscheduling can also be used to demonstrate these disadvantages of requestsscheduling.

REFERENCES

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APPENDIX A

QUESTIONNAIRE

This appendix shows the translated questionnaire referred to in the third, fourth andfifth chapter. The Dutch version of the questionnaire was sent to the nurseschedulers who participated in this research. For ease of answering, most of thequestions of this original version were multiple choice questions (including ‘Noneof the above, namely ...’). This appendix only shows the questions.

A.1 General questions

1. Which type of health care organization are you working at? 2. What is the name of this health care organization? 3. Which type of ward are you working on? 4. Which type of nursing unit are you working in? 5. What is your function?

A.2 Characteristics of the task performance

6. Is your nursing unit continuously operational? 7. Are shifts assigned to individuals or to teams of nurses? 8. Do you arrange completely new nursing schedules or do you start with a basic

schedule? 9. What is the length of the schedule period?10. Do you arrange a nursing schedule all by yourself, or do you cooperate with

others?11. If your scheduling task involves cooperation, is there a conflict of interests?

Appendix A150

A.3 Characteristics of the task domain

12. Does your scheduling task involve different types (functions) of nurses? Ifso, what are these types?

13. How many different types of qualification are relevant for your schedulingtask?

14. Do you take the working experiences of the nurse into account whilearranging a nursing schedule?

15. Which percentages of full-time equivalent are present in your nursing unit?16. How many different types of working days are relevant for your scheduling

task?17. Is your nursing unit devided into different locations? If so, how many? If not,

go to question 9.18. Do these locations differ according to work load?19. Does the work load per location change in time?20. Does your nursing unit use so-called call-up shifts?21. What types of shifts are used in your nursing unit? At what time do these

shifts start and end?22. What are the quantitative staffing demands per type of shift and type of

working day?

A.4 Policy and planning

23. Does your health care organization have a (written) staffing policy?24. Does your ward have a (written) staffing policy?25. Does your nursing unit have a (written) staffing policy?26. Is there nursing staff planning at the level of the whole organization? If so,

what is the length of the planning period?27. Is there nursing staff planning at ward level? If so, what is the length of the

planning period?28. Is there nursing staff planning at nursing unit level? If so, what is the length of

the planning period?29. Does your health care organization have a (written) admission policy?30. Does your ward have a (written) admission policy?31. Does your nursing unit have a (written) admission policy?32. Is there admission planning at the level of the whole organization? If so, what

Questionnaire 151

is the length of the planning period?33. Is there admission planning at ward level? If so, what is the length of the

planning period?34. Is there admission planning at nursing unit level? If so, what is the length of

the planning period?35. Does your health care organization have a (written) nurse scheduling policy?36. Does your ward have a (written) nurse scheduling policy?37. Does your nursing unit have a (written) nurse scheduling policy?

A.5 Nursing schedules

38. How would you define nursing schedule quality?39. To what extent can nursing schedules differ in total nursing salary?40. What is the average percentage of illness at your nursing unit?41. To what extent do these illness percentages fluctuate?42. How would you define continuity in nursing care?43. How do you maintain this continuity?44. To what extent do the number of available nurses differ per schedule period?45. To what extent do the types and numbers of admitted patients differ per

schedule period?46. To what extent do you take the distribution of the types of shifts per nurse

into account when arranging a nursing schedule?47. To what extent do you take the length of consecutive shifts into account when

arranging a nursing schedule?48. To what extent do you take the amount of rest between shifts into account

when arranging a nursing schedule?49. What is the average length of the period between the time a nursing schedule

is given to the nurse and the starting date of this schedule?50. Are the nurses of your nursing unit allowed to specify preferences and

special requests?51. Are the nurses of your nursing unit allowed to exchange shifts?52. Can the nurses of your nursing unit negotiate about changes in the scheduled

working hours?

Appendix A152

A.6 Method of scheduling

53. How many months of scheduling experience do you have?54. How did you learn to arrange nursing schedules?55. To what extent do you keep up with the latest developments in the domain of

nurse scheduling?56. Do you know the latest scheduling regulations by heart? Or do you have to

look them up?57. What is the average total amount of time that you spend on arranging a new

nursing schedule?58. Do you find nurse scheduling difficult? Or easy? To what extent?59. Do you follow a (written) method of scheduling to arrange a nursing sched-

ule?60. Do you use special techniques to arrange (parts of) the nursing schedule? If

so, what are they?61. Do you make calculations of available and required nursing time before you

start to arrange the schedule?62. How do you cope with ‘extra’ nursing time?63. Do you sometimes have to reschedule parts of the nursing schedule? How

often can this occur?64. Do you use certain tools to arrange nursing schedules? If so, what are they? If

not, then this questionnaire ends here. If these tools do not include acomputer program, then the next question is your last question.

65. What are the benefits of these tools?66. What is the name of the computer program you use to arrange nursing

schedules?67. Who developed this program?68. Would you please list the main functions of this program?69. What is your opinion of this program?

APPENDIX B

RANKINGS OF THE SHIFT PATTERNS

This appendix shows the results of the ranking experiment per decision aspect. Intotal, this experiment used thirty decision aspects. Below, each of these thirtydecision aspects will be discussed by describing the alternative shift patterns andeach pattern's position in the rankings given by the nurse schedulers. Both the shiftpatterns and the rankings will be shown in one table. In these rankings (i.e. thelower part of each table), the letters (i.e. a, b, c etc.) represent the correspondingshift pattern described in the upper part of each table. The numbers 1 to 10represent the nurse schedulers who participated in this experiment. Furthermore,the capitals refer to the codes of the shifts (see table 5.10).

The numbers within the ranking part of each table represent the position ofthe corresponding shift pattern in the ranking given by the corresponding nursescheduler. In the case of tied ranks, the average of the positions these shift patternswould have had if they had been distinguishable is given to each of these ‘tied’ shiftpatterns. Furthermore, the ranking part of each table also shows the mean positionof each shift pattern over all the given rankings (?i).

Each of the following tables represents the corresponding coefficient ofconcordance (W). Whenever these coefficients of concordance are marked with anasterisk (*), this means that the given rankings are significantly similar using anerror tolerance of one percent.

B.1 Decision aspect of completeness on normal working days (C-1)

The upper part of table B.1 shows three shift patterns. Shift pattern C-1a representsa shortage of one day shift on a normal working day (i.e. 4 scheduled day shiftsinstead of the required 5 day shifts). Shift pattern C-1b represents a shortage ofone evening shift (i.e. 2 scheduled evening shifts instead of the required 3 eveningshifts). The third alternative shift pattern (C-1c) represents a shortage of one nightshift (i.e. 1 scheduled night shift instead of the required 2 night shifts).

Appendix B154

The lower part of table B.1 shows the rankings of these three alternative shiftpatterns given by the ten nurse schedulers. Apart from nurse scheduler number one,most nurse schedulers (i.e. 9 out of 10) ranked a ‘night shortage’ as the mostimportant to avoid.

B.2 Decision aspect of completeness on special working days (C-2)

The upper part of table B.2 shows three shift patterns. Shift pattern C-2a representsa shortage of one day shift on a special working day (i.e. 3 scheduled day shiftsinstead of the required 4 day shifts). Shift pattern C-2b represents a shortage ofone evening shift (i.e. 2 scheduled evening shifts instead of the required 3 eveningshifts). The third alternative shift pattern (C-1c) represents a shortage of one nightshift (i.e. 1 scheduled night shift instead of the required 2 night shifts).

The lower part of table B.2 shows the rankings of these three alternative shiftpatterns given by the ten nurse schedulers. Apart from nurse scheduler number one,most nurse schedulers (i.e. 9 out of 10) ranked a ‘night shortage’ as the mostimportant to avoid.

B.3 Combination decision about completeness per type of working days(C-3)

The upper part of table B.3 shows both ranking objects of the combination decisionabout completeness per type of working day (i.e. normal versus special workingdays).

The lower part of table B.3 shows the rankings of these two alternative rankingobject given by the ten nurse schedulers. These rankings do not show a significantcoefficient of concordance. About half of the nurse schedulers rankedincompleteness on special days as being more important to avoid, while the otherhalf ranked incompleteness on normal days as being more important to avoid.

Rankings of the shift patterns 155

B.4 Decision aspect of day shift optimality on normal working days(O-1)

Optimality has to do with the distribution of nursing expertise over the differentshifts. This distribution concerns the proportion of registered nurses in relation tothe nursing assistants. Table B.4 shows three shift patterns with differentproportions, all concerning the day shifts on normal working days.

Six nurse schedulers ranked shift pattern O-1b as the best; three chose O-1a; andnurse scheduler number 10 ranked O-1c as the best. The corresponding coefficientof concordance was not significant when using an error tolerance of one percent.

B.5 Decision aspect of evening shift optimality on normal working days(O-2)

Table B.5 shows three shift patterns with different proportions, all concerning theevening shifts on normal working days.

The rankings of these three shift patterns given by the ten nurse schedulers show asignificant coefficient of concordance when using an error tolerance of onepercent.

B.6 Decision aspect of night shift optimality on normal working days(O-2)

Table B.6 shows three shift patterns with different proportions, concerning thenight shifts on normal working days.

The rankings shown in the lower part of table B.6 show a significant coefficient ofconcordance when using an error tolerance of one percent. Apart from one nursescheduler, all nurse schedulers ranked shift pattern O-3b as the best.

Appendix B156

B.7 Combination decision about optimality on normal working days pertype of shift (O-4)

The upper part of table B.7 shows three ranking objects, each representing one ofthe three previously-discussed decision aspects related to optimality.

The lower part of table B.7 shows a wide variation in the rankings, which resulted inan insignificant coefficient of concordance when using an error tolerance of onepercent.

B.8 Decision aspect of day shift optimality on special working days(O-5)

Table B.8 is almost similar to table B.4. The difference between both tables is thatB.8 concerns special working days instead of normal working days.

The rankings shown in the lower part of table B.8 show a significant coefficient ofconcordance when using an error tolerance of one percent. The average ranking hasO-5b as the best, then O-5a, and finally O-5c.

B.9 Decision aspect of evening shift optimality on special working days(O-6)

Table B.9 concerns the evening shifts on the special working days. The upper partof this table shows three shift patterns.

The lower part of this table shows the given rankings of these shift patterns. Theserankings show a significant coefficient of concordance when using an errortolerance of one percent.

Rankings of the shift patterns 157

B.10 Decision aspect of night shift optimality on special working days(O-7)

Table B.10 concerns the night shifts on the special working days. The upper part ofthis table shows three shift patterns.

The lower part of this table shows the given rankings of these shift patterns. Theserankings show a significant coefficient of concordance when using an errortolerance of one percent.

B.11 Combination decision about optimality on special working days pertype of shift (O-8)

Table B.11 is almost similar to table B.7. The difference between both tables isthat B.11 concerns optimality on special working days instead of normal workingdays.

The lower part of table B.11 shows a wide variation in the rankings, which resultedin an insignificant coefficient of concordance when using an error tolerance of onepercent.

B.12 Combination decision about optimality per type of working day (O-9)

Combination decision O-9 combines combination decisions B.7 and B.11. Thisdecision forces nurse schedulers to decide whether optimality on normal workingdays is more important than optimality on special working days.

The given rankings of both ranking objects show a light preference for optimalityon normal working days. However, when the given rankings are re-interpreted byintroducing a third virtual ranking object (i.e. ranking object O-9b is copied to O-9c), the insignificant coefficient of concordance when using an error tolerance ofone percent becomes clear.

Appendix B158

B.13 Decision aspect of proportionality concerning the numbers per type ofshift (P-1)

The upper part of table B.13 shows seven distinct shift patterns, all related toproportionality concerning the numbers per type of shift. For instance, shift patternP-1b consists of 13 day shifts, 7 evening shifts and 4 night shifts.

The lower part of table B.13 shows that the ten nurse schedulers differed stronglyin the rankings of these seven shift patterns. As a result, the coefficient ofconcordance when using an error tolerance of one percent was not significant.

B.14 Decision aspect of proportionality concerning the distribution of daysoff (P-2)

The upper part of table B.14 shows seven distinct shift patterns, all related toproportionality concerning the distribution of days off. For instance, shift patternP-2a consists of a pattern of several days on, followed by 2 days off, followed byseveral days on, followed by 3 days off, followed by several days on, followed by 2days off, followed by several days on, followed by 3 days off, followed by severaldays on, followed by 1 day off, and ends with several days on.

The lower part of this table shows the given rankings of these seven shift patterns.These rankings show a significant coefficient of concordance when using an errortolerance of one percent. In the average ranking, shift pattern P-2c is the best,followed by P-2d, while P-2e is the worst.

B.15 Decision aspect of proportionality concerning the distribution of week-ends off (P-3)

The upper part of table B.15 shows four distinct shift patterns, all related toproportionality concerning the distribution of weekends off. For instance, shiftpattern P-3a represents an alternating pattern of a weekend on always followed byweekend off.

Rankings of the shift patterns 159

The lower part of table B.15 shows that all ten nurse schedulers ranked these fourshift patterns in the same way, which resulted in a coefficient of concordance withthe maximum value.

B.16 Combination decision about the importance per decision aspectconcerning proportionality (P-4)

The upper part of table B.16 shows three ranking objects, each representing one ofthe three previously-discussed decision aspects related to proportionality.

As the lower part of table B.16 shows, the ten nurse schedulers differed strongly inthe ranking of these three ranking objects. As a result, the coefficient ofconcordance when using an error tolerance of one percent was not significant.

B.17 Decision aspect of healthiness concerning the number of consecutivenight shifts (H-1)

The upper part of table B.17 shows seven distinct shift patterns, all related tohealthiness concerning the number of consecutive night shifts. For instance, thenurse schedulers had to decide whether they believe that four night shifts in a row(i.e. shift pattern H-1d) is healthier or unhealthier than five night shifts in a row(i.e. shift pattern H-1e). There were no shift patterns of eight or more consecutivenight shifts, because these shift patterns are not allowed by Dutch law.

Most nurse schedulers did, in fact, believe that four night shifts in a row ishealthier then five night shifts in a row. In the average ranking, four and three nightsin the row are the healthiest shift patterns of consecutive night shifts. Thecorresponding coefficient of concordance when using an error tolerance of onepercent is significant.

Appendix B160

B.18 Decision aspect of healthiness concerning the number of consecutiveevening shifts (H-2)

Table B.18a is almost similar to table B.17. The difference between both tables isthat B.18a concerns evening shifts in a row, instead of night shifts. There were noshift patterns of eleven or more consecutive evening shifts, because these shiftpatterns are not allowed by Dutch law.

In the resulting average ranking, three, four and two evening shifts in a row are thethree most healthiest shift patterns of consecutive evening shifts, respectively.Furthermore, the lower part of table B.18a also shows that six or more eveningshifts in a row are the least healthy shift patterns of consecutive evening shifts. Thecorresponding coefficient of concordance when using an error tolerance of onepercent is significant. As shown in table B.18b, this significance is still presentwhen the shift patterns representing seven evening shifts or more (i.e. shift patternsH-2g, H-2h, H-2i and H-2j) are clustered into a single ranking object (i.e. shiftpattern H-2g).

B.19 Decision aspect of healthiness concerning the number of consecutiveday shifts (H-3)

Table B.19a is almost identical to table B.18a. The difference between both tablesis that B.19a concerns days shifts in a row, instead of evening shifts. There were noshift patterns of eleven or more consecutive day shifts, because these shift patternsare not allowed by Dutch law.

In the resulting average ranking, four, three and five day shifts in a row are the threehealthiest shift patterns of consecutive day shifts, respectively. Furthermore, thelower part of table B.19a also shows that six or more day shifts in a row are theleast healthy shift patterns of consecutive day shifts. The corresponding coefficientof concordance when using an error tolerance of one percent is significant. Asshown in table B.19b, this significance is still present when the shift patternsrepresenting seven day shifts or more (i.e. shift patterns H-3g, H-3h, H-3i and H-3j) are clustered into a single ranking object (i.e. shift pattern H-3g).

Rankings of the shift patterns 161

B.20 Decision aspect of healthiness concerning the number of consecutiveworking days (H-4)

Just like the three previously-discussed decision aspects, the upper part of tableB.20 shows shift patterns that represent shifts in a row. These seven shift patternsshow different numbers of consecutive days on. There were no shift patterns ofeleven or more consecutive days on, because these shift patterns are not allowed byDutch law.

As shown in the lower part of table B.20, the resulting rankings show a significantcoefficient of concordance when using an error tolerance of one percent. In theresulting average ranking, seven, six, and five consecutive days on are the threehealthiest shift patterns of consecutive days on.

B.21 Combination decision about the importance per decision aspect con-cerning healthiness of consecutive shifts (H-5)

The upper part of table B.21 represents four ranking objects related to acombination decision. This combination decision concerns the importance perdecision aspect concerning healthiness of consecutive shifts. It combines the fourpreviously discussed decision aspects of healthiness. These decision aspects H-1,H-2, H-3 and H-4 are represented as the ranking objects H-5a, H-5b, H-5c and H-5d, respectively.

The lower part of table B.21 shows that eight of the ten nurse schedulers ranked‘not too many consecutive days on’ as the most important. The correspondingcoefficient of concordance when using an error tolerance of one percent issignificant.

B.22 Decision aspect of healthiness concerning the amount of rest after aperiod of night shifts (H-6)

The six shift patterns shown in the upper part of table B.22 represent differentamounts of rest after a night shift period. These patterns differ from 47.5 hours of

Appendix B162

rest after a night shift period for the ‘shortest’ pattern (H-6a) to 103.5 hours ofnight shift recovery time for the ‘longest’ shift pattern (H-6f).

As shown in the lower part of table B.22, the resulting rankings show a significantcoefficient of concordance when using an error tolerance of one percent. Theaverage ranking shows that healthy working schedules involve at least about eightyhours of night shift recovery time.

B.23 Decision aspect of healthiness concerning the amount of rest between achange of shift without days off (H-7)

The four shift patterns shown in the upper part of table B.23 represent differentamounts of rest between a shift change without days off. These patterns differ fromeight hours of rest for the ‘shortest’ pattern (H-7c) to thirty-two hours for the‘longest’ shift pattern (H-7b).

The lower part of table B.23 shows that all but one nurse scheduler rank shiftpattern H-7a is the healthiest of these four. The corresponding coefficient ofconcordance when using an error tolerance of one percent is significant.

B.24 Decision aspect of healthiness concerning the amount of rest between achange of shift with days off (H-8)

The six shift patterns shown in the upper part of table B.24 represent differentamounts of rest between a shift change with days off. These patterns differ fromthirty-two hours of rest for the ‘shortest’ pattern (H-8d) to fifty-six hours for the‘longest’ shift pattern (H-8c).

Although the given rankings shown in the lower part of table B.24 seem to differstrongly, the corresponding coefficient of concordance when using an errortolerance of one percent is significant.

Rankings of the shift patterns 163

B.25 Combination decision about the importance per decision aspect con-cerning healthiness of scheduled rest (H-9)

The upper part of table B.25 represents four ranking objects related to a com-bination decision. This combination decision concerns the importance per decisionaspect concerning healthiness of scheduled rest. It combines the three decisionaspects H-6, H-7 and H-8. These decision aspects are represented as H-9a, H-9band H-9c, respectively.

In the resulting average ranking, ‘the amount of rest after a period of night work’ isranked as the most important. The corresponding coefficient of concordance whenusing an error tolerance of one percent is significant.

B.26 Combination decision about the importance of healthiness of consecu-tive shifts versus healthiness of scheduled rest (H-10)

Both ranking objects represented in the upper part of table B.26 represent theimportance of decision aspects H-5 and the importance of decision aspects H-9,respectively. This combination decision concerns the importance of healthiness ofconsecutive shifts (H-10a) versus healthiness scheduled rest (H-10b).

As the lower part of table B.26 shows, the ten nurse schedulers differed strongly inthe rankings of these three ranking object. As a result, the coefficient ofconcordance when using an error tolerance of one percent was not significant.

B.27 Decision aspect of continuity during night shifts (T-1)

The upper part of table B.27 shows five distinct shift patterns, all related tocontinuity during night shifts. Shift pattern T-1a represents two blocks of four nightshifts in a row assigned to two nurses, followed by three night shifts in a rowassigned to two other nurses (i.e. twice ‘(4,3)’). Shift pattern T-1b represents twoblocks of five night shifts in a row assigned to two nurses, followed by two nightshifts in a row assigned to two other nurses (i.e. twice ‘(5,2)’). Shift pattern T-1crepresents a repetition of two blocks of three night shifts in a row assigned to two

Appendix B164

(other) nurses (i.e. twice ‘(3,3)’). Shift pattern T-1d represents a repetition of twoblocks of seven night shifts in a row assigned to two (other) nurses (i.e. twice‘(7)’). Finally, shift pattern T-1e represents a mixture of the shift patterns T-1a andT-1b (i.e. ‘(4,3)’ and ‘(5,2)’).

The lower part of table B.27 shows that all but one nurse scheduler rank shiftpattern T-1a as the one with the highest continuity of these five. The correspondingcoefficient of concordance when using an error tolerance of one percent issignificant.

B.28 Decision aspect of continuity during evening shifts (T-2)

The upper part of table B.28 shows five distinct shift patterns, all related tocontinuity during evening shifts. All five shift patterns contain blocks of two, threeor four consecutive evening shifts. However, these patterns differ in the numbersper type of length, and also in the order in which these different blocks arescheduled. As a consequence of this distribution, the pattern with the highestcontinuity (T-2d) involves the scheduling of seven nurses a week, while the patternwith the lowest continuity (T-2e) involves the scheduling of nine nurses a week.

The given rankings shown in the lower part of table B.24 differ strongly. Thecorresponding coefficient of concordance when using an error tolerance of onepercent is not significant.

B.29 Decision aspect of continuity during day shifts (T-3)

The upper part of table B.29 shows five distinct shift patterns, all related tocontinuity during day shifts. All five shift patterns contain blocks of two, three,four or five consecutive day shifts. However, these patterns differ in the numbersper type of length, and also in the order in which these different blocks arescheduled. As a consequence of this distribution, the pattern with the highestcontinuity (T-3a) involves the scheduling of ten nurses a week, while the patternwith the lowest continuity (T-3e) involves the scheduling of fourteen nurses aweek.

Rankings of the shift patterns 165

The lower part of table B.29 shows that all but two nurse schedulers rank shiftpattern T-3a as the one with the highest continuity of these five. The correspondingcoefficient of concordance when using an error tolerance of one percent issignificant.

B.30 Combination decision about the importance of continuity per type ofshift (T-4)

The upper part of table B.16 shows three ranking objects, each representing one ofthe three previously-discussed decision aspects related to proportionality. Thesedecision aspects T-1, T-2 and T-3 are represented as the ranking objects T-4a, T-4band T-4c, respectively.

The lower part of table B.30 shows that all but two nurse schedulers rank‘continuity during day shifts’ as the most important. The corresponding coefficientof concordance when using an error tolerance of one percent is significant.

Appendix B166

Table B.1 DECISION ASPECT OF COMPLETENESS ON NORMAL WORKING

DAYS (C-1)

D E N

(a shortage on a day shift)

(a shortage on an evening shift)

(a shortage on a night shift)

C-1a

C-1b

C-1c

4

5

5

3

2

3

2

2

1

C-1

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.52*

2.6 2.2 1.2

1

3

2

3

3

3

2

3

3

3

2

2

3

2

2

2

3

2

2

2

3

1

1

1

1

1

1

1

1

1

C-1

Rankings of the shift patterns 167

Table B.2 DECISION ASPECT OF COMPLETENESS ON SPECIAL WORKING

DAYS (C-2)

D E N

(a shortage on a day shift)

(a shortage on an evening shift)

(a shortage on a night shift)

C-2a

C-2b

C-2c

3

4

4

3

2

3

2

2

1

C-2

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.57*

2.7 2.1 1.2

2

3

2

3

3

3

2

3

3

3

1

2

3

2

2

2

3

2

2

2

3

1

1

1

1

1

1

1

1

1

C-2

Appendix B168

Table B.3 COMBINATION DECISION ABOUT COMPLETENESS PER TYPE

OF WORKING DAY (C-3)

C-3a

C-3b

incompleteness on normal working days

incompleteness on special working days

a b

S

_

i

1

2

3

4

5

6

7

8

9

10

1.45 1.55

1

2

1

1.5

2

2

1

2

1

1

2

1

2

1.5

1

1

2

1

2

2

W = 0.11

C-3

Rankings of the shift patterns 169

Table B.4 DECISION ASPECT OF DAY SHIFT OPTIMALITY ON NORMAL

WORKING DAYS (O-1)

O-1a

O-1b

O-1c

registered

nurses

nursing

assistants

O-1

3

2

1

2

3

4

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.23

1.9 1.4 2.7

2

1

2

3

2

2

2

1

1

3

1

2

1

1

1

1

1

2

2

2

3

3

3

2

3

3

3

3

3

1

O-1

Appendix B170

Table B.5 DECISION ASPECT OF EVENING SHIFT OPTIMALITY ON

NORMAL WORKING DAYS (O-2)

O-2a

O-2b

O-2c

registered

nurses

nursing

assistants

2

1

0

1

2

3

O-2

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.77*

1.65 1.35 3

2

1

1

2

2

2

2

1

1.5

2

1

2

2

1

1

1

1

2

1.5

1

3

3

3

2

3

3

3

3

3

3

O-2

Rankings of the shift patterns 171

Table B.6 DECISION ASPECT OF NIGHT SHIFT OPTIMALITY ON

NORMAL WORKING DAYS (O-3)

O-3a

O-3b

O-3c

registered

nurses

nursing

assistants

2

1

0

0

1

2

O-3

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.86*

2.0 1.1 2.9

2

1

2

2

2

2

2

2

2

3

1

2

1

1

1

1

1

1

1

1

3

3

3

2

3

3

3

3

3

2

O-3

Appendix B172

Table B.7 COMBINATION DECISION ABOUT OPTIMALITY ON NORMAL

WORKING DAYS PER TYPE OF SHIFT (O-4)

O-4a

O-4b

O-4c

optimality during day shifts on normal working days

optimality during evening shifts on normal working days

optimality during night shifts on normal working days

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.05

2.2 1.75 2.05

3

3

1

3

2

3

1

1

3

2

2

2

2

2

1

2

2

2

1.5

1

1

1

3

1

3

1

3

3

1.5

3

O-4

Rankings of the shift patterns 173

Table B.8 DECISION ASPECT OF DAY SHIFT OPTIMALITY ON SPECIAL

WORKING DAYS (O-5)

O-5a

O-5b

O-5c

registered

nurses

nursing

assistants

O-5

1

2

3

3

2

1

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.48*

2.0 1.4 2.6

3

1

2

3

2

1

2

1

2

3

1

2

1

1

1

2

1

2

1

2

2

3

3

2

3

3

3

3

3

1

O-5

Appendix B174

Table B.9 DECISION ASPECT OF EVENING SHIFT OPTIMALITY ON

SPECIAL WORKING DAYS (O-6)

O-6a

O-6b

O-6c

registered

nurses

nursing

assistants

O-6

2

1

0

1

2

3

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.70*

1.85 1.25 2.9

2

1

2

3

2

2

2

1

1.5

2

1

2

1

1

1

1

1

2

1.5

1

3

3

3

2

3

3

3

3

3

3

O-6

Rankings of the shift patterns 175

Table B.10 DECISION ASPECT OF NIGHT SHIFT OPTIMALITY ON

SPECIAL WORKING DAYS (O-7)

O-7a

O-7b

O-7c

registered

nurses

nursing

assistants

O-7

2

1

0

0

1

2

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.73*

2.1 1.1 2.8

2

1

2

3

2

2

2

2

2

3

1

2

1

1

1

1

1

1

1

1

3

3

3

2

3

3

3

3

3

2

O-7

Appendix B176

Table B.11 COMBINATION DECISION ABOUT OPTIMALITY ON SPECIAL

WORKING DAYS PER TYPE OF SHIFT (O-8)

O-8a

O-8b

O-8c

optimality during day shifts on special working days

optimality during evening shifts on special working days

optimality during night shifts on special working days

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.05

2.2 1.75 2.05

3

3

1

3

2

3

1

1

3

2

2

2

2

2

1

2

2

2

1.5

1

1

1

3

1

3

1

3

3

1.5

3

O-8

Rankings of the shift patterns 177

Table B.12 COMBINATION DECISION ABOUT OPTIMALITY PER TYPE OF WORKING DAY

(O-9)

O-9a

O-9b

=

=

optimality on normal working days

optimality on special working days

a b

S

_

i

re-interpretation of given rankings by introducing a third virtual item (b ? b and c)

a b

S

_

i

1.35 1.65W = 0.35

c

W = 0.07 1.7 2.15 2.15

O-9

1

2

3

4

5

6

7

8

9

10

1

2

1

1.5

2

2

1

1

1

1

2

1

2

1.5

1

1

2

2

2

2

O-9

1

2

3

4

5

6

7

8

9

10

1

3

1

2

3

3

1

1

1

1

2.5

1.5

2.5

2

1.5

1.5

2.5

2.5

2.5

2.5

2.5

1.5

2.5

2

1.5

1.5

2.5

2.5

2.5

2.5

Appendix B178

Table B.13 DECISION ASPECT OF PROPORTIONALITY CONCERNING

THE NUMBERS PER TYPE OF SHIFT (P-1)

D E N

P-1a

P-1b

P-1c

P-1d

P-1e

P-1f

P-1g

14

13

13

12

11

11

10

6

7

6

7

8

7

8

4

4

5

5

5

6

6

P-1

a b c d e f g

3.4 2.9 3.75 3.45 4.4 4.9 5.2

W = 0.16

S

_

i

1

2

3

4

5

6

7

8

9

10

1

3

5

4

2

6

1

7

4

1

2

1

4

4

1

3

2

5

5

2

3

2

7

4

5

2

3.5

6

2

3

4

6

2

4

6

1

3.5

3

1

4

5

5

1

4

7

4

6

4

3

5

6

4

6

4

3

5

7

2

6

6

7

7

3

4

4

7

5

1

7

7

P-1

Rankings of the shift patterns 179

Table B.14 DECISION ASPECT OF PROPORTIONALITY CONCERNING

THE DISTRIBUTION OF DAYS OFF (P-2)

P-2a

P-2b

P-2c

P-2d

P-2e

P-2f

P-2g

P-2 1 2 3 4 5 6

2

4

2

4

2

1

4

3

1

2

2

1

2

2

2

2

3

2

4

2

2

3

1

2

3

2

2

2

1

3

2

-

2

2

1

-

-

-

-

-

2

-

a b c d e f g

4.4 6.15 2.2 2.8 4.65 4.1 3.7

W = 0.36*

S

_

i

1

2

3

4

5

6

7

8

9

10

4

5

6

4

5

4

4

5

4

3

6

6.5

3

4

7

7

7

7

7

7

3

1

5

4

1

3

1

2

1

1

7

2

1

4

2

1

2

1

2

6

5

6.5

4

4

5

3

5

4

6

4

1

3

7

4

3

6

6

6

3

2

2

4

2

4

4

5

3

3

5

5

P-2

Appendix B180

Table B.15 DECISION ASPECT OF PROPORTIONALITY CONCERNING

THE DISTRIBUTION OF WEEKENDS OFF (P-3)

P-3a

P-3b

P-3c

P-3d

P-3 1 2 3 4 5

1

1

1

1

0

1

1

1

1

0

1

1

0

0

0

1

1

1

0

0

a b c d

1 2 3 4S

_

i

1

2

3

4

5

6

7

8

9

10

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

W = 1.00*

P-3

Rankings of the shift patterns 181

Table B.16 COMBINATION DECISION ABOUT THE IMPORTANCE PER

DECISION ASPECT CONCERNING PROPORTIONALITY (P-4)

P-4a

P-4b

P-4c

proportionality concerning the numbers per type of shift

proportionality concerning the distribution of days off

proportionality concerning the distrubution of weekend off

a b c

1.95 1.75 2.3S

_

i

1

2

3

4

5

6

7

8

9

10

2

1

1

2.5

3

2

2

2

3

1

1

2

3

2.5

2

1

1

1

2

2

3

3

2

1

1

3

3

3

1

3

W = 0.08

P-4

Table B.17 on p. 186

Appendix B182

table B.18a

Rankings of the shift patterns 183

table B.18b

Appendix B184

table B.19a

Rankings of the shift patterns 185

table B.19b

Appendix B186

Table B.17 DECISION ASPECT OF HEALTHINESS CONCERNING THE

NUMBER OF CONSECUTIVE NIGHT SHIFTS (H-1)

shift

pattern

H-1a

H-1b

H-1c

H-1d

H-1e

H-1f

H-1g

1

2

3

4

5

6

7

H-1

a b c d e f g

6.55 4.6 2.1 1.6 3.5 4.9 4.75

W = 0.64*

S

_

i

1

2

3

4

5

6

7

8

9

10

7

6.5

7

7

6

7

7

4

7

7

6

4.5

4

3.5

3

4

6

3

6

6

2

1.5

2

3.5

1

1

4

2

2

2

1

1.5

1

3.5

2

2

2

1

1

1

4

4.5

3

3.5

4

3

1

5

4

3

5

6.5

6

3.5

5

5

3

6

5

4

3

3

5

3.5

7

6

5

7

3

5

H-1

Rankings of the shift patterns 187

Appendix B188

Table B.20 DECISION ASPECT OF HEALTHINESS CONCERNING THE

NUMBER OF CONSECUTIVE WORKING DAYS (H-4)

S = number of

consecutive

days on

a b c d e f g

W = 0.46*

S

_

i

1

2

3

4

5

6

7

8

9

10

4.15 2.75 2.75 2.55 4.05 5.35 6.4

7

6

5

3.5

4

4

4

2

2

4

6

4

4

3.5

3

1

1

1

1

3

5

3

2

3.5

2

2

2

3

3

2

4

1

1

3.5

1

3

3

4

4

1

2

2

3

3.5

5

5

5

5

5

5

3

5

6

3.5

6

6

6

6

6

6

1

7

7

7

7

7

7

7

7

7

H-4

S

? 4

? 5

? 6

? 7

? 8

? 9

? 10

H-4a

H-4b

H-4c

H-4d

H-4e

H-4f

H-4g

H-4

Rankings of the shift patterns 189

Table B.21 COMBINATION DECISION ABOUT THE IMPORTANCE PER

DECISION ASPECT CONCERNING HEALTHINESS OF

CONSECUTIVE SHIFTS (H-5)

not too many consecutive night shifts

not too many consecutive evening shifts

not too many consecutive day shifts

not too many consecutive days on

P-3a

P-3b

P-3c

P-3d

a b c d

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.49*

2.6 3.0 3.2 1.2

2

1

4

3

2

4

4

2

1

3

3

4

3

3

4

3

2

3

3

2

4

3

2

3

3

2

3

4

4

4

1

2

1

1

1

1

1

1

2

1

H-5

Appendix B190

Table B.22 DECISION ASPECT OF HEALTHINESS CONCERNING THE

AMOUNT OF REST AFTER A PERIOD OF NIGHT SHIFTS (H-6)

shift

patterns

hours of

rest

47.5

55.5

71.5

79.5

95.5

103.5

NNNOOD

NNNOOE

NNNOOOD

NNNOOOE

NNNOOOOD

NNNOOOOE

H-6a

H-6b

H-6c

H-6d

H-6e

H-6f

H-6

a b c d e f

W = 0.29*

S

_

i

1

2

3

4

5

6

7

8

9

10

5.25 4.05 3.35 2.55 2.85 2.95

6

2

6

5.5

6

6

6

3

6

6

1

1

5

5.5

5

5

5

6

2

5

5

5

3

1.5

2

2

4

2

5

4

2

3

2

1.5

3

4

3

5

1

1

4

6

4

3.5

1

1

2

1

4

2

3

4

1

3.5

4

3

1

4

3

3

H-6

Rankings of the shift patterns 191

Table B.23 DECISION ASPECT OF HEALTHINESS CONCERNING THE

AMOUNT OF REST BETWEEN A CHANGE OF SHIFT

WITHOUT DAYS OFF (H-7)

a b c d

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.54*

1.1 2.8 3.2 2.9

1

1

1

1

2

1

1

1

1

1

3

4

2

2

3

3

3

3

3

3

4

2

3

4

4

4

2

4

2

3

2

3

4

3

1

2

4

2

4

4

H-7

shift

patterns

hours of

rest

24

32

8

24

H-7a

H-7b

H-7c

H-7d

DE

DN

ED

EN

H-7

Appendix B192

Table B.24 DECISION ASPECT OF HEALTHINESS CONCERNING THE

AMOUNT OF REST BETWEEN A CHANGE OF SHIFT WITH

DAYS OFF (H-8)

shift

patterns

hours of

rest

40

48

56

32

40

48

DOD

DOE

DON

EOD

EOE

EON

H-8a

H-8b

H-8c

H-8d

H-8e

H-8f

H-8

a b c d e f

W = 0.23*

S

_

i

1

2

3

4

5

6

7

8

9

10

2.35 2.45 3.55 3.95 4.35 4.35

1

3

3

3.5

4

3

2

1

2

1

5

1

1

3.5

3

4

1

2

2

2

6

2

2

3.5

2

5

4

6

2

3

4

6

5

3.5

1

1

5

4

5

5

3

4

4

3.5

6

6

3

5

5

4

2

5

6

3.5

5

2

6

3

5

6

H-8

Rankings of the shift patterns 193

Table B.25 COMBINATION DECISION ABOUT THE IMPORTANCE PER

DECISION ASPECT CONCERNING HEALTHINESS OF

SCHEDULED REST (H-9)

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

1.4 2.0 2.6

1

2

2

1

1

1

1

2

1

2

2

1

1

2

2

2

3

3

3

1

3

3

3

3

3

3

2

1

2

3

W = 0.36*

H-9

amount of rest after a period of night work

amount of daily rest

amount of weekly rest

H-9a

H-9b

H-9c

Appendix B194

Table B.26 COMBINATION DECISION ABOUT THE IMPORTANCE OF

HEALTHINESS OF CONSECUTIVE SHIFTS VERSUS

HEALTHINESSS SCHEDULED REST (H-10)

H-10a

H-10b

consecutive shifts

rest

a b

S

_

i

1

2

3

4

5

6

7

8

9

10

1.4 1.6

1

2

1

1

1

1

2

2

1

2

2

1

2

2

2

2

1

1

2

1

W = 0.04

H-10

Rankings of the shift patterns 195

Table B.27 DECISION ASPECT OF CONTINUITY DURING NIGHT SHIFTS

(T-1)

(4,3) (5,2) (3,3) (7) continuity

T-1a

T-1b

T-1c

T-1d

T-1e

2

0

0

0

1

0

0

2

0

1

2

0

0

0

0

0

0

0

2

0

2, 2, 2, 0, 2, 2, 0

2, 2, 2, 2, 0, 2, 0

2, 2, 0, 2, 2, 0

2, 2, 2, 2, 2, 2, 0

2, 2, 2, 1, 1, 2, 0

(10 / 7)

(10 / 7)

(8 / 6)

(12 / 7)

(10 / 7)

T-1

a b c d e

S

_

i

1

2

3

4

5

6

7

8

9

10

1.2 4.5 3.4 2.9 3.0

1

1

1

3

1

1

1

1

1

1

4

5

4

5

5

4

5

3

5

5

2

3

5

4

3

5

3

2

3

4

5

2

2

1

4

2

4

5

2

2

3

4

3

2

2

3

2

4

4

3

W = 0.57*

T-1

Appendix B196

Table B.28 DECISION ASPECT OF CONTINUITY DURING EVENING SHIFTS

(T-2)

(4,3) (3,4) (3,2,2) (2,3,2) continuity

T-2a

T-2b

T-2c

T-2d

T-2e

(2,2,3)

0

0

0

1

1

2, 1, 2, 1

1, 2, 1, 2

2, 1, 2, 2

2, 2, 2, 2

1, 1, 1, 1

(6 / 4)

(6 / 4)

(7 / 4)

(8 /4)

(4 / 4)

0

0

1

1

0

2

1

1

0

1

0

0

0

1

1

1

2

1

0

1

T-2

a b c d e

S

_

i

1

2

3

4

5

6

7

8

9

10

W = 0.01

2.95 3.25 2.95 2.8 3.05

1

3

1

3

4.5

5

3.5

5

2.5

1

2

3

2

5

4.5

4

3.5

4

2.5

2

4

3

4

2

2

2

3.5

1

4

4

5

3

3

1

1

1

1

3

5

5

3

3

5

4

3

3

3.5

2

1

3

T-2

Rankings of the shift patterns 197

table B.29

Appendix B198

Table B.30 COMBINATION DECISION ABOUT THE IMPORTANCE OF

CONTINUITY PER TYPE OF SHIFT (T-4)

continuity during night shifts

continuity during evening shifts

continuity during day shifts

T-4a

T-4b

T-4c

a b c

S

_

i

1

2

3

4

5

6

7

8

9

10

2.5 2.3 1.2

2

1

3

2

2

3

3

3

3

3

3

3

2

2

3

2

2

2

2

2

1

2

1

2

1

1

1

1

1

1

W = 0.49*

T-4

APPENDIX C

THE ZKR SCHEDULING SUPPORT SYSTEM

This appendix gives additional information about the ZKR scheduling supportsystem (ZKR is an acronym of a description of the program in Dutch). Figure C.1shows a representation of a nursing schedule in the this program.

The members of the nursing staff are represented vertically. The nurses with thecodes ‘vk-01’ up to ‘vk-09’ are registered nurses, while the nurses with the codes‘vm-10’ up to ‘vm-23’ are nursing assistants. From top to bottom, the shiftsrepresented in this nursing schedule are night shift, evening shift, day shift (thesethree in the second week), holiday, day off and ‘not available’ (these three in thethird week).

The current ZKR system (version 2.0) was developed by a Dutch firm calledIKS-Produkten b.v. (IKS stands for Institute for Knowledge (-Based) Systems).This system supports all the administrative tasks involved in scheduling, and is alsoable implement to all sorts of computations. Furthermore, this system can generatealternative shift patterns. For more information about this system, contact:

IKS-Produkten b.v.P.O. Box 253

9700 AG GroningenThe Netherlands

? +31 50 5270 929

Table D.1 FACTOR VALUES OF THE ORIGINAL SCHEDULE

C O P H C Q

1.00 0.48 0.62 1.00 0.59 7.4

APPENDIX D

REFERENCE CASE STUDY

On the basis of the results of the scheduling experiment, an additional case studywas conducted. The objective of this case study was to determine if qualityindication scheduling also improves nursing schedule quality when the initialschedule is less flexible. This case study used an initial schedule with twice asmany fixed vacations as the one used in the scheduling experiment. Figure D.1shows this initial schedule.

In total, ten vacations, each consisting of five holidays, were already arranged inthis initial schedule. Furthermore, on eight occasions, a nurse was not available fora day-, evening- or night shift.

One nurse scheduler was asked to arrange a final nursing schedule on thebasis of this initial schedule. This nurse scheduler also participated in the sched-uling experiment. Because this nurse scheduler was aware of all low-quality shiftpatterns penalized by the quality indicators, this nurse scheduler was able to arrangea high-quality nursing schedule. Table D.1 shows the resulting values of the qualityfactors.

Table D.2 shows the corresponding numbers of occurrences of low-qualitypatterns in this original final schedule.

It took this nurse scheduler 128 minutes to arrange this original final sched-ule. Figure D.2 shows this final schedule.

Subsequently, the information about the quality factors was presented to thenurse scheduler. On the basis of this information, the nurse scheduler rearranged

Appendix D202

Table D.2 NUMBERS OF OCCURRENCES OF LOW-QUALITY PATTERNS IN THE

ORGINAL FINAL SCHEDULE

O1 O2 O5 P2 T1 total

1 1 1 1 2 6

the original final schedule into a new final schedule. This rearranging took 18minutes. In this rearranging, the nurse scheduler succeeded in eliminating all sixoccurrences of low-quality patterns in the original final schedule. Therefore, thevalues for all five quality factors for the rearranged new final schedule are 1.00,which results in an estimated total schedule quality of 10.0 (i.e. an improvement intotal schedule quality of 35 percent). Figure D.3 shows this rearranged new finalschedule.

SUMMARY

This thesis describes a study on the support of nurse scheduling. Nurse sched-uling is defined as the procedure for providing nursing care by assigning shiftsto nursing personnel. This involves a process of determining when each nurse(of a nursing unit) will be on or off duty, which shift will be worked, by whom(of the on-duty nurses), and how weekends, the number of consecutive daysworked, requests and vacations will be accounted for. This determination pro-cess results in a nursing schedule.

The focus of this study has been on the consequences of the nursingschedules for the performance of the nursing unit. This performance can bedivided into three parts: the effectiveness in providing nursing care, theefficiency of a nursing unit and the job satisfaction of the nursing staff. In thisstudy, the influence of a nursing schedule on the nursing unit's performance isidentified by means of the concept of ‘nursing schedule quality’.

During the last thirty years, many researchers tried to develop a computerprogram that supported the task of nurse scheduling. In this thesis, thesestudies are divided into seven distinct approaches. Subsequently, these sevenapproaches were compared on the effect they have on the performance of thenursing unit (i.e. effectiveness, efficiency and job satisfaction). This com-parison showed that none of the discussed approaches scores positively on allcomparison criteria.

This study investigated a new approach to supporting nurse scheduling.This approach is called ‘Quality Indication Scheduling’. This approach is basedon three hypotheses. The hypothesis of formalization states that the concept ofnursing schedule quality can be modelled as a concept consisting ofindependent quality factors and that each of these factors can be opera-tionalized. The hypothesis of robustness asserts that nurse schedulers mightgive different weights to each of these quality factors when assessing the totalquality value of a nursing schedule. And thirdly, the hypothesis of effective-ness asserts that informing nurse schedulers on the values of the quality factorswill improve the quality of nursing schedules.

Four research questions were formulated to test these three hypotheses:

1. What are the independent factors of nursing schedule quality?

Summary208

2. How can one operationalize each of these quality factors?3. Can the total nursing schedule quality be explained on the basis of a

weighted sum of factor values?4. Does ‘Quality Indication Scheduling’ improve the quality of nursing

schedules?

Four research phases were designed to answer the research questions shownabove: a questionnaire, a ranking experiment, an auditing experiment and ascheduling experiment. For each phase, both the design and the results arediscussed below.

QUESTIONNAIRE

The analysis of the concept of nursing schedule quality was guided by the firstresearch question. This question asked about the independent factors ofnursing schedule quality. Three steps were taken to answer to this question.

Firstly, a survey of literature was conducted in order acquire candidatesfor these quality factors. This resulted in eight candidates (i.e. possible qualityfactors).

Subsequently, these candidates were analyzed on independence and per-ceivability. Three candidates did not survive this analysis. Thus, this step re-sulted in a working set of five independent and perceivable quality factors ofnursing schedules.

The third step involved a questionnaire. The answers given by eighteennurse schedulers to the question “How would you define nursing schedulequality?” were then qualitatively analyzed in order to validate the working setof five quality factors. The results of this analysis supported each of the fivequality factors of this working set.

The results of the analysis of the concept of nursing schedule qualityshow that this concept consists of five independent quality factors (i.e. ‘Qualityin Fives’). These factors were identified as completeness, optimality, propor-tionality, healthiness and continuity. The completeness factor represents thedegree to which the quantitative demands for occupation per shift are met. Theoptimality factor represents the degree to which nursing expertise is distributedover the different shifts. The proportionality factor represents the degree towhich each nurse has been given about the same number of night shifts,

Summary 209

evening shifts and weekends off. The healthiness factor represents the degreeto which care has been taken of the welfare and health of the nursing staff. Andfinally, the continuity factor represents the degree to which there is continuityin the nursing staff during the different shifts.

RANKING EXPERIMENT

The operationalization of the concept of nursing schedule quality was guidedby the second research question. This question asked about how each of thefive quality factors could be operationalized. The ranking experiment was de-signed to answer this question.

In the ranking experiment, ten nurse schedulers were asked to rankseveral alternative shift patterns according to their own view on nursing sched-ule quality. In total, each nurse scheduler was asked to make thirty rankings ofa maximum of ten ranking objects (i.e. alternative shift patterns).

The results of the ranking experiments showed that nurse schedulers havethe same notion about the values of (most) alternative shift patterns percorresponding quality factor. Those decision aspects, of which the rankings ofalternative shift patterns showed a significant coefficient of concordance, wereincluded in the specification of each of the five quality factors. On the basis ofthese specifications, each quality factor was operationalized into a so-called‘quality indicator’. These quality indicators measure the value of the corre-sponding quality factor on a scale from zero to one. These quality indicatorsprovide an answer to the second research question. Therefore, the results of theranking experiment support the hypothesis of formalization.

AUDITING EXPERIMENT

The third research question asked whether the total nursing schedule qualitycan be explained on the basis of a weighted sum of factor values. The auditingexperiment was designed to answer this question.

In the auditing experiment, nurse schedulers were asked to audit fifteennursing schedules by giving each nurse schedule a quality mark on a scale fromone to ten. The results of this auditing experiment showed that the total quality

Summary210

values of nursing schedules (i.e. the given quality marks) can be explained onthe basis of a weighted sum of factor values. In this explanation, the factorvalues are generic (i.e. vary per nursing schedule), while the summationweights are specific (i.e. vary per nurse scheduler).

The research results of the auditing experiment answer the third researchquestion positively. Therefore, these results support the hypothesis ofrobustness.

SCHEDULING EXPERIMENT

The application of the concept of nursing schedule quality in order toeffectively support the task of nurse scheduling is guided by the fourth and lastresearch question. This research questions asked whether ‘Quality IndicationScheduling’ improves the quality of nursing schedules. This ‘Quality Indica-tion Scheduling’ informs nurse schedulers about the factor values of thearranged nursing schedule. This application of the operationalized concept ofnursing schedule quality is based on the hypothesis that this information willenable the nurse scheduler to improve the nursing schedule's quality (i.e. thehypothesis of effectiveness). The scheduling experiment was designed to testthis hypothesis and thus to answer the fourth and final research question.

The results of the scheduling experiment showed an improvement ofthirty percent in nursing schedule quality caused by ‘Quality Indication Sched-uling’. This improvement consisted of a decrease in low-quality patterns byforty-five percent. This provides a positive answer to the fourth and final re-search question. Therefore, the results of the scheduling experiment support thehypothesis of effectiveness.

Additionally, the results of the scheduling experiment also showed that allnurse schedulers arranged original final schedules that scored low on thehealthiness factor. However, the indication of these schedules' healthinesscould be used by the schedulers to increase the healthiness of these schedules.This finding stresses the importance of informing nurse schedulers about thishealthiness factor.

CONCLUSIONS

Summary 211

The objective of this study was to develop nurse scheduling support in such away that it increased the performance of a nursing unit (i.e. effectiveness, effi-ciency and job satisfaction). The approach designed to attain this objectivefocused on the operationalization of the causal relation between the nursingschedule and this performance (i.e. the nursing schedule quality).

This study showed how to analyze, operationalize and apply the conceptof nursing schedule quality. The analysis was based on the search for inde-pendent factors. The operationalization used the communality among nurseschedulers about the interpretation of these factors. And finally, the applicationshowed the effectiveness of informing nurse schedulers about the values ofthese factors.

Therefore, this study showed that task of nurse scheduling can be effec-tively supported by means of ‘Quality Indication Scheduling’. This approachsupports the nurse scheduler by providing quality indicators that measure theschedule's value for each of the quins of quality factors.

SAMENVATTING

(Summary in Dutch)

Dit proefschrift beschrijft de resultaten van een onderzoek naar computer-ondersteuning bij het opstellen van dienstroosters voor het verplegend perso-neel in de intramurale gezondheidszorg. Dergelijke dienstroosters bepalen dewerktijden van het verplegend personeel van een bepaalde verpleegeenheidvoor een aantal weken (meestal zo'n vier tot zes weken).

Het uitgevoerde onderzoek heeft zich gericht op de gevolgen van eenopgesteld dienstrooster voor het functioneren van de verpleegeenheid. Dezegevolgen zijn verdeeld in drie groepen: doeltreffendheid in het geven van ver-pleegkundige zorg, doelmatigheid in het inzetten van het verplegend personeelen arbeidsvreugde van het verplegend personeel. Het geheel van deze gevolgenis aangeduid als roosterkwaliteit.

Gedurende de laatste dertig jaar hebben verschillende onderzoekersgeprobeerd computerprogramma's te ontwikkelen ter ondersteuning van dedienstroosterplanning. In dit proefschrift zijn deze onderzoeken opgedeeld inzeven verschillende benaderingen. Vervolgens bleek uit een onderlinge verge-lijking van deze benaderingen op grond van de gevolgen van een dienstroostervoor de verpleegeenheid dat er niet een benadering was die op alle beoordelingcriteria goed scoorde.

Dit onderzoek heeft een nieuwe benadering voor computerondersteuningbij dienstroosterplanning onderzocht. Deze benadering is benoemd als‘roosteren middels kwaliteitsindicatoren’ (in het Engels: ‘Quality IndicationScheduling’). Deze benadering is gebaseerd op drie hypothesen. De hypothesevan formaliseerbaarheid stelt dat roosterkwaliteit bestaat uit een aantal onaf-hankelijke factoren en dat elk van deze factoren geoperationaliseerd kan wor-den. De hypothese van robuustheid stelt dat roostermakers onderling kunnenverschillen in het gewicht dat zij geven (of het belang dat zij hechten) aan elkvan deze factoren. Ten derde stelt de hypothese van effectiviteit dat de rooster-kwaliteit kan worden verhoogd door roostermakers te informeren over dewaarden van factoren.

Om de drie hypothesen te toetsen zijn vier onderzoeksvragen gefor-muleerd:

Samenvatting214

1. Welke onafhankelijke factoren van roosterkwaliteit zijn er?2. Hoe kan elk van deze factoren worden geoperationaliseerd?3. Kan de totale roosterkwaliteit verklaard worden op basis van een ge-

wogen sommatie van de factorwaarden?4. Verbetert ‘roosteren middels kwaliteitsindicatoren’ de rooster-

kwaliteit?

Voor de beantwoording van elk van deze vragen is een aparte onderzoeksfaseontworpen: een vragenlijstonderzoek, een rangordeningsexperiment, een be-oordelingsexperiment en een verroosteringsexperiment. In het onderstaandeworden het ontwerp en de resultaten van deze vier onderzoeksfasen per faseweergegeven.

VRAGENLIJSTONDERZOEK

Voorafgaand aan het vragenlijstonderzoek is een literatuurstudie verricht. Hetdoel van deze literatuurstudie was het opsporen van potentiële factoren vanroosterkwaliteit. In totaal heeft deze literatuurstudie acht potentiële kwaliteits-factoren opgeleverd.

Vervolgens zijn deze acht potentiële factoren van roosterkwaliteit geana-lyseerd op onafhankelijkheid en waarneembaarheid. Het resultaat van dezekwalitatieve analyses was dat twee van deze acht kwaliteitsfactoren blekenonderling afhankelijk te zijn, en dat van de resterende zes het effect van éénfactor niet waarneembaar is (oftewel een eventuele waarde van deze factor zouniet bepaald kunnen worden op grond van alleen het dienstrooster). Deliteratuurstudie en de kwalitatieve analyses hebben derhalve geresulteerd ineen voorlopige set van vijf waarneembare en onafhankelijke kwaliteitsfactoren.

Ter validatie van de voorlopige set van kwaliteitsfactoren is een vragen-lijst verstuurd aan achttien roostermakers van zes verschillende instellingen inde intramurale gezondheidszorg. De kernvraag die beantwoord is door alleroostermakers luidde: “Wat verstaat u onder de kwaliteit van dienstroosters?”.Vervolgens zijn de gegeven antwoorden op deze vraag onderworpen aan eenzogenaamde kwalitatieve factor analyse. Dit is gedaan door de gegeven om-schrijvingen of definities van roosterkwaliteit op te knippen in betekenisvollefrasen, waarna getracht is elk van deze frasen te verbinden met één van degevonden kwaliteitsfactoren. De resultaten van deze kwalitatieve factor ana-

Samenvatting 215

lyse onderschreven de validiteit van de voorlopige set van kwaliteitsfactoren.Het resultaat van de eerste onderzoeksfase was derhalve dat het begrip rooster-kwaliteit gemodelleerd kan worden als een geheel dat bestaat uit vijfonafhankelijke factoren. Deze factoren zijn benoemd als volledigheid, optima-liteit, evenredigheid, gezondheid en continuïteit. De factor volledigheid heeftbetrekking op de mate waarin voldaan is aan de kwantitatieve bezettingseisen.De factor optimaliteit betreft mate waarin de verhoudingen tussen de verschil-lende (verpleegkundige) deskundigheidsniveau's zo optimaal mogelijk is. Defactor evenredigheid heeft betrekking op de verhouding in de verdelingen vande verschillende diensttypen per medewerker. De factor gezondheid betreft demate waarin voldaan is aan de richtlijnen voor het behoud van het welzijn en degezondheid van het verplegend personeel. Tenslotte betreft de factorcontinuïteit de mate waarin er per diensttype voldoende dagelijkse overlap inde ingeroosterde verpleegkundigen is.

De kwaliteit van dienstroosters voor het verplegend personeel in deintramurale gezondheidszorg blijkt derhalve te bestaan uit vijf onfhankelijkefactoren. Dit is vervat in de titel van dit proefschrift: kwaliteit in vijfvoud (inhet Engels: Quality in Fives). Tevens is dit gegeven gebruikt bij de naamgevingvan het project waarbinnen dit onderzoek is uitgevoerd, namelijk het projectQUINS . QUINS is niet alleen een acroniem van QUality INdication Scheduling, hetis tevens Engels voor vijfling.

RANGORDENINGSEXPERIMENT

Het doel van het rangordeningsexperiment betrof het operationaliseren van elkvan de vijf kwaliteitsfactoren. Om dit te bereiken zijn per factor een aantalzogenaamde ‘besluitvormingsaspecten’ onderscheiden. Zo zijn bijvoorbeeldvoor de factor continuïteit besluitvormingsaspecten onderscheiden: continuï-teit in de nachtdienst, continuïteit in de avonddienst en continuïteit in de dag-dienst. Vervolgens zijn voor ieder besluitvormingsaspect een aantal mogelijkeroosterpatronen ontworpen. Een roosterpatroon is een samenstellingen van eenaantal diensten achter of onder elkaar.

In het rangordeningsexperiment zijn tien roostermakers gevraagd deroosterpatronen per besluitvormingsaspect te rangordenen op basis van huneigen visie op roosterkwaliteit. In totaal ging het om dertig rangordeningen vanmaximaal tien roosterpatronen.

Samenvatting216

De resultaten van het rangordeningsexperiment hebben aangetoond datroostermakers onderling nauwelijks verschillen in de gemaakte rangorde-ningen. Vervolgens zijn alle besluitvormingsaspecten waarbij de gegevenrangordeningen door de tien roostermakers significant overeen bleken tekomen (met een fouttolerantie van één procent) meegenomen is een operatio-nalisatie van de overeenkomstige kwaliteitsfactor. Hierbij zijn de gemiddelderangordingen vertaald naar een formule die de waarde van de kwaliteitsfactorvoor een bepaald dienstrooster weergeeft als een cijfer tussen de nul en de één.Deze operationalisaties vormen de beantwoording van de tweedeonderzoeksvraag.

BEOORDELINGSEXPERIMENT

In het beoordelingsexperiment is onderzocht of de totale roosterkwaliteitverklaard worden op basis van een gewogen sommatie van de factorwaarden(dit is de derde onderzoeksvraag). Dit is gedaan door vijf roostermakers tevragen een rapportcijfer (tussen de één en de tien) te geven aan in totaalvijftien dienstroosters op basis van hun eigen visie op roosterkwaliteit. Dezevijftien dienstroosters waren zo opgesteld dat de spreiding van de waarden vande vijf kwaliteitsfactoren statistisch gesproken ‘normaal’ was.

In de analysefase van het beoordelingsexperiment is een kleinste kwa-dratenanalyse toegepast op de gegeven kwaliteitscijfers en de factorwaarden.Het resultaat van de kleinste kwadratenanalyse leverde de gewichtsfactoren opdie de roostermakers (impliciet) hanteert bij het wegen van elk van de kwali-teitsfactoren. Middels de gevonden gewichtsfactoren bleken meer dan tachtigprocent van de gegeven kwaliteitscijfers verklaard te kunnen worden. Hieruit isgeconcludeerd dat de totale roosterkwaliteit verklaard kan op basis van eengewogen sommatie van de factorwaarden. Hierbij zijn de factorwaardengeneriek van aard (gelijk voor alle roostermakers), en zijn de gewichtsfactorenspecifiek (afhankelijk van de roostermaker).

VERROOSTERINGSEXPERIMENT

In het verroosteringsexperiment is onderzocht of ‘roosteren middels kwaliteits-

Samenvatting 217

indicatoren’ de roosterkwaliteit verbetert (dit is de vierde en laatste onder-zoeksvraag). Dit is onderzocht door een achttal roostermakers te vragen eendienstrooster voor een fictieve verpleegeenheid op te stellen. Dit opstellenvond plaats met behulp van het computerprogramma ZKR (zie appendix C voormeer informatie over dit programma). Nadat de roostermakers tevreden warenover het opgestelde dienstrooster werden zij geïnformeerd over defactorwaarden van het opstelde dienstrooster. Alle roostermakers gebruiktenvervolgens deze informatie om het oorspronkelijke rooster te wijzigen,sommigen zelfs meer dan eens.

Uit de resultaten van het verroosteringsexperiment bleek dat het infor-meren van roostermakers over de factorwaarden leidde tot een gemiddeldekwaliteitsverbetering van dertig procent. Hieruit is geconcludeerd dat ‘roos-teren middels kwaliteitsindicatoren’ de roosterkwaliteit verbetert.

CONCLUSIES

De doelstelling van dit onderzoek was het ontwikkelen van een computer-programma dat het opstellen van dienstroosters zodanig dient te ondersteunendat de resulterende dienstroosters positief zullen bijdragen aan hetfunctioneren van de verpleegeenheid. De gevolgde onderzoeksaanpak om dit tebewerkstelligen kan samengevat worden als het analyseren, operationaliserenen het toepassen van roosterkwaliteit. De analyse bestond uit een zoektochtnaar de onafhankelijke factoren van roosterkwaliteit. De operationalisatie wasgebaseerd op de gemeenschappelijkheid in de beoordeling van alternatieveroosterpatronen door roostermakers. En de toepassing liet zien datkwaliteitsindicatoren gebruikt kunnen worden om de roosterkwaliteit te ver-hogen.

Derhalve heeft dit onderzoek aangetoond dat ‘roosteren middels kwali-teitsindicatoren’ doeltreffend toegepast kan worden bij het ondersteunen vande dienstroosterplanning voor het verplegend personeel in de intramuralegezondheidszorg. Deze aanpak ondersteunt de roostermaker bij het opstellenvan dienstroosters door informatie te geven over hoe goed het opgesteldedienstrooster ‘scoort’ volgens de verschillende kwaliteitsfactoren.