models and algorithms for manpower planning and ......manpower planning and personnel rostering...
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Models and Algorithms for Manpower Planning andPersonnel Rostering:
Towards An Integrated Approach
KomarudinDepartment of Business Technology and Operations
Vrije Universiteit [email protected]
Promotor: Prof. dr. Marie-Anne Guerry
February 19, 2015
Backgrounds Research motivation
Research backgrounds
Personnelplanningresearch
Over/underqualified
personnel1
Unattractiveworking
schedule2 Qualifiedpersonnelshortage3
Ageingworkforce4
1 International Labour Organization. 2014. Skills mismatch in Europe.2 New York Times. Aug. 14, 2014. Starbucks to Revise Policies to End IrregularSchedules for Its 130,000 Baristas.3 The European Commission. 2012. Employment and Social Developments in Europe2012.4 Erixon & van der Marel. 2011. What is driving the rise in health care expenditures?An inquiry into the nature and causes of the cost disease.
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Backgrounds Research motivation
Research backgrounds
Personnelplanningresearch
Over/underqualified
personnel1
Unattractiveworking
schedule2 Qualifiedpersonnelshortage3
Ageingworkforce4
ResearchLimitation
Quantitativeapproach
Focus oncorporate/
organization
1 International Labour Organization. 2014. Skills mismatch in Europe.2 New York Times. Aug. 14, 2014. Starbucks to Revise Policies to End IrregularSchedules for Its 130,000 Baristas.3 The European Commission. 2012. Employment and Social Developments in Europe2012.4 Erixon & van der Marel. 2011. What is driving the rise in health care expenditures?An inquiry into the nature and causes of the cost disease.
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Overview
Overview of Our Work
Manpower Planningand
Personnel Rostering
PersonnelRostering
individualfairness
(Chap. 6)
Manpowerplanning
StochasticModel
(Chap. 5)
Balancingthreecriteria
(Chap. 4)
Integratedmodel
Optimizationapproach(Chap. 3)
Three-stepevaluation(Chap. 2)
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Introduction Manpower planning
Manpower planning
Manpower planning
aims to meet medium-to-long term human resource requirements
involves personnel supply-and-demand prediction
controls recruitments, personnel transition and wastage (depending on thechosen strategy)
Hospital
90 30 652015Personnelstructure
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Introduction Manpower planning
Manpower planning
Manpower planning
aims to meet medium-to-long term human resource requirements
involves personnel supply-and-demand prediction
controls recruitments, personnel transition and wastage (depending on thechosen strategy)
Hospital
90 30 652015Personnelstructure
2016
t + ..
95 35 75
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Introduction Manpower planning
Manpower planning
Manpower planning
aims to meet medium-to-long term human resource requirements
involves personnel supply-and-demand prediction
controls recruitments, personnel transition and wastage (depending on thechosen strategy)
Hospital
90 30 652015Personnelstructure
2016
t + ..
95 35 75
Recruitment
Wastage
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Introduction Personnel Rostering
Personnel rostering
Personnel rostering
short term planning to allocate personnel into shifts
involves coverage requirements, legal and personal constraints
aims to meet coverage requirements and avoid unattractive rosters.
Feb.2015 CoverageReqs.
Resttime
AbsenceRequest
PersonnelContract
ConsecutiveShift
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Introduction Personnel Rostering
Personnel rostering - Illustration
Nurse February 2015 Score1 2 3 4 5 6 7 . . . 28
. . .
Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4
3 2 2 2 2 3 2 3Score
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Introduction Personnel Rostering
Personnel rostering - Illustration
Nurse February 2015 Score1 2 3 4 5 6 7 . . . 28
. . .
Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4
3 2 2 2 2 3 2 3Score
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Introduction Personnel Rostering
Personnel rostering - Illustration
Nurse February 2015 Score1 2 3 4 5 6 7 . . . 28
. . .
Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4
3 2 2 2 2 3 2 3
Score
Over/UnderCoveraged
AbsenceRequest
UnattractiveRoster
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Integrated model (Chaps. 2 & 3)
Integrated model (Chaps. 2 & 3)
Manpower Planningand
Personnel Rostering
PersonnelRostering
individualfairness
(Chap. 6)
Manpowerplanning
StochasticModel
(Chap. 5)
Balancingthreecriteria
(Chap. 4)
Integratedmodel
Optimizationapproach(Chap. 3)
Three-stepevaluation(Chap. 2)
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Integrated model (Chaps. 2 & 3) Motivation and Contribution
Challenges and Motivation
Personnel Planning
Personnel supply-demand projection
t
demand
Manpowerplanning
Personnelrostering
Dept.1 Dept.2 Dept.3
Conductedsequentially
Different timeframe
Potentially producepoor results
Our motivation:provide feedbacks
90 30 652015
2016 95 35 75
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Integrated model (Chaps. 2 & 3) Motivation and Contribution
Challenges and Motivation
Personnel Planning
Personnel supply-demand projection
t
demand
Manpowerplanning
Personnelrostering
Dept.1 Dept.2 Dept.3
Poor rosters
Conductedsequentially
Different timeframe
Potentially producepoor results
Our motivation:provide feedbacks
90 30 652015
2016 95 35 75
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Integrated model (Chaps. 2 & 3) Motivation and Contribution
Challenges and Motivation
Personnel Planning
Personnel supply-demand projection
t
demand
Manpowerplanning
Personnelrostering
Dept.1 Dept.2 Dept.3
Poor rosters
feedback
Conductedsequentially
Different timeframe
Potentially producepoor results
Our motivation:provide feedbacks
90 30 652015
2016 95 35 75
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Integrated model (Chaps. 2 & 3) Motivation and Contribution
Contributions
The State-of-The-Art:
No Approach References Review1 Sequential plan-
ningAbernathy et al. (1973);Ozcan (2009)
Suboptimal solu-tions
2 Integratedstaffing androstering
Mundschenk and Drexl(2007); Belien et al. (2012)
Constraints arerather limited; Lesspersonalized rosters
3 Part-time/Annualizedpersonnel
Bard and Purnomo (2006);Corominas and Pastor(2010)
Only temporary so-lution
4 Staff allocation Haspeslagh (2012); Maen-hout and Vanhoucke (2013)
Focus only on staffallocation
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Integrated model (Chaps. 2 & 3) Motivation and Contribution
Contributions
The State-of-The-Art:
No Approach References Review1 Sequential plan-
ningAbernathy et al. (1973);Ozcan (2009)
Suboptimal solu-tions
2 Integratedstaffing androstering
Mundschenk and Drexl(2007); Belien et al. (2012)
Constraints arerather limited; Lesspersonalized rosters
3 Part-time/Annualizedpersonnel
Bard and Purnomo (2006);Corominas and Pastor(2010)
Only temporary so-lution
4 Staff allocation Haspeslagh (2012); Maen-hout and Vanhoucke (2013)
Focus only on staffallocation
Our Contributions:
Three-step approach for limited personnel structure modification.
Optimization approach for arbitrary personnel structure modification.
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Integrated model (Chaps. 2 & 3) Three-step approach
Three-step approach (Chap. 2)
Step 1. Consistency check
Compare the required and the available resources
Disregard many rostering constraints
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Integrated model (Chaps. 2 & 3) Three-step approach
Three-step approach (Chap. 2)
Step 1. Consistency check
Compare the required and the available resources
Disregard many rostering constraints
Step 2. Quality evaluation of the current personnelstructure
Solve the rostering problems
Identify which personnel group inappropriate
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Integrated model (Chaps. 2 & 3) Three-step approach
Three-step approach (Chap. 2)
Step 1. Consistency check
Compare the required and the available resources
Disregard many rostering constraints
Step 2. Quality evaluation of the current personnelstructure
Solve the rostering problems
Identify which personnel group inappropriate
Step 3. Quality evaluation of the neighboring personnelstructures
Small modification to the personnel structure
Evaluate the roster qualities
Currentpersonnel-structure
Neighbor 2Neighbor 1 Neighbor 3
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Integrated model (Chaps. 2 & 3) Optimization approach (Chap. 3)
Optimization approach (Chap. 3)
Response surface meth. (RSM)
Sampling the neighborhood of thecurrent solution
Perform regression analysis to findnew direction
Newsolution
Neighborhoodsampling
Regression
Initialsolution
generate
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Integrated model (Chaps. 2 & 3) Optimization approach (Chap. 3)
Optimization approach (Chap. 3)
Response surface meth. (RSM)
Sampling the neighborhood of thecurrent solution
Perform regression analysis to findnew direction
Simulated Annealing (SA)
Local search to generateneighboring solutions
Move to the best neighboringsolution with a certain probability
Newsolution
Neighborhoodsampling
Regression
Initialsolution
generate
Currentsolution
Localsearch
Accept withSA criteria
Initialsolution
move to
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Integrated model (Chaps. 2 & 3) Case study
Case studies
The data set originating from real-world nurse rostering problems is takenfrom Bilgin et al. (2012).
The three-step approach is provided for the Emergency ward only
No Ward Abbr. k∑
FTE qvT s0 ,T
s1(R(n))
1 Emergency Em 8 26.25 17,3092 Geriatrics Gr 8 17.06 11,4233 Meal Preparations MP 8 16.84 13,2234 Psychiatry Ps 9 16.50 8,7335 Reception Re 9 13.75 14,4476 Palliative Care PC 20 21.70 130,579
k : Number of subgroups∑FTE : The current total of full time equivalent in the ward
qvT s0 ,T
s1(R(n)) : The value of the roster quality (the smaller the better)
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Integrated model (Chaps. 2 & 3) Case study
Case study results (three-step approach)
Step 1. Consistency check
Subgroup: 1 2 3 4
Ratio: 0.95 0.85 0.85 0.85
Step 2. Quality evaluation of the current personnelstructure
Coverage constraint:Skill type 1: 1.6%Skill type 3: 2.2%
Skill type 4: 80.1%Counter constraint: 10.2%Series constraint: 2.9%
Ratio =Required resourcesAvailable resources
Proportion of thetotal weighted con-
straint violations
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Integrated model (Chaps. 2 & 3) Case study
Case study results (three-step approach)
Step 1. Consistency check
Subgroup: 1 2 3 4
Ratio: 0.95 0.85 0.85 0.85
Step 2. Quality evaluation of the current personnelstructure
Coverage constraint:Skill type 1: 1.6%Skill type 3: 2.2%
Skill type 4: 80.1%Counter constraint: 10.2%Series constraint: 2.9%
Ratio =Required resourcesAvailable resources
Reasonable, some slackfor vacation/illness
Proportion of thetotal weighted con-
straint violations
Skill 4 understaffed
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Integrated model (Chaps. 2 & 3) Case study
Step 3. Quality evaluation of the neighboring personnel structures
Increase the number of nurses with skill type 2, 3 or 4.
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Integrated model (Chaps. 2 & 3) Case study
Optimization approach (RSM & SA)
No Ward∑
FTE RSM SA
qvT s0 ,T
s1(R(n)) ratio ¯∑
FTE qvT s0 ,T
s1(R(n)) ratio ¯∑
FTE
1 Em 26.25 13,176 76.13% 29.20 13,301 76.85% 29.35
2 Gr 17.06 4,508 39.47% 15.05 3,728 32.64% 15.35
3 MP 16.84 4,436 33.54% 15.05 3,949 29.86% 15.33
4 Ps 16.50 5,182 59.34% 14.35 4,060 46.49% 14.20
5 Re 13.75 9,750 67.49% 14.65 10,212 70.69% 14.45
6 PC 21.7 50,583 38.74% 17.42 20,111 15.40% 15.85
Small modification on the total FTE can lead to a better roster quality
SA performs slightly better
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Manpower planning (Chaps. 4 & 5)
Overview Chapters 4 & 5
Manpower Planningand
Personnel Rostering
PersonnelRostering
individualfairness
(Chap. 6)
Manpowerplanning
StochasticModel
(Chap. 5)
Balancingthreecriteria
(Chap. 4)
Integratedmodel
Optimizationapproach(Chap. 3)
Three-stepevaluation(Chap. 2)
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Manpower planning (Chaps. 4 & 5)
Challenge and motivations
What if the desiredpersonnel structure isdifficult to reach?
How we ensure that thepromotion policy does notharm the personnelmotivation?
How we deal withuncertainties?
90 30 652015
2016
t + ..
95 35 75
Recruitment
Wastage
Motivation: develop models andalgorithms for manpower planning problems
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Manpower planning (Chaps. 4 & 5)
Contributions
The State-of-The-Art:
The degree of desirability and the degree of attainability have beenintroduced in Guerry (1999); De Feyter and Guerry (2009)
Previous approaches use an unrestricted promotion strategy that can lead topersonnel dissatisfaction (Song and Huang, 2008; Nilakantan et al., 2011)
No method has been proposed to find the most beneficial manpower planningpolicy with stochastic wastage (Davies, 1982; Guerry, 1993)
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Manpower planning (Chaps. 4 & 5)
Contributions
The State-of-The-Art:
The degree of desirability and the degree of attainability have beenintroduced in Guerry (1999); De Feyter and Guerry (2009)
Previous approaches use an unrestricted promotion strategy that can lead topersonnel dissatisfaction (Song and Huang, 2008; Nilakantan et al., 2011)
No method has been proposed to find the most beneficial manpower planningpolicy with stochastic wastage (Davies, 1982; Guerry, 1993)
Our contributions
Introduce MIP models for manpower planning problems that include thepromotion steadiness degree (Chap. 4 & 5)
Introduce a stochastic optimization problem and its complexity analysis todeal with wastage uncertainties (Chap. 5)
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Manpower planning (Chaps. 4 & 5) MP with three criteria - Chap. 4
Manpower planning with three criteria (Chap. 4)
Optimizing three criteria
The degree of attainabilityαni (t)(si ) =
0, if si < sLL,i or si > sUL,isi−sLL,i
ni (t)−sLL,i , if sLL,i ≤ si ≤ ni (t)si−sUL,i
ni (t)−sUL,i , if ni (t) ≤ si ≤ sUL,i
The degree of desirability βi (ni (t))
The degree of promotion steadinessγij(fij(t − 1, t))
Difference between n(t)and the attainable set
Difference betweenn(t) and the desiredpersonnel structure
Difference between thepersonnel transition and the’common’ promotion policy
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Manpower planning (Chaps. 4 & 5) MP with three criteria - Chap. 4
The model of Chap. 4
Optimizing three criteria
Mixed integer nonlinear program (MINLP)
Piecewise linear approximation (PLA) to handle nonlinearity
The model is solved using an iterated PLA
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Manpower planning (Chaps. 4 & 5) MP with three criteria - Chap. 4
The model of Chap. 4
Optimizing three criteria
Mixed integer nonlinear program (MINLP)
Piecewise linear approximation (PLA) to handle nonlinearity
The model is solved using an iterated PLA
Set lower &upper bounds
Increase #segments
Solve PLA model
Low ac-curacy?
Yes
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Manpower planning (Chaps. 4 & 5) MP with three criteria - Chap. 4
Experiments for model of Chap. 4
PLA IPLANo Problem k κ aComp. time κ aComp. time1 P03 3 0.633 2.67 0.633 1.092 P04 4 0.547 15.57 0.547 11.043 P05 5 0.111 11.64 0.111 1.134 P10 10 0.466 18.45 0.466 1.765 P11 11 0.627 20.00 0.627 20.556 P12 12 0.601 b3600.00 0.601 13.507 P20 20 c 0.307 3601.778 P25 25 c 0.000 32.579 P30 30 c 0.184 2.74
aIn secondsbSolver is terminated after 1 hourcSolver terminates: out of memory without encountering a feasible solution
κ: the overall objective function value
with similar value of κ, IPLA model is more efficient than the PLA
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Manpower planning (Chaps. 4 & 5) MP with stochastic wastage - Chap. 5
Manpower planning with stochastic wastage (Chap. 5)
Optimizing partially stochastic system
The degree of desirability
The degree of promotion steadiness
wastage is considered stochastic, following aprobability distribution
Difference betweenn(t) and the desiredpersonnel structure
Difference between thepersonnel transition and the’common’ promotion policy
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Manpower planning (Chaps. 4 & 5) MP with stochastic wastage - Chap. 5
Partially stochastic system
The stochastic wastage is modeled using a finite number of scenarios
The MIP model is solved using a MIP solver
The problem is proved to be NP-hard based on reduction from 3-SAT
Case study with 3 subgroups
Using the deterministic case w = w, then the result is tested under stochasticcase w, the overall degree κ = 0.78099.
Using the stochastic case wi with 1000 scenarios, the overall degreeκ = 0.8019
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Personnel rostering (Chapter 6)
Overview Chapter 6
Manpower Planningand
Personnel Rostering
PersonnelRostering
individualfairness
(Chap. 6)
Manpowerplanning
StochasticModel
(Chap. 5)
Balancingthreecriteria
(Chap. 4)
Integratedmodel
Optimizationapproach(Chap. 3)
Three-stepevaluation(Chap. 2)
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Personnel rostering (Chapter 6) Motivation and Contribution
Challenges and Motivation
Nurse February 2015 Score1 2 3 4 5 6 7 . . . 28
. . .
Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4
3 2 2 2 2 3 2 3
Score
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Personnel rostering (Chapter 6) Motivation and Contribution
Challenges and Motivation
Nurse February 2015 Score1 2 3 4 5 6 7 . . . 28
. . .
Cov. 4 4 4 5 5 5 4 4Req. 5 4 4 4 4 5 5 4
3 2 2 2 2 3 2 3
ScoreLow individual
fairness
Motivation:incorporate fairness in personnel rostering model
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Personnel rostering (Chapter 6) Motivation and Contribution
Contributions
The State-of-The-Art:
Approach ReviewThe maximum and the range (Stolletzand Brunner, 2012; Smet et al., 2012)
Neglect most of theindividual penalties
The absolute deviation and thesquared deviation (Pesant and Regin,2005; Smet et al., 2012)
Tends to level all in-dividual penalties
The sum of squared (Martin et al.,2013),
Positive trade-off isnot always preferred
Jain’s index (Martin et al., 2013). Tends to increase in-dividual penalties
Nurse Score
. . .
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Personnel rostering (Chapter 6) Motivation and Contribution
Contributions
The State-of-The-Art:
Approach ReviewThe maximum and the range (Stolletzand Brunner, 2012; Smet et al., 2012)
Neglect most of theindividual penalties
The absolute deviation and thesquared deviation (Pesant and Regin,2005; Smet et al., 2012)
Tends to level all in-dividual penalties
The sum of squared (Martin et al.,2013),
Positive trade-off isnot always preferred
Jain’s index (Martin et al., 2013). Tends to increase in-dividual penalties
Nurse Score
. . .
Our Contribution is the lexicographic objective function:
Minimize all individual penalties
maximize fairness by allowing positive trade-off.
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Personnel rostering (Chapter 6) Motivation and Contribution
Improving fairness
Minimizing the lexicographic objective function
PLexi is defined as a permutation of all individual penalties, sorted in anon-increasing order.
PLexi = (P ′H,1,P′H,2, ..,P
′H,n) s.t. P ′H,1 ≥ P ′H,2 ≥ ... ≥ P ′H,n
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Personnel rostering (Chapter 6) Motivation and Contribution
Experiments for lexicographic objective function
TP-PLexi generally produces vectors PLexi that are lexicographically smallerthan the ones produced by other approaches
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Conclusions & Future Work
Conclusions & Future Work
Conclusions
The models and algorithms presented are able to improve thepersonnel planning process
The models and algorithms are beneficial in improving thepersonnel motivation by:
Providing sufficient personnel with the right personnel-mix(Integrated model)Ensuring the career progression expectation (manpowerplanning model)Fair working schedule (personnel rostering model)
Future research
multi-level and multi-scale integrated personnel planning
global optimization approach
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Conclusions & Future Work
Thank you for your attention!
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Bibliography
References I
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(BUTO) Integrated Manpower Planning & Personnel Rostering February 19, 2015 31 / 34
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References III
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References IV
Pieter Smet, Simon Martin, Djamila Ouelhadj, Ender Ozcan, and Greet VandenBerghe. Investigation of fairness measures for nurse rostering. In theInternational Conference on the Practice and Theory of Timetabling (PATAT2012), pages 369–372, 2012.
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