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1 Copyright 2012 Health Administration Press

COMPANION WEBSITE

CHAPTER 12

Matching the supply of goods or services to the demand for those goods or services is a basic

operational problem. In a manufacturing environment, inventory can be used to respond to

fluctuations in demand. In the healthcare environment, safety stock can be used to respond to

fluctuations in demand for supplies (see Chapter 13), but it is not possible to inventory healthcare

services. Capacity, therefore, must match demand. If capacity is greater than demand, resources

are underutilized and costs are high. Idle staff, equipment, or facilities increase organizational

costs without increasing revenue. If capacity is lower than demand, patients experience long wait

times or find another provider.

To match capacity to demand, organizations can use demand-influencing strategies or

capacity management strategies. Pricing and promotions are often used to influence demand and

demand timing; however, these methods often are not a viable strategy for healthcare

organizations. In the past, many healthcare organizations used the demand-leveling strategy of

appointment scheduling; more recently, many have moved to advanced access scheduling.

Capacity management strategies allow the organization to adjust capacity to meet fluctuating

demand and use part-time employees, on-call employees, cross-training, and overtime. Effective

and efficient scheduling of patients, staff, equipment, facilities, and jobs can help match capacity

to demand and ensure that healthcare resources are used fully.

This chapter outlines issues and problems faced in scheduling and discusses tools and

techniques that can be used in scheduling patients, staff, equipment, facilities, and jobs. Here is a

breakdown of the chapters main topics:

Hospital census and resources


Staff scheduling

Job/operation scheduling and sequencing rules

Patient appointment scheduling models

Advanced access patient scheduling

The author invites readers comments, recommended readings, website suggestions, and

any other material to be added to this file or to the file for any other chapter. Please click here to

send an e-mail. Be sure to include Healthcare Operations Management, 2nd edition in the

subject line.

Downloadable Resources

PowerPoint

A PowerPoint presentation of the key points of Chapter 12 is attached to this PDF. Click on the

following icon to open/close the attachments panel:

HC Ops 2 slides - Chapter 12.ppt

Examples and Problem Data from the Text

The following file (attached to this PDF) was used to create the Riverview Clinic Urgent Care

Staffing example in the text (beginning on page 321):

C12 Staff Scheduling LP example.xls

mailto:[email protected]?subject=Healthcare%20Operations%20Management,%202nd%20edition


The following files (attached to this PDF) are available to complete the exercises in Chapter 12:

1.

C12 Problem 1 Riverview UCC LP pro

2.

C12 Problem 2 Sequencing Rules dat

Websites of Interest

Tutorials

Microsoft Excel Solverfrom Microsoft

Linear Programming Graphic Tutorialnice flash tutorial for linear programming

http://office.microsoft.com/en-us/assistance/HA011245951033.aspxhttp://www.msubillings.edu/BusinessFaculty/Harris/LP_Problem_intro.htm

Data

SunMonTueWedThuFriSat

Nurses Needed/Day5433346

Salary&Benefits/Nurse/Day:320240240240240240320

Salary&Benefits/Part-time Nurse/Day:220160160160160160220

Maximum of 2 part-time nurses

Data

PatientProcessing Time (min.)Due Time (min. from now)SlackCritical Ratio

A35470

B15190

C35440

D25320

E30380

F25340

G35450

H30420

I20230

J25340

K25340

L15200

M30410

N20230

O20280

P10130

Q1070

R15160

S20270

Information

SunMonTueWedThuFriSat

Nurses Needed/Day5433346

Salary&Benefits/Nurse/Day:320240240240240240320

Schedules set up

Daily ScheduleNumber of Employees/Day

ScheduleDays offEmployeesSunMonTueWedThuFriSatSunMonTueWedThuFriSat

ASun, Mon000111110000000

BMon, Tues010011110000000

CTues, Wed011001110000000

DWed, Thurs011100110000000

EThurs, Fri011110010000000

FFri, Sat011111000000000

GSat, Sun001111100000000

Total

Nurses Scheduled/Day:00000000

Nurses Needed/Day:543334628

Salary&Benefits/Nurse-Day:320240240240240240320

Total Salary & Benefits/Day:0000000

Salary & Benefits/Week:$0

Schedules solution



ASun, Mon100111110011111

BMon, Tues110011111001111

CTues, Wed111001111100111

DWed, Thurs111100111110011

EThurs, Fri211110012222002

FFri, Sat011111000000000

GSat, Sun001111100000000

Total





Salary & Benefits/Week:$8,080

Employees



ASun, Mon100111110011111

BMon, Tues110011111001111

CTues, Wed111001111100111

DWed, Thurs111100111110011

EThurs, Fri211110012222002

FFri, Sat011111000000000

GSat, Sun001111100000000

Total






Preference of employeesWeighted preference of employeesSchedule assigned to

EmployeeSeniority (years)Seniority factorABCDEABCDEABCDETotalPreference score

Mary50.71312452.140.711.432.863.570000000.00

Anne60.86321452.571.710.863.434.290000000.00

Susan40.57235141.141.712.860.572.290000000.00

Tom71.00324153.002.004.001.005.000000000.00

Cathy30.43345211.291.712.140.860.430000000.00

Jane20.29543211.431.140.860.570.290000000.00

Maximum7Actual:000000

Needed:11112

Employees solution



ASun, Mon100111110011111

BMon, Tues110011111001111

CTues, Wed111001111100111

DWed, Thurs111100111110011

EThurs, Fri211110012222002

FFri, Sat011111000000000

GSat, Sun001111100000000

Total






Preference of employeesWeighted preference of employeesSchedule assigned to

EmployeeSeniority (years)Seniority factorABCDEABCDEABCDETotalPreference score

Mary50.71312452.140.711.432.863.570001012.86

Anne60.86321452.571.710.863.434.290000114.29

Susan40.57235141.141.712.860.572.290010012.86

Tom71.00324153.002.004.001.005.000000115.00

Cathy30.43345211.291.712.140.860.43010001.00000000041.71

Jane20.29543211.431.140.860.570.291000011.43

Maximum7Actual:11112.000000000418.1428571435

Needed:11112

Chapter 12

Scheduling

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Scheduling and Capacity Management

Hospital census and resources

Job/operation scheduling and sequencing rules

Appointment scheduling schemes

Advanced access scheduling

Operating and market advantage

Implementing advanced access

Metrics for advanced access

*

Typical Daily Hospital Census

Hourly Census

Staff Scheduling

Optimization/mathematical programming (Chapter 6)

*

Riverview Clinic Urgent Care Staffing Using Linear Programming (LP)

Objective: Minimize salary and benefit expenses while satisfying nurses

Five consecutive days, with two days off every seven days

Schedules chosen by seniority

SunMonTuesWedThursFriSat

Nurses Needed/Day 5433346

Salary and Benefits/Nurse-Day ($/day)320240240240240240320

*

LP Problem

There are seven possible schedules (Sunday and Monday off, Monday and Tuesday off, and so forth).

Objective: minimize:

Salary and benefit expense = $320 Sun. # of nurses + $240 Mon. # of nurses + $240 Tues. # of nurses + $240 Wed. # of nurses + $240 Thurs. # of nurses + $240 Fri. # of nurses + $320 Sat. # of nurses

*

LP Problem

Subject to:

The number of nurses scheduled each day must be greater than the number of nurses needed each day.

Sun. # of nurses 5

Mon. # of nurses 4

The number of nurses assigned to each schedule must be greater than 0 and an integer.

# A (B, C, D, E, F, or G) nurses 0

# A (B, C, D, E, F, or G) nurses = integer

*

Excel Solver Setup

Minimize Salary and Benefit Expense

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Excel Solver Solution

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Excel Solver Setup

Maximize Nurse Satisfaction

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Excel Solver Solution

Maximize Nurse Satisfaction

*

Job/Operation Scheduling and Sequencing Rules

First Come, First Served (FCFS)

Earliest Due Date (EDD)

Earliest Operation Due Date (ODD)

Shortest Process Time (SPT)

Critical Ratio (CR)

*

Sequencing Rule Example

A50100

B100160

C2050

D80120

E6080

How many possible sequences for five jobs?

ProcessingDue Critical

JobTimeDateSlackRatio

*

First Come, First Served

A05050100

B50100150160

C1002017050

D17080250120

E2506031080

Average

StartProcessingCompletionDue

SequenceTimeTimeTimeDateTardiness

*

First Come, First Served

A050501000

B501001501600

C1002017050120

D17080250120130

E2506031080230

Average18696



*

Shortest Processing Time

C02020500

A2050701000

E70601308050

D1308021012090

B210100310160150

Average14858



*

Earliest Due Date

C02020500

E206080800

A805013010030

D1308021012090

E210100310160150

Average15054



*

Sequencing Rule Example

A50100100 50 = 50100/50 = 2.00

B100160160 100 = 60160/100 = 1.60

C205050 20 = 3050/20 = 2.50

D80120120 80 = 40120/80 = 1.50

E608080 60 = 2080/60 = 1.25

120 possible sequences for five jobs

ProcessingDue Critical

JobTimeDateSlackRatio

*

Slack Time Remaining

E06060800

C6020805030

D808016012040

A16050210100110

B210100310160150

Average16466



Slack for each job: A50, B60, C30, D40, E20

*

Critical Ratio

E06060800

D608014012020

B14010024016080

A24050290100190

C2902031050260

Average208110



CR for each job: A2.00, B1.60, C2.50, D1.50, E1.25

*

Summary

FCFS186963*230

SPT 148*58*3*150*

EDD 15054*3*150*

SLACK 164664150*

CR 2081104260

*Best values

AverageAverageNo. of Maximum

RuleCompletion TimeTardinessJobs TardyTardiness

*

Guidelines for Selecting a Sequencing Rule

SPT is most useful for a very busy resource.

Some jobs may never be completed.

SPT often is used with another rule.

Use EDD when only small tardiness values can be tolerated.

Use FCFS when there is excess capacity.

*

Appointment Scheduling Schemes

Purpose is to balance the competing goals of:

Maximizing resource utilization

Minimizing waiting time

Four types:

Block appointment

Individual appointment

Mixed block-individual appointment

Combinations

*

Bailey-Welch Schedule

Individual Appointment

Bailey-Welch

Time# Scheduled

0:001

0:201

0:401

1:001

1:201

Time# Scheduled

0:002

0:201

0:401

1:001

1:200

*

Appointment Scheduling Schemes

Optimal Outpatient Appointment Scheduling Tool

(must be in Slide Show mode to click on hyperlink)

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Advanced Access

Traditional scheduling systems

Long times until next appointment

High no-show rates

Double/triple bookingqueues form

Advanced access

Patients seen same day as request

Reduces no-show rate

Better continuity of care

*

Implementing Advanced Access

Obtain buy-in

Predict demand

Predict capacity

Littles law (Chapter 11)

Standardize and minimize types of visit times

Assess operations

Work down backlog

Go live

*

Advanced Access Metrics

PCP match: percentage of same-day patients who see their PCP

PCP coverage: percentage of same-day patients seen by any physician

Wait time for next appointment (or third next available appointment)

Good backlog: appointments scheduled in advance because of patient preference

Bad backlog: appointments delayed because of lack of slots

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End of Chapter 12

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OPERATIONS HEALTHCARE

MANAGEMENTs e c o n d e d i t i o n

D a n i e l B . M c L a u g h l i n a n d

J o h n R . O l s o n

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