healthcare operations management © 2008 health administration press. all rights reserved. 1

Healthcare Operations Management© 2008 Health Administration Press. All rights reserved.

1

Chapter 12

Scheduling


3

Scheduling and Capacity Management

• Staff Scheduling• Job/Operation Scheduling and Sequencing

Rules• Appointment Scheduling Schemes• Advanced Access Scheduling

– Operating and Market Advantage– Implementing Advanced Access– Metrics for Advanced Access

• Using Arena® to Model Scheduling


4

Staff Scheduling

• Optimization/mathematical programming (Chapter 6)

• Simulation (Chapter 11)


5

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

Sun Mon Tues Wed Thurs Fri Sat

Nurses Needed/Day 5 4 3 3 3 4 6Salary and Benefits/Nurse-Day ($/day)

320 240 240 240 240 240 320


6

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


7

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


8

Excel Solver SetupMinimize Salary and Benefit

Expense


9

Excel Solver Solution


10

Excel Solver SetupMaximize Nurse Satisfaction


11

Excel Solver SolutionMaximize Nurse Satisfaction


12

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)


13

Sequencing Rule Example

A 50 100

B 100 160

C 20 50

D 80 120

E 60 80

How many possible sequences for five jobs?

Processing Due CriticalJob Time Date Slack Ratio


14

First Come, First Served

A 0 50 50 100

B 50 100 150 160

C 100 20 170 50

D 170 80 250 120

E 250 60 310 80

Average

Start Processing Completion DueSequence Time Time Time Date Tardiness


15

First Come, First Served

A 0 50 50 100 0

B 50 100 150 160 0

C 100 20 170 50 120

D 170 80 250 120 130

E 250 60 310 80 230

Average 186 96



16

Shortest Processing Time

C 0 20 20 50 0

A 20 50 70 100 0

E 70 60 130 80 50

D 130 80 210 120 90

B 210 100 310 160 150

Average 148 58



17

Earliest Due Date

C 0 20 20 50 0

E 20 60 80 80 0

A 80 50 130 100 30

D 130 80 210 120 90

E 210 100 310 160 150

Average 150 54



18

Sequencing Rule Example

A 50 100 100 − 50 = 50 100/50 = 2.00B 100 160 160 − 100 = 60 160/100 = 1.60C 20 50 50 − 20 = 30 50/20 = 2.50D 80 120 120 − 80 = 40 120/80 = 1.50E 60 80 80 − 60 = 20 80/60 = 1.25

120 possible sequences for five jobs

Processing Due CriticalJob Time Date Slack Ratio


19

Slack Time Remaining

E 0 60 60 80 0

C 60 20 80 50 30

D 80 80 160 120 40

A 160 50 210 100 110

B 210 100 310 160 150

Average 164 66


Slack for each job: A—50, B—60, C—30, D—40, E—20


20

Critical Ratio (CR)

E 0 60 60 80 0

D 60 80 140 120 20

B 140 100 240 160 80

A 240 50 290 100 190

C 290 20 310 50 260

Average 208 110


CR for each job: A—2.00, B—1.60, C—2.50, D—1.50, E—1.25


21

Summary

FCFS 186 96 3* 230SPT 148* 58* 3* 150*EDD 150 54* 3* 150*SLACK 164 66 4 150*CR 208 110 4 260

*Best values

Average Average No. of MaximumRule Completion Time Tardiness Jobs Tardy Tardiness


22

Guidelines for Selecting a Sequencing Rule

1. SPT is most useful for a very busy resource.• Some jobs may never be completed.• SPT often is used with another rule.

2. Use EDD when only small tardiness values can be tolerated.

3. Use FCFS when there is excess capacity.


23

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


24

Bailey-Welch Schedule

Individual Appointment Bailey-Welch

Time # Scheduled

0:00 1

0:20 1

0:40 1

1:00 1

1:20 1

Time # Scheduled

0:00 2

0:20 1

0:40 1

1:00 1

1:20 0


25

Appointment Scheduling Schemes

Optimal Outpatient Appointment Scheduling Tool


26

Advanced Access

• Traditional scheduling systems– Long times until next appointment– High no-show rates– Double/triple booking—queues form

• Advanced access– Patients seen same day as request– Reduces no-show rate– Better continuity of care


27

Implementing Advanced Access

• Obtain buy-in• Predict demand• Predict capacity

– Little’s law (Chapter 11)– Standardize and minimize types of visit times

• Assess operations• Work down backlog• Go live


28

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 waiting because of lack of slots


29

VVH Arena Scheduling Example

Smith DemandSmith

V isit length

DemandAnderson

Billings Demand

Kumarin Demand

New Demand

treatedSmith Patients

patients treatedAnderson

treatedBillings patients

patients treatedKumarin

treatedNew patients

PatientsTotal Anderson

PatientsTotal B illings

PatientsTotal Kumarin

Dispose 1

PatientsTotal New

AndersonVisit length

B illingsV isit length

KumarinV isit length

V isit length New

PatientsTotal Smith

0

0

0

0

0

0

0

0

0

0

0

0 9 :0 0 :0 0


30

VVH Arena Scheduling—Physicians

Patient’s Primary Physician

PrimaryBackup

SecondaryBackup

TertiaryBackup

Smith Smith Anderson Billings

Billings Billings Kumarin

Anderson Anderson Billings

Kumarin Kumarin

New patient Billings Kumarin


31

VVH Scheduling—Physician Schedule

Monday Hours Tuesday Hours

Physician 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Anderson 1 1 1 1 1 1 1 1 1

Billings 1 1 1 1 1 1 1 1 1

Kumarin 1 1 1 1 1 1 1 1 1 1 1 1

Smith 1 1 1 1 1 1 1 1 1

Wednesday Hours Thursday Hours

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Anderson 1 1 1 1 1 1 1

Billings 1 1 1 1 1 1 1 1

Kumarin 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Smith 1 1 1 1 1 1

Friday

1 2 3 4 5 6 7 8 Total Weekly Hours

Anderson 1 1 1 1 20

Billings 1 1 1 1 21

Kumarin 1 1 1 1 1 1 32

Smith 15

All 88


32

VVH Scheduling Probability Distributions

Physician Arrival RateExponential Distribution

Mean (Hours)

Triangular Distribution of Service Time: Minimum, Mode, Maximum

(Hours)

Smith 1.0 0.15, 0.50, 0.80

Billings 1.2 0.10, 0.20, 0.60

Anderson 1.0 0.10, 0.20, 0.60

Kumarin 2.0 0.15, 0.50, 0.80

New patient 0.8 0.25, 0.50, 1.00


33

VVH Arena Scheduling Sub-Model

STATE(Smit h) == -1

Else

S mith available? PatientSmith sees Smith

A nderson A vailable ?

STATE(Anderson) == -1

Else

Smith patientAnderson sees

Smith patientBil l ings sees

by AndersonSmith patient seen

by SmithSmith patient seem

by Bil lingsSmith patient seen

Smith Anderson Billings Kumarin

B illings available?

STATE(Billings) == -1

Else

0

0

0


34

Baseline Results

• Dr. Smith– 33.4 patients per week– Average queue of 3.5 hours– PCP coverage ratio of 74.5 percent

• Dr. Anderson– Busy 56.5 percent of his time


35

Improvements

• Dr. Anderson moved to first choice for new patients

• Dr. Billings allocated as first backup to Dr. Smith

• Dr. Anderson and Dr. Billings increase hours slightly


36

VVH Scheduling Improved—Physicians

Patient’s Primary Physician

PrimaryBackup

SecondaryBackup

TertiaryBackup

Smith Smith Billings Anderson

Billings Billings Kumarin

Anderson Anderson Billings

Kumarin Kumarin

New patient Billings Kumarin


37

VVH Scheduling ImprovedMonday Hours Tuesday Hours

Physician 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Anderson 1 1 1 1 1 1 1 1 1 1 1

Billings 1 1 1 1 1 1 1 1 1

Kumarin 1 1 1 1 1 1 1 1 1

Smith 1 1 1 1 1 1 1 1 1

Wednesday Hours Thursday Hours

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Anderson 1 1 1 1 1 1 1 1 1

Billings 1 1 1 1 1 1 1 1

Kumarin 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Smith 1 1 1 1 1 1

Friday

1 2 3 4 5 6 7 8 Total Weekly Hours

Anderson 1 1 1 1 24

Billings 1 1 1 1 1 1 1 24

Kumarin 1 1 1 1 1 1 32

Smith 15

All 95


38

Improvement Results

• Dr. Smith sees 28.6 patients/week—decreased backlog.

• Utilization of staff is more balanced—no one is over 91 percent utilization.

• Dr. Billings now gets Friday afternoon off.

End of Chapter 12

healthcare operations management © 2008 health administration press. all rights reserved. 1

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