1. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 1

2. Chapter 12 Scheduling

3. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 4 Staff Scheduling Optimization/mathematical programming (Chapter 6) Simulation (Chapter 11)

5. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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 SunMonTuesWedThursFriSat Nurses Needed/Day 5433346 Salary and Benefits/Nurse-Day ($/day) 320240 320

6. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 8 Excel  Solver Setup Minimize Salary and Benefit Expense

9. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 9 Excel  Solver Solution

10. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 10 Excel  Solver Setup Maximize Nurse Satisfaction

11. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 11 Excel  Solver Solution Maximize Nurse Satisfaction

12. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 13 Sequencing Rule Example A50100 B100160 C2050 D80120 E6080 How many possible sequences for five jobs? ProcessingDue Critical JobTimeDateSlackRatio

14. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 14 First Come, First Served A05050100 B50100150160 C1002017050 D17080250120 E2506031080 Average StartProcessingCompletionDue SequenceTimeTimeTimeDateTardiness

15. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 15 First Come, First Served A050501000 B501001501600 C1002017050120 D17080250120130 E2506031080230 Average18696 StartProcessingCompletionDue SequenceTimeTimeTimeDateTardiness

16. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 16 Shortest Processing Time C02020500 A2050701000 E70601308050 D1308021012090 B210100310160150 Average14858 StartProcessingCompletionDue SequenceTimeTimeTimeDateTardiness

17. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 17 Earliest Due Date C02020500 E206080800 A805013010030 D1308021012090 E210100310160150 Average15054 StartProcessingCompletionDue SequenceTimeTimeTimeDateTardiness

18. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 18 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

19. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 19 Slack Time Remaining E06060800 C6020805030 D808016012040 A16050210100110 B210100310160150 Average16466 StartProcessingCompletionDue SequenceTimeTimeTimeDateTardiness Slack for each job: A—50, B—60, C—30, D—40, E—20

20. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 20 Critical Ratio (CR) E06060800 D608014012020 B14010024016080 A24050290100190 C2902031050260 Average208110 StartProcessingCompletionDue SequenceTimeTimeTimeDateTardiness CR for each job: A—2.00, B—1.60, C—2.50, D—1.50, E—1.25

21. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 21 Summary FCFS186963*230 SPT 148*58*3*150* EDD 15054*3*150* SLACK 164664150* CR 2081104260 *Best values AverageAverageNo. of Maximum RuleCompletion TimeTardinessJobs TardyTardiness

22. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 24 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

25. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 25 Appointment Scheduling Schemes Optimal Outpatient Appointment Scheduling Tool

26. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 29 VVH Arena Scheduling Example

30. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 30 VVH Arena Scheduling—Physicians Patient’s Primary Physician Primary Backup Secondary Backup Tertiary Backup Smith AndersonBillings Kumarin Anderson Billings Kumarin New patientBillingsKumarin

31. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 31 VVH Scheduling—Physician Schedule Monday HoursTuesday Hours Physician1234567812345678 Anderson111111111 Billings111111111 Kumarin111111111111 Smith111111111 Wednesday HoursThursday Hours 12345678123456 78 Anderson11111 11 Billings11111111 Kumarin111111111111 11 Smith111111 Friday 12345678Total Weekly Hours Anderson111120 Billings111121 Kumarin11111132 Smith15 All88

32. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 32 VVH Scheduling Probability Distributions PhysicianArrival Rate Exponential Distribution Mean (Hours) Triangular Distribution of Service Time: Minimum, Mode, Maximum (Hours) Smith1.00.15, 0.50, 0.80 Billings1.20.10, 0.20, 0.60 Anderson1.00.10, 0.20, 0.60 Kumarin2.00.15, 0.50, 0.80 New patient0.80.25, 0.50, 1.00

33. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 33 VVH Arena Scheduling Sub-Model

34. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 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. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 36 VVH Scheduling Improved— Physicians Patient’s Primary Physician Primary Backup Secondary Backup Tertiary Backup Smith BillingsAnderson Billings Kumarin Anderson Billings Kumarin New patientBillingsKumarin

37. Healthcare Operations Management © 2008 Health Administration Press. All rights reserved. 37 VVH Scheduling Improved Monday HoursTuesday Hours Physician1234567812345678 Anderson 1 1 1 1 1 111111 Billings111111111 Kumarin1 1 1 111111 Smith111111111 Wednesday HoursThursday Hours 12345678123456 78 Anderson111 1 1 11 11 Billings11111111 Kumarin111111111111 11 Smith111111 Friday 12345678Total Weekly Hours Anderson111124 Billings1111 1 1 1 24 Kumarin11111132 Smith15 All95

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

39. End of Chapter 12