1. Scheduling Staff, Patients, and Jobs
Chapter 9

2. Outline Learning Objectives What Are the Threats to Timely Care?
Consequences of Care Delays
Staff Scheduling
Job Scheduling
Patient Appointment Scheduling
Summary
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.2

3. Figure 9.1- Mind Map for Delivery With Scheduling
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.3

4. Learning Objectives
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.4

5. After reading the chapter, you will be able to:
Determine the major causes of care delays and waits
Identify the outcomes of excessive waits and delays
Establish staffing schedules using linear programming
Use job scheduling rules to speed up the flow of jobs through a process
Understand and evaluate various approaches to patient appointment scheduling
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.5

6. What Are the Threats to Timely Care?
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.6

7. Phoenix VA Health Care System
2014 Investigation
Thousands of veterans have been waiting to see doctors
40 dead
While on the electronic waiting list
Severe understaffing
Unable to process the test results

8. Access Varies across geographic location
2014 survey
Average appointment waiting time to see
primary care physician
Boston: 66 days
Dallas: 5 days
Cardiologist: 16.8 days
Orthopedic: 9.9 days
Accept Medicaid
Cardiologist: 63%
Dermatologist: 27%
Atlanta: 90%
Minneapolis: 7%

9. Threats to Timely Care Capacity is inaccurately defined as
Reasons why many scheduling systems fall short of meeting patients’ needs and expectations
Superficial examination of variations in capacity and demand
Capacity is inaccurately defined as
the number of slots available (每天、每週)
should include additional resources
Alternative clinicians
大聯盟 (MLB)、大學聯賽 (NCAA)、local clubs
Backup arrangements with other clinics 轉診
Telemedicine
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.7

10. Demand is inaccurately defined as should includes
number of filled appointment slots (每天、每週)
should includes
Number of calls for appointment
Walk-ins
Emergencies
Follow-up appointments
追求者眾，卻不自知

11. Threats to Timely Care Demand in primary care setting
Provider-centered systems misaligned with patients’ needs
Scheduling systems should accommodate patients’ needs rather than providers’ convenience
Demand in primary care setting
Early in the morning
Evening following work hours
Mondays
Winter months
Providers do not plan for rather than react to demand changes

12. Threats to Timely Care Shortage of clinical staff (understaff)
25% calls do not require an on-site visits
Failing to exploit resources
Physicians
Non-physician clinicians
Redefine responsibilities among various providers
Inefficient process design with disrupted flows
Fragmented care with uncoordinated handoffs

13. Consequences of Care Delays
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.8

14. Consequence of Care Delays
Lower quality patient experience of care
When patients are unable to make timely appointments, they seeks alternative forms of treatment or forgo healthcare
Higher cost
Lower or no insurance reimbursement for noncovered forms of care
or when patients are forced to see an out-of-network provider
Patient dissatisfaction
Results from long delays in getting appointments
Increase in no-shows
Loss of revenue for providers due to no-shows
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.9

15. Staff Scheduling Definition Integer linear programming
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.10

16. Staff Scheduling
Involves assignment of personnel in various departments and time slots such as shifts
Fairly complex process
Numerous software packages available
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.11

17. Integer Linear Programming
Will generate optimal schedules in simple cases
Example
The nurse manager is preparing the schedule for Friday
Part-time nurses work 4-hour shifts and are paid $100/shift
Full-time nurses work 8-hour shifts and are paid $330/shift
The number of full-time nurses should exceed or be equal to the number of part-time nurses
There should be at least three full-time nurses in each time period
The objective is to meet capacity needs at the lowest possible cost
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.12

18. Integer Linear Programming (cont.)
Staffing requirements are shown below
TABLE 9.1 – Staffing Requirements at Orthopedics Department
Time Period
Required Number of Nurses
8:00 a.m.–12:00 p.m. 8
12:00–4:00 p.m. 12
4:00–8:00 p.m. 16
8:00 p.m.–12:00 a.m. 10
12:00–4:00 a.m. 6
4:00–8:00 a.m. 5
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.13

19. Integer Linear Programming (cont.)
Decision variables
FNi = number of full-time nurses starting in period i (i = 1-6)
PNi = number of part-time nurses starting in period i (i = 1-6)
Objective function
Minimize: Cost = 330 FN FN FN FN FN FN PN PN PN PN PN PN6
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.14

20. Integer Linear Programming (cont.)
First set of constraints
FN1 + FN6 + PN1 ≥ 8 (the number of full-time nurses [who started their shift at 8:00 a.m.
who started their shift at 4:00 a.m.]
+ the number of part-time nurses who started their shift at 8:00 a.m.)
FN1 + FN2 + PN2 ≥ 12 (capacity requirement for nurses working from 12:00 to 4:00 p.m.)
FN2 + FN3 + PN3 ≥ 16 (capacity requirement for nurses working from 4:00 to 8:00 p.m.)
FN3 + FN4 + PN4 ≥ 10 (capacity requirement for nurses working from 8:00 p.m. to 12:00 a.m.)
FN4 + FN5 + PN5 ≥ 6 (capacity requirement for nurses working from 12:00 to 4:00 a.m.)
FN5 + FN6 + PN6 ≥ 5 (capacity requirement for nurses working from 4:00 to 8:00 a.m.)
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.15

21. Integer Linear Programming (cont.)
Second set of constraints
FN1 ≥ 3 (the number of full-time nurses must be 3 or more in a given time period)
FN2 ≥ 3
FN3 ≥ 3
FN4 ≥ 3
FN5 ≥ 3
FN6 ≥ 3
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.16

22. Integer Linear Programming (cont.)
Third set of constraints
FN1 + FN6 ≥ PN1 (the number of full-time nurses must be greater than
or equal to the number of part-time nurses)
FN1 + FN2 ≥ PN2
FN2 + FN3 ≥ PN3
FN3 + FN4 ≥ PN4
FN4 + FN5 ≥ PN5
FN5 + FN6 ≥ PN6
Logical constraints
FNi, PNi ≥ 0 and integer (i= 1–6)
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.17

23. Figure 9.2 – Excel Solution for Nurse Scheduling Problem
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.18

24. Job Scheduling
Sequencing rules (Fcfs, Spt, Edd, Str, Cr, Rush, Moore’s algorithm)
Performance measures
Example
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.19

25. Job Sequencing Rules Sequencing rules
Tactic used to sequence a series of jobs for processing
Heuristics (rules of thumb) 經驗法則
Solve problems quickly
Do Not guarantee an optimal solution
Sequencing rules
First come, first served (FCFS) 先進先出
Jobs are processed in their order of arrival into the system
Fair system

26. Shortest processing time (SPT) 最短作業時間
Jobs are processed according to the time it takes to complete them, starting with the job that takes the least amount of time to perform
作業時間長的工作，永遠都在排隊 (爹不疼、娘不愛)
等待時間超過 [一小時 / 一天 / …] 就進入作業
Earliest due date (EDD) 最早到期 (完工) 日
Jobs are processed according to their due date, with the job having the earliest due date being processed first
短工時、完工日期久遠的工作，會排對排很久

27. Slack time remaining (STR) 餘裕時間
Jobs with the least slack time are processed first
避免大訂單 (需大量作業時間)、交期久遠的工作，被拖延

28. Critical ratio (CR) 時間急迫度
Priority is given to the job with the lowest critical ratio
準時完工機率較低者，先做
IF CR = 1, 擁有剛好能準時完成工作的作業時間
IF CR > 1, 擁有超過能準時完成工作的作業時間
IF CR < 1, 擁有不足以準時完成工作的作業時間

29. Rush
緊急者優先 (急診)
重要顧客優先 (金卡、銀卡)
容易造成作業中斷
非優先作業永遠排隊

30. Performance Measures Makespan: 完工總時間 Tardiness: 完工逾時
total time required to complete a set of jobs
Tardiness: 完工逾時
amount of time by which the completion time exceeds the due date
Weighted tardiness: 權重式完工逾時
product of the weight assigned to a job and its tardiness
Number of tardy jobs 完工逾時件數
Flow time: 流程總時間
total time a job spends in the system 顧客停留在系統中的時間
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.21

31. Example Table 9.2 - Assigned Jobs at BPH Lab Job Arrival Time
Processing Time (min)
Due Date/Time (min)
Importance Weight
(1–20)
Slack Time
Critical Ratio A 20 5 1 B 10 15 14
1.5 C 30 50 8
1.67 D 12
2.0 E 40 6 28
3.33
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.22

32. Example (cont.) Table 9.3 – Schedule with FCFS Job Sequence Start Time
Proc. Time
End Time/Flow Time
Due Date
Tardiness
Weighted Tardiness
Tardy?
(Yes/No) A 20 No B 10 30 15
210
Yes C 60 50 80 D 75 45
540 E 12 87 40 47
282
Total
272 min
117 min
1,112 min
4 jobs
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.23

33. Example (cont.) Table 9.4 – Schedule with SPT Job Sequence Start Time
Proc. Time
End Time/Flow Time
Due Date
Tardiness
Weighted Tardiness
Tardy?
(Yes/No) B 10 15 No E 12 22 40 D 37 30 7 84
Yes A 20 57
185 C 87 50
296
Total
213 min
81 min
565 min
3 jobs
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.24

34. Example (cont.) Table 9.5 – Schedule with EDD Job Sequence Start Time
Proc. Time
End Time/Flow Time
Due Date
Tardiness
Weighted Tardiness
Tardy?
(Yes/No) B 10 15 No A 20 30 50
Yes D 45
180 E 12 57 40 17
102 C 87 37
296
Total
229 min
79 min
628 min
4 jobs
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.25

35. Example (cont.)
A B D C E
STR = (Due date – Today’s date) – Processing time
Job
Arrival Time
Processing Time (min)
Due Date/Time (min)
Importance Weight
(1–20)
Slack Time
Critical Ratio A 20 5 1 B 10 15 14
1.5 C 30 50 8
1.67 D 12
2.0 E 40 6 28
3.33
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.26

36. Example (cont.) Table 9.6 – Schedule with STR Job Sequence Start Time
Proc. Time
End Time/Flow Time
Due Date
Tardiness
Weighted Tardiness
Tardy?
(Yes/No) A 20 No B 10 30 15
210
Yes D 45
180 C 75 50 25
200 E 12 87 40 47
282
Total
257 min
102 min
872 min
4 jobs
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.26

37. Example (cont.)
A has the lowest CR (Table 9.2). It will be assigned first
Job
Arrival Time
Processing Time (min)
Due Date/Time (min)
Importance Weight
(1–20)
Slack Time
Critical Ratio A 20 5 1 B 10 15 14
1.5 C 30 50 8
1.67 D 12
2.0 E 40 6 28
3.33
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.27

38. Example (cont.) Table 9.7(a) – Schedule with CR; A was assigned
Job Sequence
Proc. Time
Due Date CR A — B 10 15
(15−20)/10 = −0.5 * C 30 50
(50−20)/30 = 1 D
(30−20)/15 = 0.67 E 12 40
(40−20)/12 = 1.67
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.28

39. Example (cont.) Table 9.7(b) – Schedule with CR; B was assigned
Job Sequence
Proc. Time
Due Date CR A — B C 30 50
(50−30)/30 = 0.67 D 15
(30−30)/15 = 0* E 12 40
(40−30)/12 = 0.83
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.29

40. Example (cont.) Table 9.7(c) – Schedule with CR; D was assigned
Job Sequence
Proc. Time
Due Date CR A — B C 30 50
(50−45)/30 = 0.17 D E 12 40
(40−45)/12 = −0.42*
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.30

41. Example (cont.) Table 9.7(d) – Schedule with CR Job Sequence
Start Time
Proc. Time
End Time/Flow time
Due Date
Tardiness
Weighted Tardiness
Tardy?
(Yes/No) A 20 No B 10 30 15
210
Yes D 45
180 E 12 57 40 17
102 C 87 50 37
296
Total
239 min
84 min
788 min
4 jobs
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.31

42. Patient Appointment Scheduling
Types of scheduling systems
ambulatory care
Inpatient and emergency care
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.35

43. Types of Scheduling Systems
Block scheduling
Common for surgery cases—surgeons are assigned blocks of time in the OR for their cases
Modified block scheduling
A small number of patients are assigned to short time blocks
Individual scheduling
A single patient is scheduled at a particular time on a specific day according to the providers’ availability
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.36

44. Ambulatory Care 門診掛號
Kaandorp and Koole’s (2007) optimal outpatient appointment scheduling model (calculator.gerkoole.com/appointment-scheduler/) 
Time available is divided into time intervals of equal length
(20分鐘、30分鐘 ‧‧‧)
Objectives of the schedule:
minimize the weighted average
patients’ wait times,
providers’ idle time, and
tardiness
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.37

45. Alpha reflects the importance of the performance measure in the optimization function
patients’ wait times,
providers’ idle time, and
tardiness
The percentage of no-shows based on historical data can also be inputted

46. αw = 0.5
αw = 1.0
αw = 2.0
αw = 10.0

47. Figure 9.3 – Appointment Schedule for Dr. Baker’s Patients
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.38

48. 一天看診 6小時，分為 12 時段 (每診 30分鐘)，兩個不同預約方式之比較

49. Ambulatory Care (cont.)
Open access scheduling
(Advanced access or Same-day scheduling)
Patient-centered system
Principles
Gain capacity by doing all of today’s work today
今日事、今日畢
供、需必須先平衡
Trim the backlog or appointment debt
Current backlog = All future appointments on the schedule
回診 (不是積壓門診)
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.39

50. Simplify the system with fewer appointment types
Urgent (patients need to be seen now)
Routine (patient can wait)
Open access will see everyone today
P (personal) for patients seeing their regular provider
T (team) for patients seeing an alternate provider in the medical practice
U (unestablished) for patients who are not associated with any provider in particular

51. Standardize appointment times
Some appointment may take longer
The face-to-face time between the patient and the physician
15 ~ 20 minutes
Plan for unusually high demand
Increase the number of appointment slots later in day
Break the patient-provider continuity of care if patient agree
Midlevel providers
Available colleagues

52. Reduce demand for face-to-face appointments
Chronic diseases require regular monitoring
Telemedicine

53. Ambulatory Care (cont.)
Open access scheduling (cont.)
Benefits
Better continuity of care because of increased efforts to match patients with their preferred physicians.
Decreased number of no-shows
More productive visits as patients forge relationships with their preferred providers and feel more comfortable discussing a wider range of health concerns
Increased utilization of physicians’ time resulting in higher revenues
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.40

54. Lower use of urgent care services because patients are able to make same-day appointments
Lesser need for triage nurses due to the simplification of visit types
Improved patient satisfaction because patients tend to regard their regular provider as more competent and knowledgeable about their health history
Less frustration among schedulers, nurses, and physicians as they stop struggling with the backlog

55. Some Caveats (愛心提醒) of Same-day Access
Few facilities were able to achieve same-day access
No-show rates improved
Other performance either neutral or positive
Visit volume
Physician compensation
Productivity
Patients prefer convenient time rather than the same day
Patients may have strict work schedule

56. Third Next Available (TNA)

57. Ambulatory Care (cont.)
Smoothing flow scheduling
Variability
Can not be totally Avoided but somewhat Managed
Phases
Use 3 months of historical data to analyze the case mix
in terms of urgency and
establish a schedule with a number of slots
matching the demand both in terms of volume and mix.
Adjust the capacity accordingly (Chapter 8).
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.41

58. Streamline the flow for scheduled patients and
Surgeons provide orders of surgeries
大手術、小手術
address bottlenecks as explained in Chapters 6, 7, and 8.
A smooth flow for scheduled patients will free up capacity for unscheduled visits (e.g. same-day referrals). Monitor flow performance.
Track cancellations and no-shows.
Overbook appointments if the percentage is less than 10%.
For example, if for a particular weekday, there are usually two no- shows, then
two patients can be overbooked.

59. Examine the artificial variability resulting from provider and staff preferences that is injected into the scheduling system.

60. Inpatient and Emergency Care
Smoothing flow techniques also apply to inpatient care
Accurate assessment of capacity and demand is a requirement
Standard protocols are needed to reduce artificial variability
Emergence of patient-tracking systems
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.43

61. Summary Connecting concepts
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.44

62. Figure 9.5 – Interrelationships Among Scheduling Types
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.45

63. Figure 9.6 – Connecting Scheduling to Competitive Priorities
Copyright © Springer Publishing Company, LLC. All Rights Reserved.
9.46