1. © J. Christopher Beck 20081 Lecture 25: Hospital Scheduling

2. © J. Christopher Beck 2008 2 Outline Healthcare & Scheduling Operating room scheduling at Mt. Sinai Problem Models Results

3. © J. Christopher Beck 2008 3 Readings Blake & Donald, Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time, Interfaces, pp 63-87, 32(2), 2002.

4. © J. Christopher Beck 2008 4 Healthcare & Scheduling A growth opportunity for scheduling research Staff scheduling (nurses, doctors, orderlies) Operating room scheduling Patient scheduling operations, clinics, … Therapy (e.g., radiation) Historically, much less attention than manufacturing

5. © J. Christopher Beck 2008 5 Healthcare & Scheduling Challenges Uncertainty ER, going into labour, complications in surgery, … Large, interacting systems The law of unintended consequences Complex “people” constraints in a high- stress job Many stakeholders

6. © J. Christopher Beck 2008 6 OR Room Scheduling How to allocate OR time among different surgical specialties e.g., ophthalmology, gynecology, surgery, oral surgery, … Cyclical schedule Number and type of ORs available Assign specialties who will be given priority at different times

7. © J. Christopher Beck 2008 7

8. 8 3-Step Process Management: total number of OR hours available Nurse manager: # of template schedules # of rooms and hours of opening each day must meet total hours must be feasible with nurses’ collective agreement

9. © J. Christopher Beck 2008 9 3-Step Process Nurse manager: using template, assign available time to departments Competing objectives: hospital wants to reduce cost  fewer hours doctors want to maximize income  more hours equity among surgical departments

10. © J. Christopher Beck 2008 10 Constraints & Preferences One department per day share by assigning alternate weeks to different departments i.e., alternate Mondays to different depts Consistent schedule from week to week Min/max bounds on number of blocks assigned to each department in a given day/week

11. © J. Christopher Beck 2008 11 Model i – operating room type j – department k – day of week x ijk - # of blocks of type i assigned to department j on day k d ik – duration of block i on day k (long, short) X (main, EOPS)

12. © J. Christopher Beck 2008 12 Model Assign x ijk such that the sum of the time allocated for a department is equal to their target number of hours penalty for dept j target time for dept j

13. © J. Christopher Beck 2008 13 Model s j + – amount of oversupply for dept j s j - – amount of undersupply for dept j

14. © J. Christopher Beck 2008 14 minimize penalty allocated time ± over/under supply all available rooms are allocated bounds on number of rooms assigned to a dept in a day bounds on number of specific type of room assigned to a dept in a day

15. © J. Christopher Beck 2008 15 bounds on number of specific type of room assigned to a dept in a week arbitrary bound on max. under allocation

16. © J. Christopher Beck 2008 16 Results Full production since 1997 Time to produce schedule reduced from days to 1 or 2 hours OR manager’s time reduced saving $20K/year Faster scheduling  more alternatives investigated  increased quality Objective measure of quality

17. © J. Christopher Beck 2008 17 Other Points Background section provides an interesting description of how & why the Canadian healthcare system is set- up economic incentives, etc. Political realities old process (p. 68) objective criteria reduces conflict

18. © J. Christopher Beck 2008 18 What Do I Have to Know about this Paper? As this is a fairly simple, mostly non- technical paper, you should have a detailed understanding of both the problem and the model I could give you an OR scheduling problem and ask you to give me a MIP model for it