1. Developing a Multi- Methodology Operating Theatre Scheduling Support System Marion Penn With: Prof. Chris Potts and Prof. Paul Harper IMA 29 th March 2010

2. Outline Introduction to topic and literature Soft OR - Understanding the problem Hard OR - Master Timetable –Set Up –Formulation –Results to date –Future Work

3. Background Hospitals face the challenges of; Demanding Targets –Shorter waits for operations –Reduced cancellations Financial Constraints Resource Constraints

4. Theatre Scheduling My Objective To develop a methodology that can be used in hospitals to produce efficient theatre schedules.

5. Literature Over 100 papers Methods – LP, Simulation, Queuing … Whole system … narrow aspects Factors –Theatre Time –Staff –Beds

6. Gaps in the Literature Key Factors not brought together Lack of Implementation Addressing Stochastic Elements

7. Cognitive mapping Visual Brings together ideas Enables joint understanding Explores links Causal relationships

9. Hard OR – From Literature Strategic –Planning work load –Dividing theatre time Longer term tactical planning –Developing a Master Theatre Timetable Day to day scheduling of electives –Booking into slots –Live changes to the schedule

10. Master Timetable What –Assigns slots of theatre time to surgeons –Cyclic How –Linear / Goal Programming –Heuristics –Simulation –Column Generation

11. Inputs Theatre types and availability Numbers of theatre slots required Surgeon (and other staff) availability Surgeon preferences Expected bed usage (by ward) Equipment availability Bed availability and usage

12. Variables X i,t,d,s Assigns surgeons to slots. Y i,t,d,s If a slot has been assigned to a surgeon with a low preference score for it. U i,t,d,s If surgeon in same theatre for consecutive slots. V i,t,d,s If surgeon in different theatres for consec. slots. W i,t,d,s If slot repeated weekly. Expected beds required each day. Z Min difference between beds required and beds available. X, Y, U, V and W are all binary variables. Index i represents an individual surgeon, t a theatre, d a day in the cycle and s a daily theatre slot.

13. Significant Parameters G h,t Types of theatres 1 if t is of type h, 0 otherwise R h,t Number of slots of type h required by surgeon i B i,t,j,w Expected number of patients in beds in ward k, j days after surgeon i has a slot in theatre t D d,w Number of beds available on day d in ward k

14. ‘Straightforward’ Constraints Only use available slots Surgeons can only be in one place Surgeons availability Limit on surgeons no. slots per day Equipment constraint

15. Demand Constraints Cover demand by theatre type Meet each surgeon’s overall demand exactly Surgeons don’t use any theatre more than their total demand for its type(s)

16. Bed Constraints Assigns Assigns Z Based on Gallivan & Utley’s formulation Gallivan S. and Utley M. (2005) ‘Modelling admissions booking of elective in-patients into a treatment centre’, IMA Journal of Management Mathematics 16, p. 305-315

17. Other Constraints Assign values to; –U –V –W –Y Based on the values in X

18. Objectives Find a feasible timetable Smooth Bed usage Max surgeon pref. score Min low pref. scores Max all day slots Repeat slots weekly Avoid consecutive slots in different theatres

19. Output Weekly / Monthly Schedule –Slots for Surgeons Expected Bed Usage Ratings against objectives

20. Early Results IndicatorOriginal Timetable LP Timetable Max beds used 9083 No. Surgeons changing theatres 00 No. of all day slots 3055 Repeat weekly 166178

21. Bed Smoothing

22. Future Work Further Develop Master Timetable Day to day scheduling tool Warning systems

23. Questions/ Comments