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IMA 29 th March 2010

Developing a Multi-Methodology Operating Theatre Scheduling Support System Marion Penn With: Prof. Chris Potts and Prof. Paul Harper. IMA 29 th March 2010. Outline. Introduction to topic and literature Soft OR - Understanding the problem Hard OR - Master Timetable Set Up Formulation

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IMA 29 th March 2010

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

  8. 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

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

  10. 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

  11. Variables • Xi,t,d,s Assigns surgeons to slots. • Yi,t,d,s If a slot has been assigned to a surgeon with a low preference score for it. • Ui,t,d,sIf surgeon in same theatre for consecutive slots. • Vi,t,d,s If surgeon in different theatres for consec. slots. • Wi,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.

  12. Significant Parameters • Gh,tTypes of theatres 1 if t is of type h, 0 otherwise • Rh,tNumber of slots of type h required by surgeon i • Bi,t,j,wExpected number of patients in beds in ward k, j days after surgeon i has a slot in theatre t • Dd,w Number of beds available on day d in ward k

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

  14. 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)

  15. 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

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

  17. 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

  18. Output • Weekly / Monthly Schedule • Slots for Surgeons • Expected Bed Usage • Ratings against objectives

  19. Early Results

  20. Bed Smoothing

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

  22. Questions/ Comments

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