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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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Developing a Multi-Methodology Operating Theatre Scheduling Support System Marion PennWith: Prof. Chris Potts and Prof. Paul Harper IMA 29th March 2010
Outline • Introduction to topic and literature • Soft OR - Understanding the problem • Hard OR - Master Timetable • Set Up • Formulation • Results to date • Future Work
Background Hospitals face the challenges of; • Demanding Targets • Shorter waits for operations • Reduced cancellations • Financial Constraints • Resource Constraints
Theatre Scheduling My Objective • To develop a methodology that can be used in hospitals to produce efficient theatre schedules.
Literature • Over 100 papers • Methods – LP, Simulation, Queuing … • Whole system … narrow aspects • Factors • Theatre Time • Staff • Beds
Gaps in the Literature • Key Factors not brought together • Lack of Implementation • Addressing Stochastic Elements
Cognitive mapping • Visual • Brings together ideas • Enables joint understanding • Explores links • Causal relationships
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
Master Timetable • What • Assigns slots of theatre time to surgeons • Cyclic • How • Linear / Goal Programming • Heuristics • Simulation • Column Generation
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
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.
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
‘Straightforward’ Constraints • Only use available slots • Surgeons can only be in one place • Surgeons availability • Limit on surgeons no. slots per day • Equipment constraint
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)
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
Other Constraints • Assign values to; • U • V • W • Y • Based on the values in X
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
Output • Weekly / Monthly Schedule • Slots for Surgeons • Expected Bed Usage • Ratings against objectives
Future Work • Further Develop Master Timetable • Day to day scheduling tool • Warning systems