Long term policies for operating room planning

1. Long termpoliciesforoperatingroom planning A. Agnetis1, A. Coppi1, G. Dellino2, C. Meloni3, M. Pranzo1 1Dept. of Information Engineering, Universityof Siena, Italy 2 IMT InstituteforAdvancedStudies, Lucca, Italy 3Dept. ofElectronics and ElectricalEngineering, Polytechnicof Bari, Italy

2. Outline • Introduction • Problemdescription • Optimizationmodels and heuristics • Case study • Preliminaryresults • Conclusions

3. Introduction • Operatingtheatre (OT) among the mostcriticalresources in a hospital • Significant impact on costs • Affectsqualityof service • Improve the efficiencyof the OT management process • Focus on operatingroom (OR) planning

4. Decisionproblemsin OT management MSSP SCAP Tue Wed Thu Fri Mon OR1 ESSP OR2 OR3 OR4 Gynecology Urology Daysurgery Generalsurgery Otolaryn-gology Orthopedicsurgery OR5 ____________________ ____________________ ____________________ ____________________ ____________________ ____________________ OR6

5. Organizationalcomplexityvs. MSS variation • Staffing and shift planning • MSS fixedovertime ↑ stability, ↓ flexibility • MSS differentevery week  ↓ stability, ↑ flexibility

6. Maincontributions • Alternative policiesproposedtotrade off efficient management of the surgerywaitinglists and organizationalcomplexity • MSSP and SCAP solvedthroughmathematicalprogrammingmodels and heuristics • Performance evaluationoverone-yeartimehorizon • Assumptions: • Deterministic data • Electivepatientsonly

7. Problemdescription (1) • Input: waitinglistofelectivepatientsforeachsurgicalspecialty • Data foreach case surgery in the list: • Output: one-weekassignment (Mon-Fri) ofelectivesurgeriestoORs Waitinglist – Daysurgery Surgery code Surgeryduration (min) Priorityclass Entrancetime Waitingtime (days) Due date 6210 28 B 15/06/2010 27 15/08/2010

8. Problemdescription (2) • OR sessions: morning/afternoon/full-day • Assignmentrestrictions • Objectives: • Max ORsutilization, withoutovertime • Schedule case surgerieswithintheirdue-date, reducingpatients’ waitingtime based on case surgeriesduration and a score, relatedto: • case surgerywaitingtime and priorityclass • case surgeryslacktime

9. Optimizationmodels ILP mathematicalformulations, solvedby CPLEX • Unconstrained MSS model Determines MSS and SCA every week, based on the actualwaitinglistforeachspecialty • Constrained MSS model Determines MSS and SCA, bounding the numberofchanges in OR sessionassignmentstodifferentsurgicalspecialtiesw.r.t. a reference MSS • Fixed MSS model Determines SCA, givenan MSS

10. Unconstrained MSS model • ‘Unconstrained’ w.r.t.long-term planning • Constraints • Bounds on the numberofweekly OR sessionsassignedto a specialty • MinnumberofORsassignedto a specialtyeveryday (eitherhalf-day or full-daysessions) • Max numberofparallel OR sessionsforeachspecialty • Restrictions on specialty-to-ORassignments • Max OR sessionduration (no overtime)

11. Constrained MSS model • ‘Constrained’ w.r.t.long-term planning • Block time = # weeksduringwhich the MSS isfixed • Set a reference MSS • Distance (Δ) betweentwoMSSs: # ORsforeachday and sessiontypeassignedtodifferentsurgicalspecialties in the MSSs • Oneconstraintaddedto the previousmodel, boundingsuch a distancebetween the new MSS and the reference MSS

12. Fixed MSS model • The MSS hasbeenalreadydetermined OR sessionsalreadyassignedtosurgicalspecialties • Assignmentof case surgeriesto OR sessions; i.e., SCAP issolved

13. Heuristicmethods MSSP OR sessions = bins; Surgeries = items • Candidate OR sessions (half-day/full-day) foreachspecialty→first-fit-decreasingrule • Selectionof candidate sessionsassignedto OR • MSS isretained, discardingallsurgicalcasesfillingit SCAP

14. Planning policies Unconstrained MSS model MSSP SCAP Exactly solved Exactly solved Constrained MSS model Heuristically solved Heuristically solved Δ = 1, block = 1 Δ = 2, block = 4 Fixed MSS model

15. Case study: OT characteristics Medium-size public Italian hospital (Empoli, Tuscany) • OT = 6 operatingrooms; twoORs are bigger • 6 surgicalspecialties: generalsurgery, otolaryngology, gynecology, orthopedicsurgery, urology, daysurgery • Surgicalspecialtyrestrictions • Gynecologymustuse the same OR for the whole week • Orthopedicsneeds big ORs • Twoparallel OR sessions can bebothassignedtogeneralsurgery (the samefororthopedics) • Furtherrestrictions • One OR quicklymadeavailable, everymorning • One OR free everyafternoon

16. Case study: experimental design • MSSP and SCAP solvedevery week • Simulationoveroneyear • Weeklyarrivals: • nonparametricbootstrappingfrom the initialwaitinglist • sample sizefrom a uniformdistributioncenteredaround the averageweeklyarrival rate • Twoscenariostested: base/stressed scenario

17. PreliminaryresultsBase scenario f1 f2

18. PreliminaryresultsStressed scenario f1 f2

19. Preliminaryresults • Stabilityof the MSS • The unconstrained MSS modelhasanaveragedistancebetweentwoadjacent MSS of 12-13  20% of the MSS changesfromone week to the next • Worst case: 67% changes in the MSS • Trade-offprovidedby the constrained MSS model

20. Conclusions • Long-termevaluationof alternative policiesfor OR planning ofelectivesurgeries • Simulation on a real case study (medium-size public hospital in Italy) • Promisingresultstoimprovewaitinglists’ management • For future research: • Surgeons and resourcesavailabilityconstraints • Differentobjectivefunctions and policies • Uncertainty on surgeryduration and surgeryarrivals

21. Unconstrained MSS modelMathematicalformulation

22. Constrained MSS • ‘Constrained’ w.r.t.long-term planning • Block time = # weeksduringwhich the MSS isfixed • Set a reference MSS • Distance (Δ) betweentwoMSSs: # ORsforeachday and sessiontypeassignedtodifferentsurgicalspecialties in the MSSs • Oneconstraintaddedto the previousmodel, boundingsuch a distancebetween the new MSS and the reference MSS

23. Fixed MSS modelMathematicalformulation