Long term policies for operating room planning A. Agnetis1, A. Coppi1, G. Dellino2, C. Meloni3, M. Pranzo1 1 Dept. of Information Engineering, University of Siena, Italy 2 IMT Institute for Advanced Studies, Lucca, Italy 3 Dept. of Electronics and Electrical Engineering, Polytechnic of Bari, Italy

Outline Introduction Problem description Optimization models and heuristics Case study Preliminary results Conclusions

Introduction Operating theatre (OT) among the most critical resources in a hospital Significant impact on costs Affects quality of service Improve the efficiency of the OT management process Focus on operating room (OR) planning Health care expenditure QoS as perceived by patients

Decision problems in OT management Mon Tue Wed Thu Fri OR1 OR2 OR3 OR4 OR5 OR6 MSSP SCAP ESSP Gynecology Urology Day surgery General surgery Otolaryn-gology Orthopedic surgery ____________________ ____________________ ____________________ ____________________ ____________________ ____________________

Organizational complexity vs. MSS variation Staffing and shift planning MSS fixed over time  ↑ stability, ↓ flexibility MSS different every week  ↓ stability, ↑ flexibility Staffing patterns favour staff satisfaction

Main contributions Alternative policies proposed to trade off efficient management of the surgery waiting lists and organizational complexity MSSP and SCAP solved through mathematical programming models and heuristics Performance evaluation over one-year time horizon Assumptions: Deterministic data Elective patients only

Problem description (1) Input: waiting list of elective patients for each surgical specialty Data for each case surgery in the list: Output: one-week assignment (Mon-Fri) of elective surgeries to ORs Waiting list – Day surgery Surgery code Entrance time Surgery duration (min) Priority class Waiting time (days) Due date 6210 15/06/2010 28 B 27 15/08/2010

Problem description (2) OR sessions: morning/afternoon/full-day Assignment restrictions Objectives: Max ORs utilization, without overtime Schedule case surgeries within their due-date, reducing patients’ waiting time based on case surgeries duration and a score, related to: case surgery waiting time and priority class case surgery slack time

Optimization models ILP mathematical formulations, solved by CPLEX Unconstrained MSS model Determines MSS and SCA every week, based on the actual waiting list for each specialty Constrained MSS model Determines MSS and SCA, bounding the number of changes in OR session assignments to different surgical specialties w.r.t. a reference MSS Fixed MSS model Determines SCA, given an MSS

Unconstrained MSS model ‘Unconstrained’ w.r.t. long-term planning Constraints Bounds on the number of weekly OR sessions assigned to a specialty Min number of ORs assigned to a specialty every day (either half-day or full-day sessions) Max number of parallel OR sessions for each specialty Restrictions on specialty-to-OR assignments Max OR session duration (no overtime)

Constrained MSS model ‘Constrained’ w.r.t. long-term planning Block time = # weeks during which the MSS is fixed Set a reference MSS Distance (Δ) between two MSSs: # ORs for each day and session type assigned to different surgical specialties in the MSSs One constraint added to the previous model, bounding such a distance between the new MSS and the reference MSS

Fixed MSS model The MSS has been already determined  OR sessions already assigned to surgical specialties Assignment of case surgeries to OR sessions; i.e., SCAP is solved

Heuristic methods MSSP SCAP OR sessions = bins; Surgeries = items Candidate OR sessions (half-day/full-day) for each specialty → first-fit-decreasing rule Selection of candidate sessions assigned to OR MSS is retained, discarding all surgical cases filling it SCAP

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

Case study: OT characteristics Medium-size public Italian hospital (Empoli, Tuscany) OT = 6 operating rooms; two ORs are bigger 6 surgical specialties: general surgery, otolaryngology, gynecology, orthopedic surgery, urology, day surgery Surgical specialty restrictions Gynecology must use the same OR for the whole week Orthopedics needs big ORs Two parallel OR sessions can be both assigned to general surgery (the same for orthopedics) Further restrictions One OR quickly made available, every morning One OR free every afternoon

Case study: experimental design MSSP and SCAP solved every week Simulation over one year Weekly arrivals: nonparametric bootstrapping from the initial waiting list sample size from a uniform distribution centered around the average weekly arrival rate Two scenarios tested: base/stressed scenario

Preliminary results Base scenario f1 f2

Preliminary results Stressed scenario f1 f2

Preliminary results Stability of the MSS The unconstrained MSS model has an average distance between two adjacent MSS of 12-13  20% of the MSS changes from one week to the next Worst case: 67% changes in the MSS Trade-off provided by the constrained MSS model Commentare anche i risultati sulla gestione delle liste d’attesa?

Conclusions Long-term evaluation of alternative policies for OR planning of elective surgeries Simulation on a real case study (medium-size public hospital in Italy) Promising results to improve waiting lists’ management For future research: Surgeons and resources availability constraints Different objective functions and policies Uncertainty on surgery duration and surgery arrivals

Unconstrained MSS model Mathematical formulation

Constrained MSS ‘Constrained’ w.r.t. long-term planning Block time = # weeks during which the MSS is fixed Set a reference MSS Distance (Δ) between two MSSs: # ORs for each day and session type assigned to different surgical specialties in the MSSs One constraint added to the previous model, bounding such a distance between the new MSS and the reference MSS

Fixed MSS model Mathematical formulation

Introduction Decision problems faced by managers in OR planning/scheduling: Assigning surgical specialties to OR sessions over time [Master Surgical Schedule problem (MSSP)] Assigning elective surgeries to OR sessions [Surgical Case Assignment problem (SCAP)] Sequencing surgeries within OR sessions [Elective Surgery Sequencing problem (ESSP)] Extensive literature studies on elective patients only Recent works on uncertainty affecting the system; e.g., due to stochastic surgery duration or urgencies Add some references!

Problem description (2) INPUT ______________________________ ____________________ Spec. 6 Spec. 2 Spec. 1 Spec. 3 Spec. 4 Spec. 5 Mon Tue Wed Thu Fri OR1 OR2 OR3 OR4 OR5 OR6 OUTPUT

Mon Tue Wed Thu Fri OR1 OR2 OR3 OR4 OR5 OR6 gynecology urology day surgery general surgery otolaryngo-logy orthopedic surgery

Heuristic Methods Decomposition scheme, addressing MSSP and SCAP sequentially MSSP – For each surgical specialty Sort the waiting list by non-increasing score Generate a set of candidate OR sessions (both half-day and full-day), by assigning surgical case i to the first available session Select a subset of candidate sessions for a complete case surgery assignment The corresponding MSS is retained, discarding all surgical cases filling it SCAP – For each surgical specialty [da completare] Oppure pseudo-codice dal paper? Forse diventa più compatto