Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

Man Yiu Tsang (), Karmel S. Shehadeh (), Frank E. Curtis (), Beth R. Hochman () and Tricia E. Brentjens ()
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Man Yiu Tsang: Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Karmel S. Shehadeh: Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Frank E. Curtis: Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Beth R. Hochman: Department of Surgery, Columbia University Irving Medical Center, New York, New York 10032
Tricia E. Brentjens: Department of Anesthesiology, Columbia University Irving Medical Center, New York, New York 10032

Operations Research, 2025, vol. 73, issue 3, 1430-1458

Abstract: We propose combined allocation, assignment, sequencing, and scheduling problems under uncertainty involving multiple operation rooms (ORs), anesthesiologists, and surgeries as well as methodologies for solving such problems. Specifically, given sets of ORs, regular anesthesiologists, on-call anesthesiologists, and surgeries, our methodologies solve the following decision-making problems simultaneously: (1) an allocation problem that decides which ORs to open and which on-call anesthesiologists to call in, (2) an assignment problem that assigns an OR and an anesthesiologist to each surgery, and (3) a sequencing and scheduling problem that determines the order of surgeries and their scheduled start times in each OR. To address the uncertainty of each surgery’s duration, we propose and analyze stochastic programming (SP) and distributionally robust optimization (DRO) models with both risk-neutral and risk-averse objectives. We obtain near-optimal solutions of our SP models using sample average approximation and propose a computationally efficient column-and-constraint generation method to solve our DRO models. In addition, we derive symmetry-breaking constraints that improve the models’ solvability. Using real-world, publicly available surgery data and a case study from a health system in New York, we conduct extensive computational experiments comparing the proposed methodologies empirically and theoretically, demonstrating where significant performance improvements can be gained. Additionally, we derive several managerial insights relevant to practice.

Keywords: Optimization; operating rooms; surgery scheduling; integer programming; stochastic programming; distributionally robust optimization (search for similar items in EconPapers)
Date: 2025
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