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Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • Man Yiu Tsang & Karmel S. Shehadeh & Frank E. Curtis & Beth R. Hochman & Tricia E. Brentjens, 2025. "Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem," Operations Research, INFORMS, vol. 73(3), pages 1430-1458, May.
  • Handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1430-1458
    DOI: 10.1287/opre.2022.0258
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