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A Distributionally Robust Optimization Approach for Stochastic Elective Surgery Scheduling with Limited Intensive Care Unit Capacity

Karmel S. Shehadeh (kshehadeh***at***lehigh.edu)
Rema Padman (rpadman***at***cmu.edu)

Abstract: In this paper, we study the decision process of assigning elective surgery patients to available surgery blocks under random surgery durations, random length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distribution of random parameters is assumed to be ambiguous, and only the mean and ranges are known. We propose a distributionally robust elective surgery scheduling (DRESS) model that seeks optimal surgery scheduling decisions to minimize the cost of performing and postponing surgeries and the worst-case expected cost of overtime and idle time of operating rooms and lack of ICU capacity. We evaluate the worst-case over a family of distributions characterized by the known means and ranges of random parameters. We leverage the separability of DRESS in deriving an exact mixed-integer nonlinear programming reformulation. We linearize and derive a family of symmetry breaking inequalities to improve the solvability of the reformulation using an adapted column-and-constraint generation algorithm. Finally, we conduct extensive numerical experiments that demonstrate the superior performance of our DR approach as compared to the existing stochastic programming approach and provide insights into DRESS.

Keywords: OR in Health Services, Surgery Scheduling, Downstream Resource Constraint, Distributionally Robust Optimization, Column-and-Constraint Generation, Mixed-integer Programming

Category 1: Applications -- OR and Management Sciences (Scheduling )

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Stochastic Programming

Citation: Shehadeh, K. S., Padman, R. A Distributionally Robust Optimization Approach for Stochastic Elective Surgery Scheduling with Limited Intensive Care Unit Capacity. Preprint version. 2020.

Download: [PDF]

Entry Submitted: 04/26/2020
Entry Accepted: 04/26/2020
Entry Last Modified: 04/27/2020

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