Chance-Constrained Surgery Planning Under Conditions of Limited and Ambiguous Data

32 Pages Posted: 4 May 2014 Last revised: 13 May 2018

Yan Deng

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Siqian Shen

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Brian Denton

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Date Written: June 29, 2016

Abstract

Surgery planning decisions include which operating rooms (ORs) to open, allocation of surgeries to ORs, sequence and time to start each surgery. They are often made under uncertain surgery durations with limited data that lead to unknown distributional information. Moreover, cost parameters for criteria such as overtime and surgery delays are often difficult or impossible to estimate in practice. In this paper, we formulate distributionally robust (DR) chance constraints on surgery waiting and OR overtime, which recognize practical limitations on data availability and cost parameter accuracy. We use $\phi$-divergence measures to build an ambiguity set of possible distributions of random surgery durations, and derive a branch-and-cut algorithm for optimizing a mixed-integer linear programming reformulation based on finite samples of the random surgery durations. We test instances generated from real hospital-based surgery data. The results show computational efficacy of our approaches, and provide insights for DR surgery planning.

Keywords: Chance-constrained surgery planning; distributionally robust optimization; $\phi$-divergence; mixed-integer linear programming; branch-and-cut

Suggested Citation

Deng, Yan and Shen, Siqian and Denton, Brian, Chance-Constrained Surgery Planning Under Conditions of Limited and Ambiguous Data (June 29, 2016). Available at SSRN: https://ssrn.com/abstract=2432375 or http://dx.doi.org/10.2139/ssrn.2432375

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