Solving 0-1 Semidefinite Programs for Distributionally Robust Allocation of Surgery Blocks

14 Pages Posted: 7 Jul 2017

See all articles by Yiling Zhang

Yiling Zhang

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

Saadet Erdogan

San Jose State University

Date Written: February 13, 2017

Abstract

We consider the problem of allocating surgeries in operating rooms (ORs) under random surgery durations. We minimize the cost of opening ORs and surgery assignments, while restricting OR overtime risk via distributionally robust (DR) chance constraints using the first two moments to construct an ambiguous set of the unknown distribution of surgery durations. Following the conic duality, the DR chance-constrained model is equivalent to a 0-1 semidefinite program (SDP) and that is solved by a cutting-plane algorithm. We also propose a 0-1 second-order conic program (SOCP) reformulation that approximates the result with a less conservative solution. We conduct numerical studies to show the performance of each method on randomly generated instances. The 0-1 SDP outperforms the 0-1 SOCP and a benchmark Sample Average Approximation approach in terms of CPU time and the out-of-sample reliability of having no overtime.

Keywords: distributionally robust optimization, chance-constrained programming, 0-1 semidefinite program, 0-1 second-order conic program, cutting-plane algorithm

JEL Classification: C02, C44, C61

Suggested Citation

Zhang, Yiling and Shen, Siqian and Erdogan, Saadet, Solving 0-1 Semidefinite Programs for Distributionally Robust Allocation of Surgery Blocks (February 13, 2017). Available at SSRN: https://ssrn.com/abstract=2997524 or http://dx.doi.org/10.2139/ssrn.2997524

Yiling Zhang

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

489 Shepherd Lab, 100 Union St SE
University of Minnesota
Minnespolis, MN 55455
United States

Siqian Shen (Contact Author)

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

1205 Beal Avenue
Ann Arbor, MI 48109
United States

Saadet Erdogan

San Jose State University ( email )

San Jose, CA 95192-0066
United States

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