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

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