Data-Driven Distributionally Robust Optimization for Elective Operating Room Allocation Under Moment-Based Ambiguity Sets: Exact Reformulations and a Column Generation Approach

Abstract

Allocating elective patients to operating rooms (ORs) under uncertain surgery durations and limited historical data requires balancing, opening costs against overtime risk. We develop a data-driven distributionally robust optimization model (DDRO) that jointly determines OR openings and patient assignments, with room-level risk measured by worst-case expected overtime over a Delage–Ye moment-based ambiguity set. We derive exact semidefinite reformulations under box and nonnegative ellipsoidal supports. OR homogeneity and separable risk yield an equivalent set-partitioning model, solved by a tailored column-generation algorithm (DDRO-CG) using exact full-enumeration pricing for small instances and heuristic candidate-pool pricing for larger ones. Experiments using the MSS-Adjusted Surgery Data validate DDRO-CG on small instances and show empirical tractability on the larger tested instances, although candidate-pool pricing provides no global optimality certificate. Out-of-sample evaluations and paired tests under controlled distributional shift show that DDRO reduces cost variability and upper-tail risk relative to deterministic and SAA benchmarks at a small average-cost premium over SAA.