Decision-Focused Learning for Surgical Resource Allocation

Abstract

Hospitals allocate operating-room (OR) capacity before future surgical demand is fully known, so they must rely on demand predictions when making resource-allocation decisions. A conventional predict-then-optimize approach trains a demand predictor for statistical accuracy and subsequently optimizes against its point forecast. We study whether the predictor should instead be trained directly for the quality of the OR allocation it induces. We formulate a contextual, multi-period OR-capacity allocation problem and develop a decision-focused learning approach that trains the demand predictor through the downstream allocation objective. We first establish consistency of empirical decision-risk minimization. We then analyze a two-class specialization to characterize the difference between decision-focused training and accuracy-based training using squared loss. We show that under suitable conditions, decision-focused training is decision-consistent, whereas squared-loss training targets the conditional mean and can incur a strictly positive decision regret that persists even with unlimited data. The analysis identifies capacity scarcity, reward–urgency asymmetry, and demand uncertainty as key drivers of this gap. Extensive numerical experiments confirm our analytical results. Using five years of data from a public hospital, decision-focused training reduces out-of-sample regret from 3.69% to 1.98%, eliminating 46.1% of the regret incurred by the accuracy-based predictor.