A distributionally robust optimization approach for surgery block allocation

Operating Rooms (ORs) are a critical resource in hospitals. Managing ORs efficiently is a difficult task for hospital managers, as patients’ surgery durations have high variability and cannot be accurately predicted in advance. This paper considers a Surgery Block Allocation (SBA) problem, which includes determining the ORs to open and assigning the surgeries in a daily listing to the ORs, towards minimizing the weighted sum of OR opening costs and expected overtime (relative to a fixed length-of-day) penalty costs. Based on real-life surgery durations’ data, we construct an ambiguity set of distribution, which incorporates the empirical means, the mean absolute deviations and the support set. In particular, we help the ambiguity-averse managers develop a distributionally robust model for the SBA problem, where the overtime costs are evaluated over the worst-case probability distribution within the ambiguity set. Bounds on the objective value are discussed. Due to its intractability, we reformulate it as a Mixed Integer Linear Programming (MILP) model using the duality theory. To solve large-scale instances, we employ the linear decision rule technique and develop an approximated MILP model, and propose another approximated MILP model by heuristically constructing a discrete distribution that is “close to” the worst-case distribution. Computational experiments show that our models outperform an existing stochastic programming model in terms of computational time and upper-decile performance. In particular, the heuristic method greatly improves the computational efficiency without pulling down the out-of-sample performances.