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We study the elective surgery planning problem in a hospital with operationrooms shared by elective and emergency patients. This problem can be split intwo distinct phases. First, a subset of patients to be operated in the nextplanning period has to be selected, and the selected patients have to beassigned to a block and a tentative starting time. Then, in the online phase ofthe problem, a policy decides how to insert the emergency patients in theschedule and may cancel planned surgeries. The overall goal is to minimize theexpectation of a cost function representing the assignment of patient toblocks, case cancellations, overtime, waiting time and idle time. We model theoffline problem by a two-stage stochastic program, and show that thesecond-stage costs can be replaced by a convex piecewise linear surrogate modelthat can be computed in a preprocessing step. This results in a mixed integerprogram which can be solved in a short amount of time, even for very largeinstances of the problem. We also describe a greedy policy for the online phaseof the problem, and analyze the performance of our approach by comparing it toeither heuristic methods or approaches relying on sampling averageapproximation (SAA) on a large set of benchmarking instances. Our simulationsindicate that our approach can reduce the expected costs by as much as 20%compared to heuristic methods and is able to solve problems with $1000$patients in about one minute, while SAA-approaches fail to obtain near-optimalsolutions within 30 minutes, already for $100$ patients.

Surgery Scheduling in Flexible Operating Rooms by using a Convex Surrogate Model of Second-Stage Costs