We consider the problem of allocating daily hospital service capacity among several types of elective surgical procedures. Our focus is on the interaction between two major constraining hospital resources: operating room and recovery bed capacity. In our model, each type of surgical procedure has an associated revenue, stochastic procedure duration and stochastic length-of-stay. We consider arbitrary distributions of procedure and length-of-stay durations and derive a two-moment approximation for the total procedure duration and the daily number of occupied beds for a given portfolio of procedures. For each procedure type, we consider a task of selecting the optimal daily number of elective procedures in the presence of random numbers of urgent procedures described by arbitrary finite-support distributions. We treat the available operating room and the recovery bed capacity as nominal, allowing them to be exceeded at a cost. The resulting model is a novel, multi-dimensional variant of the inverse newsvendor problem, where multiple demand types compete for multiple types of service capacity.

We characterize the optimal number of the elective procedures for single-specialty hospitals. In addition, we derive an optimality bound for the “front-end" capacity management approach that focuses exclusively on the operating room capacity. For the setting with two dominant procedure types, we provide an analytical characterization of the optimal portfolio composition under a condition where all procedures are elective, and both procedure types have associated revenues proportional to the expected resource use, but are asymmetric in terms of the second moments of their resource usage.

For an arbitrary number of procedure types, we use “elective-only" setting to derive a general analytical description of the optimal portfolio, and easy-to-compute expressions for the optimal portfolio values in the setting where all procedure types have proportional second moments of their resource usage as well as revenues proportional to the expected use of both resources.

For the general case of an arbitrary number of procedure types in the presence of urgent procedures, we conduct a numerical study using data we have collected at a medium-size teaching hospital. Our numerical study illustrates the composition of the optimal portfolios of elective procedures in different practical settings and investigates the degree of effectiveness of the “front-end" approach to hospital capacity management.