Managing Portfolio of Elective Surgical Procedures : A Multidimensional Inverse Newsvendor Problem

We consider the problem of allocating daily hospital service capacity among several types of elective surgical procedures, in the presence of random numbers of urgent procedures described by arbitrary finite-support distributions. Our focus is on the interaction between two major, constraining hospital resources: operating room (OR) and recovery bed capacity. In our model, each type of surgical procedure has an associated revenue, stochastic procedure duration, and stochastic length-of-stay (LOS). We consider arbitrary distributions of procedure and LOS durations and derive a two-moment approximation based on the Central Limit Theorem (CLT) for the total procedure duration and the daily number of occupied beds for a given portfolio of procedures. An important novel element of our model is accounting for correlation among the surgical and patient LOS durations for the procedures performed by the same surgical team. We treat the available OR and 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 elective procedures for single-specialty hospitals, and derive an optimality bound for a "front-end" capacity management approach that focuses exclusively on OR capacity. For a setting with two dominant procedure types, we provide an analytical characterization of the optimal portfolio composition under the condition that the revenue from each procedure is proportional to the expected use of hospital resources. We also derive a general analytical description of the optimal portfolio for an arbitrary number of procedure types. 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 quality of the CLT-based approximation and the effectiveness of the "front-end" approach to hospital capacity management