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. Our focus is on the interaction between two major constraining hospital resources: operating room and bed capacity. In our model, each type of surgical procedure has an associated revenue, deterministic procedure duration and stochastic hospital length of stay. In our modeling of length of stay durations, we consider arbitrary distributions and derive a two-moment approximation for the daily numbers of occupied beds for a given portfolio of procedures. We demonstrate the complexity of the problem of optimizing daily portfolio of procedures in the presence of limited operating room and bed capacity and derive a complete characterization of the optimal portfolio for the case of two procedure types. For arbitrary number of procedure types, we use linearization of the bed constraint to propose a heuristic solution to the portfolio optimization problem, derive a bound for its performance, and illustrate its effectiveness using the data reported in the 2010 Nationwide Inpatient Sample.