Bounding the Likelihood of Exceeding Ward Capacity in Stochastic Surgery Scheduling

Abstract

The stochastic high-patient-throughput surgery scheduling problem under a limited number of staffed ward beds is addressed in this paper. This work proposes a novel way to minimize the risk of last-minute cancellations by bounding the likelihood of exceeding the staffed ward beds. Given historical data, it is possible to determine an empirical distribution for the length of stay in the ward. Then, for any given combinations of patients, one can estimate the likelihood of exceeding the number of staffed ward beds using Monte Carlo sampling. As these ward patient combinations grow exponentially, an alternative, more efficient, worst-case robust ward optimization model is compared. An extensive data set was collected from the National University Hospital of Iceland for computational experiments, and the models were compared with actual scheduling data. The models proposed achieve high quality solutions in terms of overtime and risk of overflow in the ward.

Keywords

• surgery scheduling
• uncertainty
• downstream resource
• Monte Carlo sampling
• mixed integer programming
• robust optimization