A two-stage stochastic optimization framework to allocate operating room capacity in publicly-funded hospitals under uncertainty

Surgery demand is an uncertain parameter in addressing the problem of surgery block allocations, and its typical variability should be considered to ensure the feasibility of surgical planning. We develop two models, a stochastic recourse programming model and a two-stage stochastic optimization (SO) model with incorporated risk measure terms in the objective functions to determine a planning decision that is made to allocate surgical specialties to operating rooms (ORs). Our aim is to minimize the costs associated with postponements and unscheduled demands as well as the inefficient use of OR capacity. The results of these models are compared using a case of a real-life hospital to determine which model better copes with uncertainty. We propose a novel framework to transform the SO model based on its deterministic counterpart. Three SO models are proposed with respect to the variability and infeasibility of the measures of the objective function to encode the construction of the SO framework. The analysis of the experimental results demonstrates that the SO model offers better performance under a highly volatile demand environment than the recourse model. The originality of this work lies in its use of SO transformation framework and its development of stochastic models to address the problem of surgery capacity allocation based on a real case.