An adjustable robust optimisation method for elective and emergency surgery capacity allocation with demand uncertainty

This article addresses the problem of allocating limited operating room (OR) capacity among subspecialties in hospitals where two types of demands exist: elective surgeries and emergency surgeries. In many medium- and small-scale hospitals, no OR capacity is affiliated with a particular subspecialty, but several subspecialties share the OR capacity in the hospital. The administrator needs to decide how much OR capacity to assign to each subspecialty and how much to reserve for emergency surgeries. Because such an allocation is usually decided several weeks or even months before, the only information about future demands is their range. We focus on finding a robust solution that handles disturbances in the surgery demand. An adjustable robust model is developed to solve this surgery capacity allocation problem with demand uncertainty. The worst-case revenue loss resulting from a shortage of OR resources is minimised. We examine the impact of conservativeness of the robust model on the revenue loss of the surgery department, which provides hospital administrators guidance for setting the adjustable parameters. An implementer-adversary algorithm is applied to solve the robust optimisation model. We present computational results comparing the proposed robust optimisation approach with a scenario-based stochastic optimisation; the results show that by adjusting the conservatism, the expected objective value realised by the robust solution is very close to that obtained by the stochastic programming approach. Moreover, the robust optimisation method has the benefit of limiting the worst-case outcome of the surgery capacity allocation problem.