Multi-resource Allocation Scheduling of Elective and Emergency Surgery in Dynamic Environments

We formulate the first model of allocation scheduling for emergency and elective surgeries in a dynamic environment, where distributional information about demand and resource availability is continually updated and scheduling decisions exploit new information as it arises. We allow multiple resources to be considered, and patients to renege if they are made to wait for too long. We prove that similar to the problem with independent and identically distributed demands, our formulation is convex, and the optimal amount of capacity reserved for emergency surgery in each period decreases with the number of patients waiting for elective surgery. However, the optimal policy is difficult to compute exactly due to state-space explosion. We develop the idea of a limit policy starting at a particular time. Our primary theoretical contribution is a method to obtain upper and lower bounds on the decisions of an optimal policy in each period using limit policies. We also develop several computationally-efficient policies based on limit policies that are consistently superior to the naive myopic policy, which merely minimizes the immediate cost in each period. We show in computational experiments that our best policy performs within 1.8% of an optimal policy on average.