Simulation-based optimization for surgery appointment scheduling of multiple operating rooms

This study is devoted to the appointment scheduling (AS) for a sequence of surgeries with random durations served by multiple operating rooms (Multi-OR). Surgeries are assigned to ORs dynamically on a first-come, first-serve (FCFS) basis. It materially differs from past literature in the sense that dynamic assignments are proactively anticipated in the determination of appointment times. A discrete-event framework is proposed to model the execution of the surgery schedule and to evaluate the sample path gradient of a total cost incurred by surgeon waiting, OR idling, and OR overtime. The sample path cost function is shown to be unimodal, Lipchitz-continuous, and differentiable w.p.1 and the expected cost function continuously differentiable. A stochastic approximation algorithm based on unbiased gradient estimators is proposed and extensive numerical experiments suggest that it converges to a global optimum. A series of numerical experiments is performed to show the significant benefits of the Multi-OR setting and properties of the optimal solution with respect to various system parameters such as cost structure and numbers of surgeries and ORs.