Stochastic sequencing of surgeries for a single surgeon operating in parallel operating rooms

We develop algorithms for a stochastic two-machine single-server sequencing problem with waiting time, idle time and overtime costs. Scheduling surgeries for a single surgeon operating in two parallel operating rooms (ORs) motivates the work. The basic idea is that staff perform cleanup and setup in one OR while the surgeon is operating in the other. The benefit is less waiting time for the surgeon between surgeries, but may also result in added idle time for staff if cleanup and set-up are completed prior to completion of surgery in the other OR. When surgeries are long relative to cleanup and setup times, parallel OR scheduling is not attractive as significant OR and staff idle time will result. The problem we address consists of assigning surgeries to ORs and sequencing them, and is formulated as an integer stochastic program using sample average approximation. A decomposition based solution approach is developed. Computational testing based on real data shows that the proposed methods solve the problems to optimality in acceptable processing times. Using the solution methodology, we conduct additional experiments to provide insight as to the conditions when scheduling a single surgeon in parallel operating rooms is cost effective.