Surgery Sequencing and Scheduling in Multiple ORs with PACU Constraints

This paper addresses a surgery sequencing and scheduling problem in multiple operating rooms (OR) constrained by shared downstream post-anesthesia care unit (PACU) capacity. We propose a two-stage solution method to minimize the expected value of a cost function that includes patient waiting time, surgeon idle time, OR blocking time, OR overtime and PACU overtime. In the first stage, we propose a time-indexed mixed-integer programming model with a surrogate objective that is easier to solve than the impractically difficult original problem. The Lagrangian relaxation of the surrogate model can be decomposed by patients into network-structured subproblems which can be efficiently solved by dynamic programming. The first-stage model is thus solved by the subgradient method to determine the surgery sequence in each OR. Given the surgery sequence, scheduled start times of surgeries are determined in the second stage using a sample-gradient-based algorithm. Our solution method is shown to outperform benchmark heuristics in numerical experiments. We demonstrate that possible cost savings are significant in hospitals with constrained PACU capacity. We also provide some insights into the PACU utilization after considering PACU constraints.