The effect of multiple operating room scheduling on the sterilization schedule of reusable medical devices

Abstract

We study scheduling problems of operating rooms (ORs) and sterilization of reusable medical devices (RMDs) where RMDs are the tools that have to be sterilized in order to be reused in the other surgeries. During their sterilization, RMDs are batched and reprocessed extensively by sterilization machines to prevent possible nosocomial infections. Unlike other renewable resources, such as, nurses or anesthesiologists, RMDs do not become available for the next coming surgeries right after the surgery they are used is finished. Inadequate number of RMDs causes postponement of surgeries or delays in the starting times of surgeries. To study the effect of multiple operating room scheduling on the sterilization schedule of RMDs, we integrate scheduling of ORs and sterilization of RMDs by a mixed integer linear programming model to minimize the total cost that consists of the costs of sterilization, postponement of surgeries, and makespan. First, we solve the proposed model to compute the best solution found within a computation time limit. Then, we solve disaggregated versions of the problem: first step aims to schedule surgeries without considering RMDs, and second step aims to schedule RMD sterilization given the computed surgery schedule used as the earliest time surgeries may start. In the first disaggregated version, additional surgery postponement are not permitted in the second step (during RMD sterilization schedule), whereas, in the second disaggregated version additional surgery postponements are permitted. We also propose a batch-based heuristic where the problem is decomposed into two stages: assigning surgeries to ORs and batches by a mixed integer linear programming model, and then, scheduling surgeries based on the assignments computed by the previous stage via an iterative algorithm. In addition, we also model the real life practice of utilizing fixed sterilization times and a rule-of-thumb is also proposed based on sorting with respect to RMD requirements and surgery durations. We analyze the performance of these methods and we conclude that the proposed integrated mixed integer linear programming model performs better than the other methods over 375 instances with varying number of ORs and surgeries. Our computational results show that real life practice of scheduling sterilization with fixed time intervals results in an average gap of 20.2%, whereas, first and second disaggregated methods result in average gaps of 9.0% and 3.7%, respectively. In addition, 311 instances out of 375 instances could not be solved by the first disaggregated method. Our results demonstrate the usefulness of integrating OR scheduling problem and sterilization of RMDs, and it is also demonstrated that hospital administrations can not only decrease their total costs but also prevent delays due to inadequate number of RMDs required by their surgeries.