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.

中文翻译：

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多手术室排程对可重复使用医疗器械灭菌排程的影响

摘要 我们研究了手术室 (OR) 的调度问题和可重复使用医疗器械 (RMD) 的消毒，其中 RMD 是必须经过消毒才能在其他手术中重复使用的工具。在灭菌过程中，RMD 被灭菌机器分批进行广泛的再加工，以防止可能的院内感染。与其他可再生资源（例如护士或麻醉师）不同，RMD 在使用的​​手术完成后不会立即用于下一次手术。RMD数量不足导致手术推迟或手术开始时间延迟。研究多手术室排程对RMDs灭菌排程的影响，我们通过混合整数线性规划模型整合 OR 的调度和 RMD 的绝育，以最小化包括绝育、手术延迟和完工时间的总成本。首先，我们解决所提出的模型以计算在计算时间限制内找到的最佳解决方案。然后，我们解决了该问题的分解版本：第一步旨在在不考虑 RMD 的情况下安排手术，第二步旨在根据计算出的手术时间表安排 RMD 绝育，作为手术可能开始的最早时间。在第一个分解版本中，第二步（在 RMD 灭菌计划期间）不允许额外的手术延期，而在第二个分解版本中，允许额外的手术延期。我们还提出了一种基于批次的启发式方法，其中问题被分解为两个阶段：通过混合整数线性规划模型将手术分配给 OR 和批次，然后根据前一阶段通过迭代算法计算的分配来安排手术。此外，我们还模拟了使用固定灭菌时间的现实生活实践，还提出了基于 RMD 要求和手术持续时间排序的经验法则。我们分析了这些方法的性能，并得出结论，所提出的集成混合整数线性规划模型在具有不同数量的 OR 和手术的 375 个实例中的性能优于其他方法。我们的计算结果表明，以固定时间间隔安排灭菌的现实生活实践导致平均差距为 20。2 % ，而第一种和第二种分解方法分别导致 9.0 % 和 3.7 % 的平均差距。此外，375 个实例中的 311 个实例无法通过第一种分解方法解决。我们的结果证明了整合 OR 调度问题和 RMD 消毒的有用性，还证明了医院管理部门不仅可以降低总成本，还可以防止由于手术所需的 RMD 数量不足而导致延误。