Planning and scheduling of operating rooms (ORs) is important for hospitals to improve efficiency and achieve high quality of service. Due to significant uncertainty in surgery durations, scheduling of ORs can be very challenging. In this paper, surgical case scheduling problem with uncertain duration of surgeries in multi resource environment is investigated. We present a two-stage stochastic mixed-integer programming model, named SOS, with the objective of total ORs idle time and overtime. Also, in this paper a two-step approach is proposed for solving the model based on the L-shaped algorithm. Proposing the model in a multi resources environment with considering real-life limitations in academic hospitals and developing an approach for solving this stochastic model efficiently form the main contributions of this paper. The model is evaluated through several numerical experiments based on real data from Hasheminejad Kidney Center (HKC) in Iran. The solutions of SOS are compared with the deterministic solutions in several real instances. Numerical results show that SOS enjoys a better performance in 97% of the cases. Furthermore, the results of comparing with actual schedules applied in HKC reveal a notable reduction of OR idle time and over time which illustrate the efficiency of the proposed model in practice.

中文翻译：

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多资源环境下手术室调度的两步随机方法

手术室 (OR) 的规划和调度对于医院提高效率和实现高质量服务非常重要。由于手术持续时间的重大不确定性，手术室的安排可能非常具有挑战性。本文研究了多资源环境下手术时间不确定的手术病例调度问题。我们提出了一个名为 SOS 的两阶段随机混合整数编程模型，其目标是总 OR 的空闲时间和加班时间。此外，在本文中，提出了一种基于 L 型算法求解模型的两步方法。在多资源环境中提出模型并考虑学术医院的现实限制，并开发一种有效解决该随机模型的方法是本文的主要贡献。该模型是根据伊朗哈希米内贾德肾脏中心 (HKC) 的真实数据，通过多项数值实验进行评估的。SOS 的解决方案与几个实际实例中的确定性解决方案进行了比较。数值结果表明，SOS 在 97% 的情况下具有更好的性能。此外，与 HKC 中应用的实际时间表进行比较的结果显示 OR 空闲时间和随着时间的推移显着减少，这说明了所提出的模型在实践中的效率。