Abstract This paper addresses an advance surgery scheduling problem in an operating theater composed of multiple operating rooms (ORs) and a downstream surgical intensive care unit (SICU). Uncertainties in surgery durations and postoperative length-of-stays are taken into consideration. The decisions are made on a weekly basis and consist of three parts: determining the surgical blocks to open, selecting the surgeries to be performed from a waiting list, and assigning the selected surgeries to available surgical blocks. The objective is to minimize the patient-related cost as well as the hospital-related cost while respecting the SICU capacity constraints. We propose a two-stage stochastic programming model with recourse to address the studied problem. Sample average approximation is employed to translate the stochastic programming model into a deterministic integer linear programming (DILP) model, which is then solved by column-generation-based heuristic (CGBH) approaches. The CGBH approaches developed in this paper reformulate the DILP model in a column-oriented way and adopt multiple column-generation strategies and heuristic rules to improve computational efficiency. The experimental results illustrate that the proposed CGBH approaches require significantly less computation time than the conventional algorithm, and that the gaps between the resulting near-optimal solutions and the exact ones are below 1%. Moreover, numerical experiments carried out with large test problems validate the capability of the CGBH approaches in solving realistically sized cases.

中文翻译：

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具有下游容量约束的随机手术调度的基于列生成的启发式方法

摘要 本文解决了由多个手术室 (OR) 和下游外科重症监护病房 (SICU) 组成的手术室中的提前手术安排问题。考虑了手术持续时间和术后住院时间的不确定性。决定每周进行一次，由三部分组成：确定要打开的手术区、从等候名单中选择要进行的手术以及将选定的手术分配给可用的手术区。目标是在尊重 SICU 容量限制的同时，最大限度地减少与患者相关的成本以及与医院相关的成本。我们提出了一个两阶段随机规划模型，可以求助于解决所研究的问题。样本平均近似用于将随机规划模型转换为确定性整数线性规划 (DILP) 模型，然后通过基于列生成的启发式 (CGBH) 方法求解。本文开发的 CGBH 方法以面向列的方式重新制定 DILP 模型，并采用多种列生成策略和启发式规则来提高计算效率。实验结果表明，所提出的 CGBH 方法所需的计算时间明显少于传统算法，并且所得接近最优解与精确解之间的差距低于 1%。此外，对大型测试问题进行的数值实验验证了 CGBH 方法在解决实际大小案例方面的能力。