In this paper, we study the patient planning and surgeon scheduling in the operating room theatre. The problem considers the simultaneous planning of patients and the assignment of time blocks to surgeons so that they can perform the surgery of their patients. The timing and length of the allotted time blocks depend on the patient characteristics on the surgeons’ waiting lists. Solving this problem in an exact manner is challenging due to the large number of rooms, surgeons, and patients involved. To overcome this challenge, we propose an efficient branch-price-and-cut algorithm to find an optimal solution in an acceptable time span. For that purpose, we include different dedicated mechanisms to accelerate the solution-finding process. In this regard, the branch-price-and-cut tree is set up using an intelligent branching scheme, the nodes are searched in order of the lowest number of fractional variables, and improved bounds are computed to prune nodes earlier. To tighten the convex hull of the linear programming relaxation in each node, the algorithm relies on a row generation mechanism for adding valid inequalities. We conducted various computational experiments to demonstrate the performance of our algorithm and validate for each component the contribution of the implemented optimisation principles. Additionally, we show the superior performance of the proposed algorithm to alternative optimisation procedures.

中文翻译：

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专用的 branch-price-and-cut 算法，用于提前患者计划和外科医生调度


在本文中，我们研究了手术室手术室中的患者计划和外科医生调度。该问题考虑了患者的同步计划和为外科医生分配时间块，以便他们可以为患者进行手术。分配时间段的时间和长度取决于外科医生等待名单上的患者特征。由于涉及大量的房间、外科医生和患者，以精确的方式解决这个问题是具有挑战性的。为了克服这一挑战，我们提出了一种高效的 branch-price-and-cut 算法，以在可接受的时间跨度内找到最佳解决方案。为此，我们提供了不同的专用机制来加速解决方案查找过程。在这方面，使用智能分支方案设置 branch-price-and-cut 树，按最小分数变量数的顺序搜索节点，并计算改进的边界以更早地修剪节点。为了收紧每个节点中线性规划松弛的凸包，该算法依赖于行生成机制来添加有效的不等式。我们进行了各种计算实验，以证明我们的算法的性能，并验证每个组件所实施的优化原则的贡献。此外，我们展示了所提出的算法优于替代优化程序的性能。