We study the elective surgery planning problem in a hospital with operation rooms shared by elective and emergency patients. This problem can be split in two distinct phases. First, a subset of patients to be operated in the next planning period has to be selected, and the selected patients have to be assigned to a block and a tentative starting time. Then, in the online phase of the problem, a policy decides how to insert the emergency patients in the schedule and may cancel planned surgeries. The overall goal is to minimize the expectation of a cost function representing the assignment of patient to blocks, case cancellations, overtime, waiting time and idle time. We model the offline problem by a two-stage stochastic program, and show that the second-stage costs can be replaced by a convex piecewise linear surrogate model that can be computed in a preprocessing step. This results in a mixed integer program which can be solved in a short amount of time, even for very large instances of the problem. We also describe a greedy policy for the online phase of the problem, and analyze the performance of our approach by comparing it to either heuristic methods or approaches relying on sampling average approximation (SAA) on a large set of benchmarking instances. Our simulations indicate that our approach can reduce the expected costs by as much as 30% compared to heuristic methods and is able to solve problems with $1000$ patients in about one minute, while SAA-approaches fail to obtain near-optimal solutions within 30 minutes, already for $100$ patients.

翻译：我们研究了医院共享手术室中择期手术与急诊手术共存的排程问题。该问题可分为两个不同阶段：首先需从待手术患者中选择下一计划周期内接受手术的子集，并为所选患者分配手术时段及预估开始时间；随后在在线阶段，需制定策略决定如何将急诊患者插入排程，并可能取消已计划的手术。整体目标是最小化包含患者时段分配、手术取消、超时、等待时间和闲置时间的成本函数的期望值。我们通过两阶段随机规划对离线问题进行建模，并证明第二阶段成本可用预处理阶段计算出的凸分段线性替代模型替换。由此得到的混合整数规划问题即便面对超大规模实例也能在短时间内求解。我们还描述了在线阶段的贪心策略，并通过与启发式方法或基于样本均值近似（SAA）的方法在大规模基准测试实例上的对比分析，评估了所提方法的性能。仿真结果表明，相较于启发式方法，我们的方法可预期降低高达30%的成本，并能在一分钟内解决包含1000名患者的排程问题；而SAA方法在仅处理100名患者时，已无法在30分钟内获得近优解。