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 20% 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：我们研究了一类由择期与急诊患者共享手术室的医院择期手术规划问题。该问题可分为两个独立阶段：首先需从待手术患者中筛选出下一规划周期的手术对象，并为入选患者分配手术时段及预估开始时间；随后在在线阶段中，通过决策策略安排急诊患者的手术插入，并可能取消已规划的手术。整体目标是最小化患者-时段分配、手术取消、超时、等待时间及空闲时间等成本函数的期望值。我们将离线问题建模为两阶段随机规划，并证明第二阶段成本可被一种在预处理阶段计算出的凸分段线性代理模型替代。由此得到的混合整数规划模型即便面对大规模问题实例，也能在短时间内求解。此外，我们提出了一种适用于在线阶段的贪心策略，并通过与启发式方法及基于样本均值近似（SAA）的方法在大量基准实例上进行对比分析。仿真结果表明：相较于启发式方法，本方法可使期望成本降低高达20%，且能在约一分钟内求解含1000名患者的问题；而SAA方法在处理100名患者的问题时，30分钟内仍无法获得近优解。