Elective surgery patients have surgery in the operating room (OR), and then recover in one or more downstream recovery units for several consecutive hours or days after surgery. Upstream scheduling that focuses on OR alone or a resource-constrained scheduling approach that fails to account for the inherent uncertainty in surgery durations and postoperative downstream recovery times yield sub-optimal or infeasible schedules and, consequently, higher cost and reduced quality of care. However, modeling such uncertainties at multiple levels is challenging, especially with limited reliable data on the random parameters in the models. Moreover, sequencing of surgical and recovery activities, and the multiple conflicting objectives of all parties involved (including management, clinicians, patients), lead to a class of complex combinatorial and multi-criteria stochastic optimization problems. In this review, we focus on stochastic optimization (SO) approaches for elective surgery scheduling and downstream capacity planning. We describe the art of formulating and solving such a class of stochastic resource-constrained scheduling problems, provide an analysis of existing SO approaches and their challenges, and highlight areas of opportunity for developing tractable, implementable, and data-driven approaches that might be applicable within and outside healthcare operations, particularly where multiple entities/jobs share the same downstream limited resources.

择期手术患者在手术室 (OR) 进行手术，然后在手术后连续数小时或数天在一个或多个下游恢复单元中恢复。仅关注 OR 的上游调度或资源受限的调度方法未能考虑手术持续时间和术后下游恢复时间的固有不确定性，会产生次优或不可行的调度，从而导致更高的成本和更低的护理质量。然而，在多个级别对此类不确定性进行建模具有挑战性，尤其是在模型中随机参数的可靠数据有限的情况下。此外，手术和恢复活动的顺序以及所有相关方（包括管理人员、临床医生、患者）的多重冲突目标，导致一类复杂的组合和多准则随机优化问题。在这篇综述中，我们专注于择期手术安排和下游容量规划的随机优化 (SO) 方法。我们描述了制定和解决此类随机资源受限调度问题的艺术，提供对现有 SO 方法及其挑战的分析，并强调开发可能适用的易处理、可实施和数据驱动的方法的机会领域在医疗保健运营内外，尤其是在多个实体/工作共享相同的下游有限资源的情况下。