Stochastic optimization approaches for elective surgery scheduling with downstream capacity constraints: Models, challenges, and opportunities

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.