Operating room (OR) scheduling is an important operational problem for most hospitals. Uncertainty in the surgery delivery process, the existence of multiple resources and competing performance criteria are among the important aspects of OR scheduling problems in practice. Considering these aspects, this dissertation focuses on developing and efficiently solving novel stochastic programming models for multi-OR scheduling problems under uncertainty in surgery durations.

We first consider a stochastic multi-OR scheduling problem with multiple surgeons where the daily scheduling decisions are made before the resolution of uncertainty. We formulate the problem as a two-stage stochastic mixed-integer program that minimizes the sum of the fixed cost of opening ORs and the expected overtime and surgeon idling cost. Decisions in our model include the number of ORs to open, the allocation of surgeries to ORs, the sequence of surgeries in each OR, and the start times for surgeons. Realistic-sized instances of our model are difficult or impossible to solve with standard stochastic programming techniques. Therefore, we exploit several structural properties of our model and describe a novel set of widely applicable valid inequalities to achieve computational advantages. We use our results to quantify the value of capturing uncertainty and the benefit of pooling ORs, and to demonstrate the impact of parallel surgery processing on surgery schedules.

We then consider a stochastic multi-OR scheduling problem where the initial schedule is revised at a prespecified rescheduling point during the surgical day. We formulate the problem as a three-stage stochastic mixed-integer program that minimizes the sum of the fixed cost of opening ORs and the expected overtime cost. The number of ORs to open and the allocation of surgeries to ORs are the first-, and the revisions on the allocation of surgeries to ORs are the second-stage decisions in our model. For our computational study, we consider a special case, which is a two-stage stochastic mixed-integer program, where rescheduling decisions are made under perfect information. We use stage-wise and scenario-wise decomposition methods to solve our model. By using our results, we estimate the value of rescheduling, and illustrate the impact of different surgery sequencing rules on this value.

Keywords: operating room scheduling, operating room rescheduling, operating room pooling, parallel surgery processing, multiple operating rooms, two-stage stochastic mixed-integer programming, multi-stage stochastic mixed-integer programming.