Operating-Room scheduling under uncertainty: balancing elective and emergency surgeries

Balancing elective and emergency surgeries in operating room (OR) scheduling is challenging due to uncertainty in surgery durations and emergency arrivals. Traditional approaches, such as dedicated OR allocation and the Break-in-Moment (BIM) policy, can result in underutilised capacity and high emergency cancellation rates. This paper proposes a two-stage stochastic optimisation model that incorporates endogenous buffer allocation within the OR schedule. Rather than relying on policy-based or heuristically defined buffer times, the proposed framework determines the timing and placement of buffer slots as part of the optimisation process. In the first stage, elective surgeries and buffer placements are jointly determined at the beginning of the week. In the second stage, OR allocations are adjusted in response to realised emergency arrivals and surgery-duration deviations. The model is solved using the Sample Average Approximation (SAA) method and benchmarked against deterministic, perfect-information, and robust optimisation approaches. We validate the model using a synthetic dataset calibrated to real OR data from a public hospital. Computational experiments show that the proposed endogenous buffer-allocation approach achieves significant cost and cancellation reductions compared with all benchmark methods, while closely approaching the idealised perfect-information solution. Results over a six-month period indicate an 18% reduction in total weekly costs, an increase in average OR utilisation from 78% to 84%, and a substantial decrease in emergency cancellations. These findings demonstrate the value of endogenous buffer allocation for improving OR efficiency and responsiveness under uncertainty.