A sample average approximation approach for an integrated operating room planning and scheduling problem under uncertainty: A real case study

This paper presents a real case of an operating room planning and scheduling problem under stochastic surgery durations and the arrivals of non-elective patients. This problem arises from the Plastic Surgery and Major Burns service at a Spanish hospital. The objective is twofold: (1) to determine the best sequence of patients in each operating room per day to minimize the total expected cost of surgical resources, and (2) to prioritize elective patients with the highest clinical weights (medical priority and waiting time). The service uses a dedicated operating room distribution policy, i.e., each operating room available on a given day within the planning horizon is assigned exclusively to either elective or non-elective patients. To the best of our knowledge, this problem has not been previously reported in the literature. To solve this stochastic problem in practice, we propose a sample average approximation approach that combines a deterministic metaheuristic and Monte Carlo simulation. To decide which deterministic metaheuristic to embed most efficiently in the procedure, we compare a new iterated greedy algorithm with the most promising metaheuristics from the literature. The results show that the proposed iterated greedy metaheuristic is statistically the best method for solving the deterministic version of the problem. Regarding the sample average approximation, the results show that this procedure converges at an exponential rate with the number of samples using real data from the service under study, resulting in an optimality index value of approximately 1.0%. We also analyze the impact of the sample size in solving the real problem, aiming to balance the robustness of the solution and the key performance indicators set by the hospital. Finally, we discuss several managerial insights for the service under study, including a comparison of dedicated and flexible operating room distribution.