Optimizing a multi-objective master surgical scheduling under probabilistic length of stay and demand uncertainty

The Master surgical scheduling (MSS) program is used at the tactical level of operating room scheduling, and its optimal creation can reduce the waiting queue of patients, as well as hospital costs. The patients’ length of stay (LOS) has a great impact on the downstream resources management. The uncertain nature of LOS and surgeries demand increases the challenges of MSS creation. The aim of the article is to determine the MSS program integrated with combination of surgical operations of each block of the operating rooms. For this purpose, a novel mathematical model was proposed for multi-objective MSS problems with a probabilistic LOS. Then, the chance-constrained programming method was employed to cope with the uncertain demands. The ε-constraint method was used for small-scale problems. Moreover, two metaheuristic algorithms including the multi-objective gray wolf optimizer (MOGWO) and the non-dominated sorting genetic algorithm-II (NSGAII) were designed to deal with large-scale problems. Based on the results, the MOGWO outperforms the NSGAII in terms of both the MID measure and the run time. The sensitivity analysis on the capacity of the wards parameter at different levels of demand uncertainty was performed to help managers to decide about the appropriate capacity of the wards.