Mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy

Abstract

The planning of operating rooms under block strategy is addressed in this study. The decisions are about opening the operating rooms and assigning specialties and surgeons to blocks at the tactical level, and sequencing the surgeries at the operational level. This problem aims to minimize the costs of opening the operating rooms and their overtime, the waiting costs of patients, and the surgeons' idle costs. We propose two mixed-integer linear programming models, a constraint programming (CP) model and a constraint programming-based column generation (CPCG) method for handling the problem. The performance of the models is evaluated by random test instances. The results indicate that CP and CPCG models are more efficient than the linear programming models in terms of computational time, and the number of variables and constraints. The proposed method CPCG generates optimal solutions for problem instances of up to 30 surgeries in less than 4 min. The CP model finds the optimal solutions in about one minute but proving the optimality of the found solutions is time-consuming in some instances. The maximum optimality gap for the proposed two-step linear programming model is 2%, while its run time is less than 20 s. A sensitivity analysis is done on the main parameters of the problem like objectives' weights, opening cost of ORs, unit waiting cost of patients, and the maximum available time in surgery blocks. Among the three objectives, the unit waiting cost of patients has the most sensitivity to variations of the objective function weights.