A Benders decomposition for the location-allocation and scheduling model in a healthcare system regarding robust optimization

The hospital location and service allocation is one of the most important aspects of healthcare systems. Due to lack of studies on covering location-allocation and scheduling problems with respect to the uncertain budget, this paper develops a bi-objective hybrid model to locate hospitals and allocate machines and services scheduled. The costs of establishing facilities are assumed to be uncertain, while a robust counterpart model is employed to overcome the uncertainty. Covering the demand of each service is limited as well. Moreover, hospitals have a limited space to the specialized equipment like CT scan and MRI machines, while there is a cost constraint on hospitals and the specialized equipment. The aim of this paper is to find a near-optimal solution including the number of hospitals and the specialized equipment, the location of hospitals, the assignment of demand of each service and the specialized equipment to hospitals, the determination of allowable number of each service of hospitals, the determination of demand that should be transferred from one hospital to another (patient transfer), and schedule services. As the proposed model, minimizing the total costs and the completion time of demand simultaneously, is an NP-hard problem, it is impossible to solve its large-scale version with exact methods in a reasonable time. Thus, a hybrid algorithm including simulated annealing optimization and the Benders decomposition is employed to solve it. The CPLEX optimizer verifies the presented algorithm to solve the proposed model. The sensitivity analysis is performed to validate the proposed robust model against of uncertain situations while the Monte Carlo simulation is used to analyze the quality and the robustness of solutions under uncertain situations. The results show that the uncertainty used in the proposed model properly formulates real-world situations compared to the deterministic case. Finally, the contributions and the future research are presented.