A queuing location-allocation model for a capacitated health care system

The aim of the present paper is to propose a location-allocation model for a capacitated health care system. this paper develops a discrete modeling framework to determine the optimal number of facilities among candidates and optimal allocations of the existing customers to operating health centers in a coverage distance. in doing so, the total sum of customer and operating facility costs is minimized. our goal is to create a model that is more practical in the real world. therefore, setup costs of hospitals are based on the costs of customers, xed costs of establishing health centers, and costs based on the available resources in each level of hospitals. in this paper, the idea of hierarchical structure has been used. there are two levels of service in hospitals, including low and high levels, and sections at di erent levels that provide di erent types of services. the patients refer to di erent sections of the hospital according to their requirements. to solve the model, two meta-heuristic algorithms, including genetic and simulated annealing algorithms and their combination, are proposed. to evaluate the performance of the three algorithms, some numerical examples are produced and analyzed using the statistical test in order to determine which algorithm works better.