Fuzzy Multi-Period Mathematical Programming Model for Maximal Covering Location Problem

In this paper, a model is presented to locate ambulances, considering backup facility (to increase reliability) and the restriction of ambulance capacity. This model is designed for emergencies. In this model the covered demand for each demand point depends on the number of coverage times and the amount of demand. The demand amount and ambulance coverage radius are consideredfuzzy in various periods, with respect to the conditions and application of the model. Ambulances have the ability to be relocated in different periods. In this model we have considered two types of ambulances to locate: ground and air ambulance. Air ambulances are considered as backup facilities. It is assumed that ground ambulances are major facilities, taking into account capacity limitations. To solve this model, making chromosomes (initial solution) is presented in such a way that location chromosome for both ground and air ambulances are appears as a general chromosome. Since this is a complicated model, apopulation-based simulated annealing algorithm (MultipleSimulated Annealing) with a chromosome combinatorial approach is used to solve it. Finally, the results of the algorithm presented to solve the model are compared with the simulated annealing (SA) algorithm. The results showed that the quality of the presented algorithm (MSA) is better than the SA algorithm.