A Fuzzy Goal Programming Approach for Facility Location Problem; Case Study: Service Providers

Location problems are usually known as multidimensional problems in particular when sustainable development planning is required, so multi-criteria approaches seem to be appropriate techniques for solving location problems. Since small percentage of the studies published in this area, a multi-objective goal programming model has been presented based on fuzzy definition techniques for formulation facility location problem. The proposed model consists of three steps. In the first step, several criteria have been considered for selecting service providers for customers. Then utilizing linguistic variables which are convertible to triangular fuzzy numbers and the importance weights of criteria as well as the evaluation of alternatives are determined through a survey conducted based on the viewpoints of decision makers. Finally, the compromise indexes are computed for all alternatives. The computed compromise indexes are then utilized as objective functions coefficients. In the second step, a multi-objective mixed-integer linear programming model has been developed consists of three main objectives including minimizing transportation and fixed costs, minimizing values from assigning service and opening service facilities and eventually maximizing the utility of selected service providers. The above proposed model has been used in a case study and results have been discussed. Results show that the above process is capable for selecting service providers in a multi-dimensional situation while a fuzzy goal programming technique is used for solving the problem of facility location.

Fuzzy goal programming; Multi-objective programming; Facility location problem; Fuzzy theory; Multiple Criteria Decision Making