A fuzzy goal programming approach for facility location problem (case study: Service providers)

Location problems are usually known as multi-dimensional problems in particular when sustainable development planning is required, so multi-criteria approaches are appropriate techniques for solving location problems. Since small percentage of studies carried out in this area, a three-stage multi-objective goal programming model has been presented based on fuzzy definition techniques for formulation facility location problem. In the first step, several criteria have been considered for selecting service providers. Then using linguistic variables which are convertible to triangular fuzzy numbers, the importance weights of criteria and the evaluation of alternatives are determined through a survey conducted based on the viewpoints of decision makers. Finally, the computed compromise indexes are used 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.