A Possibilistic Mixed Integer Nonlinear Programming Approach in Solving the Fuzzy Facility Location – Allocation Problem

In this paper, Fuzzy Facility Location-Allocation (FLA) problem is proposed in which customers have fuzzy demands in nature. In the real world problems, such as disaster situations, demands will be occurred with different possibility degrees. Therefore, developing more applicable models will result to the better decisions made by the Decision Makers. To construct the problem, a possibilistic model based on experts’ views is proposed. The proposed model is formulated as a fuzzy mixed integer nonlinear programming in which decision variables are obtained as fuzzy numbers. Because of the complexity of solving the developed model and also in order to infer the optimum or near optimum values for location and allocation variables, a new Fuzzy Logic Controller is designed based on the resulting fuzzy decision variables. Finally, the efficiency of the proposed model is demonstrated by a numerical example.