Fuzzy Single Facility Goal Location Problems with Asymmetric Penalty Function

In this paper, a fuzzy goal single facility location problem under to asymmetric Linex loss function is discussed. The aim of this paper is to determine the location of a facility center in the ideal radius to each of the demand points. In general, such a response is not always available. Therefore, minimizing the error function obtained from the distance of facility center to the ideal point is desirable. As, in many real-life situations, positive error and negative error of the same size often have different economic and material implications, a asymmetric Linex loss function is used for the first time where distinguishes between positive and negative errors with the same distance. In this paper, first, this problem is first investigated in a definite manner and by proving a theorem it is shown that the problem has a feasible solution and the optimal solution of the problem lies in the expanded rectangular shell of the demand points. In the following, To determine the optimal solution of the problem, a gradient quasi-Weisfield algorithm is presented, and by proposing some theorems, it is shown that this algorithm is convergent to the optimal solution of the problem. Also, to confirm the accuracy of the results obtained from this method, the obtained results are compared with the metaheuristic colonial competition algorithm. Finally, for the first time, the problem is modeled in fuzzy mathematical mode, and using a three-objective genetic algorithm its answers are compared and analyzed with a definite model.