Facility location problems with fuzzy demands based on parametric assessment

Abstract

We discuss uncertainty included in demands in facility location problem in this paper. The uncertain demand is named as fuzzy demand in the paper. In the facility location model, the parameters of fuzzy demand are determined by calculating the estimated expected value of the fuzzy demand, which is obtained by using estimated parameters of underlying probability distribution function of fuzzy data. Moreover, we propose a defuzzification formula of the fuzzy demand named a realization of fuzzy demand. The defuzzification formula of fuzzy demand composes the upper bound of fuzzy demand and the lower bound of fuzzy demand. Moreover, an error of fuzzy demand is assessed as mean absolute percentage error of fuzzy demand. Empirical studies show that we can solve the real-life location problem by using the defuzzification formula of fuzzy demand and get higher profit in our facility location model than conventional methods.