a new hybrid algorithm to optimize stochastic-fuzzy capacitated multi-facility location-allocation problem

facility location-allocation models are used in a widespread variety of applications to determine the number of required facility along with the relevant allocation process. in this paper, a new mathematical model for the capacitated multi-facility location-allocation problem with probabilistic customer's locations and fuzzy customer’s demands under the hurwicz criterion is proposed. this model is formulated as α-cost minimization model according to different criteria. since our problem is strictly np-hard, a new hybrid intelligent algorithm is presented to solve the stochastic-fuzzy model. the proposed algorithm is based on a vibration damping optimization (vdo) algorithm which is combined with the simplex algorithm and fuzzy simulation (sfvdo). finally, a numerical example is presented to illustrate the capability of the proposed solving methodologies.