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
