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

A Cross Entropy-Based Heuristic for the Capacitated Multi-Source Weber Problem with Facility Fixed Cost: Cross entropy for continuous location problems

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones