new mathematical modeling for a facilities location and vehicle routing problem solving by a hybrid imperialist competitive algorithm

increasing of the distribution efficiency is one of the most objectives of an integrated logistic system developed as a new management philosophy in the past few decades. the problem is examind in two parts: facilities location problem (flp) for long policies and vehicle routing problem (vrp) to meet the customer demand. these two components can be solved separately; however, this solution may not be the optimum solution of the original problem. hence, in this paper, facilities location and vehicle routing problems are considered simultaniously to visit the facilities that should be serviced. due to the complexity of the integrated problem in large sizes, a hybrid imperialist competitive algorithm (ica) is proposed. furthermore, to show the efficiency of the proposed hybrid ica, a number of test problems in small and large sizes are solved. finally, the obtained results are evaluated with the results obtained by cplex. finally, the conclusion is provided.