A Hybrid Algorithm for Solving Location and Routing Multi-Commodity Problems with Cross-Docking in the Supply Chain

Location-Routing problem with Cross-docking is as a New Research Area for Distribution Networks in The supply chains. The purpose of this paper is to simultaneously design a location for cross-docking center and routing vehicles due to the system cost minimization which, is known as an NP-hard problem. This paper presents a two-stage mixed-integer programming (MIP) model for the location-routing multi-commodity problem with cross-docking due to potential applications in the distribution networks. The principal innovation of this paper includes multiple commodities and its solution method as a hybrid algorithm based on the artificial immune system (AIS) and artificial fish swarm (AFS) algorithms. Also, assumptions are given in the proposed model that distinguishes it from the models are presented in this area. Finally, to evaluate the efficiency of the proposed algorithm small and large-scale test problems are randomly generated and the proposed MIP model solved by artificial immune system (AIS) and artificial fish swarm (AFS) and a sample algorithm and then compared with each other. The computational results for different problems show that the proposed hybrid algorithm performs well and converges fast to reasonable solutions.