A mathematical model and two meta-heuristics for location and vehicle routing problem through a two-echelon supply chain

In this research, a three echelon supply chain consisting of production, distribution and sale levels is dealt with. In order to design an efficient supply chain, in addition to optimizing the considered system in a macro level, optimum decisions are desired in lower levels. To this aim, an integrated chain is designed with special regard to transportation planning. In the following, a mathematical model is presented on the basis of the assumptions, constraints and other considerations, adopted from the related literature. The model is presented through a mixed integer non-linear mathematical programming. Then, the non-linear terms are linearized. To solve this problem, Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) are employed. Regarding the obtained results, ICA is not capable of providing acceptable solutions. On the other hand, GA can provide high quality results in less time even for largesized problems.

Keywords:

Supply chain , Genetic algorithm , Imperialistic competitive algorithm , Location routing problem