Heuristics Based on Genetic Algorithms for the Capacitated Multi Vehicle Production Distribution Problem

In this paper, we consider the integration of production, inventory and distribution decisions in a supply chain composed of one production facility supplying several retailers located in the same region. The supplier is far from the retailers compared to the distance between retailers. Thus, the traveling cost of each vehicle from the supplier to the region is assumed to be fixed and there is a fixed delivery (service) cost for each visited retailer. The objective is to minimize the sum of the costs at the production facility and at the retailers. The problem is more general than the One-Warehouse Multi-Retailer problem and is a special case of the Production Routing Problem. Five heuristics based on a Genetic Algorithm are proposed to solve the problem. In particular, three of them include the resolution of a Mixed Integer Program as subproblem to generate new individuals in the population. The results show that the heuristics can find optimal solutions for small and medium size instances. On large instances, the gaps obtained by the heuristics in less than 300 s are better than the ones obtained by a standard solver in two hours.