Vehicle Capacity Planning in a Multi-Objective Vehicle Routing Problem With Heterogeneous Fleet

Carrying goods from points of supply to different customers is an important task in the supply chain. In this regard, the problem of vehicle routing is of particular importance. In this paper, the Vehicle Routing Problem with Time Windows (VRPTW) is presented using the concept of heterogeneities. The concept of heterogeneities is concerned with the ownership of fleet. Ownership heterogeneities occur when the private fleet is not sufficient and the company has to rent some vehicles from freight companies. Moreover, unlike prior attempts to minimize cost by minimizing overall traveling distance, the proposed model incorporates energy minimizing. In this paper, two different scenarios have been analyzed and for each of them a mathematical multi-objective model is proposed. The first scenario investigates VRPTW regardless of the concept of heterogeneity and in the second scenario, there are some rental vehicles provided by freight companies. In senario II, the number of these vehicles, the time of contract and generally their capacity must be specified. Therefore, the strategy of changing the capacity of the rental fleet is determined based on the proposed model. The proposed solution method of this paper is based on a hybrid artificial immune system, artificial fish swarm, and NSGAII. Metaheuristics finally, small and large-scale test problems are randomly generated, solved and compared by those algorithms. The computational results show that using rental fleet significantly saves costs and energy. Also, the proposed model can be used as a decision support system for carriers to investigate capacity strategies.