Comparing Two-Echelon and Single-Echelon Multi-Objective Capacitated Vehicle Routing Problems

Abstract

This paper aims to compare a two-echelon and a single-echelon distribution system. A mathematical model for the Single-Echelon Capacitated Vehicle Routing Problem (SE-CVRP) is proposed. This SE-CVRP is the counterpart of Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) introduced in the authors' previous work. The proposed mathematical model is Mixed-Integer Non-Linear Programming (MINLP) and minimizes 1) the total travel cost, 2) total waiting time of customers, and 3) total carbon dioxide emissions, simultaneously, in distributing perishable products. Applying some linearization methods changes the MINLP model into the Mixed Integer Linear Programming (MILP). In 2E-CVRP, shipments are delivered to customers by using intermediate depots named satellites while in SE-CVRP, direct shipments are used. Considering SE-CVRP, it was assumed that, by eliminating satellites, the large vehicles in depot were used for distribution. Because of the NP-hardness of the Vehicle Routing Problem (VRP) and its extensions, the NSGA-II algorithm was applied to solve the model. The objective functions of both distribution systems were compared in different size issues. The obtained results indicated that by considering large vehicles in an SE-CVRP, this distribution system would outperform the two-echelon one for all objectives of the small-size problems, the first two objectives of medium-size problems, and the first and third objectives of large-size problems.