Application of variable neighbourhood search method for vehicle-routing problems in an integrated forward and reverse logistic chain

Abstract

A closed-loop problem in which vehicles deliver new products to the consumer and pick up products that have reached the end of their life is considered in this paper. It is assumed that capacities of vehicles and locations are limited. The aim is to minimize the total distances between locations in forward and reverse flow. A new mixed integer programming model (MILP) is presented. For its solution four variants of the variable neighbourhood search (VNS) method are proposed. The vehicle-routing search contains two steps, in which algorithms based on VNS are applied. Four VNS variants are also presented. The problems are solved optimally for a small number of nodes using MATLAB. The effectiveness of the presented model is evaluated with numerical examples.