A clustering algorithm for solving the vehicle routing assignment problem in polynomial time

Abstract

The Vehicle Routing Problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two sub-problems: The first sub-problem is an assignment problem where both the vehicles that will be used as well as the customers assigned to each vehicle are determined. The second sub-problem is the routing problem in which for each vehicle having a number of cus-tomers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles as well as optimal total distance should be achieved. In this paper, an approach for solving the first sub-problem, the assignment problem, is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters. Also, a solution to the assignment problem is provided. The proposed approach was evaluated using Solomon’s C1 benchmarks where it reached optimal number of clusters for all the benchmarks in this category. The proposed approach succeeds in solving the assignment problem in VRP achieving a solving time that surpasses the state-of-the-art approaches provided in the literature. It also provides a means of working with varying num-ber of customers without major increase in solving time. Â