A Hybrid Greedy Algorithm for the Capacitated Vehicle Routing Problem

Abstract

The Vehicle Routing Problem (VRP) is one of the most common problems in logistics and supply chain. In this study, we propose a hybrid greedy algorithm for the capacitated vehicle routing problem (CVRP) which is a variant of the VRP with vehicle capacity constraint. The algorithm adapts the minimal spanning tree algorithm to decompose the CVRP into many smaller traveling salesman problems (TSPs), and solves each sub-problem by using the Nearest Neighbor (NN) greedy algorithm. The hybrid algorithm is tested by using instances from the CVRPLIB library. The algorithm provides relatively good performances with optimality gaps varying from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$4-30 \%$</tex> across all tested instances, and the computational time is less than 1 second in all cases.