A Vehicle Routing Problem with Time Windows Subject to the Constraint of Vehicles and Good’s Dimensions

Abstract

A vehicle routing problem (VRP) can be defined as a problem finding the optimal route to minimize the travel distance, time, and cost used in a distribution process. A VRP with time windows, also known as a Time Window Priority Model (TWPM), prioritizes time windows using mathematical modeling so that vehicles would not be delayed at any point during the distribution process. Scant literature exists discussing TWPMs subject to load carrying capacity. They only consider the vehicle container volume and the volume of items being carried, arbitrarily assigning 90% of the vehicle’s capacity, which leads to a large, unused capacity. The utilization of capacity, defined as the ratio of the actual weight of the items being transported to the maximum weight of the total items with full capacity, is an important factor for efficient transportation. We believe that the vehicle’s capacity can be increased when considering the actual dimensions of goods (i.e., their lengths, widths, and heights), as well as the dimensions of the vehicle’s containers. This study considers a three-dimensional loading constraint—length, width, and height—of both items and vehicles. Based on the study results, it can be concluded that taking into account the actual dimensions of items and containers in the capacity constraint increases the utilization of vehicles. Moreover, in some cases, the total travel distance and the total number of routes can be reduced.