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 of finding the optimal route with the goal to minimize the travel distance, time, and cost used in a distribution process. A vehicle routing problem with time windows also known as a Time Window Priority Model (TWPM) prioritizes time windows in the mathematical modelling so that vehicles would not delay at any point during the distribution process. There exist few literatures discussing a TWPM subject to carrying capacity. They only consider the volume of vehicle container and the volume of items being carried, arbitrary using 90% of the vehicle’s capacity which causes a large unused capacity. The utilization of capacity which is defined as the ratio the actual weight of the items being transported to the maximum weight of the total items with full capacity, is an important factor for an efficient transportation.  We believe that the utilization of the vehicle’s capacity can be increased when taking into account the actual dimensions of goods, such as their lengths, widths, and heights, as well as the dimensions of the vehicle’s containers. In this study, we consider a 3-dimensional loading constraints i.e. the length, width, and height of both items and vehicles. Based on the results of the study, it can be concluded that taking into account the actual dimensions of items and containers in the capacity constraint increases the utilization of vehicles as well as reduces the total travel distance. Moreover, in some cases the total number of routes can be reduced.

Keywords

• capacity loading constraint
• three-dimensional loading constraint
• time window priority model
• vehicle routing problem