Optimization and Machine Learning

1Vehicle Routing Problems with Loading Constraints: An Overview of Variants and Solution Methods

Ines SBAI¹ and Saoussen KRICHEN¹

¹Université de Tunis, Institut Supérieur de Gestion de Tunis, LARODEC Laboratory, Tunisia

This chapter combines two of the most studied combinatorial optimization problems, namely, the capacitated vehicle routing problem (CVRP) and the two/three-dimensional bin packing problem (2/3D-BPP). It focuses heavily on real-life transportation problems such as the transportation of furniture or industrial machinery. An extensive overview of the CVRP with two/three-dimensional loading constraints is presented by surveying over 76 existing contributions. We provide an updated review of the variants of the L-CVRP studied in the literature and analyze some of the most popular optimization methods presented in the existing literature. Alongside this, we discuss their variants and constraints, their applications for solving real-world problems, as well as their impact on the current literature.

1.1. Introduction

Although the vehicle routing problem (VRP) is the most studied combinatorial optimization problem, the challenge still remains to achieve the most optimal and effective results (Sbai et al. 2020a). The VRP aims to minimize total traveling cost in cases where a fleet of identical vehicles is used to visit a set of customers. The VRP is used in many real-world applications, for example: pharmaceutical distribution, food distribution, the urban bus problem ...