1. An Overview of Vehicle Routing Problems

Abstract
1.1 Introduction The last decades have seen an increasing utilization of optimization packages, based on Operations Research and Mathematical Programming techniques, for the effective management of the provision of goods and services in distribution systems. The large number of real-world applications, both in North America and in Europe, have widely shown that the use of computerized procedures for the distribution process planning produces substantial savings (generally from 5% to 20%) in the global transportation costs. It is easy to see that the impact of these savings on the global economic system is significant. Indeed, the transportation process involves all stages of the production and distribution systems and represents a relevant component (generally from 10% to 20%) of the final cost of the goods. The success of the utilization of Operations Research techniques is due to the development of computer systems, from both the hardware and the software points of view, and to the increasing integration of information systems into the productive and commercial processes. A different factor of success, as important as the others, is the development of modeling and algorithmic tools implemented in recent years. Indeed, the proposed models take into account all the characteristics of the distribution problems arising in real-world applications, and the corresponding algorithms and computer implementations find good solutions for real-world instances within acceptable computing times. In this book, we consider only the problems concerning the distribution of goods between depots and final users (customers). These problems are generally known as Vehicle Routing Problems (VRPs) or Vehicle Scheduling Problems.