A generic verbal definition of the family of vehicle routing problems can be the following:Given: A set of transportation requests and a fleet of vehicles.The problem is then to find a plan for the following:Task: Determine a set of vehicle routes to perform all (or some) transportation requests with the given vehicle fleet at minimum cost; in particular, decide which vehicle handles which requests in which sequence so that all vehicle routes can be feasibly executed.In this type of problem, subsumed under the term Vehicle Routing Problem (VRP), the transportation requests to be served are generally concentrated in specific points of a road network as opposed to the Arc Routing Problems (ARP; see the companion book by Corberán and Laporte [35]), where the requests are dispersed along the arcs, i.e., street segments of the underlying road network. The following sections will shed light on the basic VRP components, which are the transportation requests and how they can be performed, the fleet of vehicles, the related costs and profits (if relevant), and the feasibility of routes.Before going into the details, however, we discuss the economic relevance of computersupported vehicle routing. Indeed, the large number of real-world applications have widely shown that the use of computerized solution methods for the solution of VRP, both at the planning and the operational levels, yields substantial savings in the global transportation costs. The success of the utilization of optimization techniques is due not only to the power of the current computer systems and to the full integration of the information systems into the operations and commercial processes, but it can also be attributed to the development of rigorous mathematical models, which are able to take into account al-1 Downloaded 12/15/14 to 132.236.27.111. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 2 Chapter 1. The Family of Vehicle Routing Problems most all the characteristics of the VRP arising in real-world applications. Furthermore, the corresponding algorithms and their computer implementations (software tools) play an essential role in finding high-quality feasible solutions for real-world instances within acceptable computing times. Compared to procedures not based on optimization techniques, significant cost savings and a better utilization of the vehicle fleet can be achieved. In addition, by means of such planning software it is possible to improve the automation, standardization, and integration into the organizations' overall planning processes, leading to less time-consuming and more cost-efficient planning processes with respect to manual planning. Moreover, computerized planning allows planners to compare several different planning scenarios, and herewith to choose a best one through a careful and fast evaluation of cost and service-related performance indicators.In the last years, software tools integrating telematics services (electronic data transmission between vehicles and planners) have b...