Si>ecial issue on Rich Vehicle Routing Problems

Editorial The VehJcJe Routing Problem (VRP) is a key to efficient transportation manageincni and supply-chain coordination. In broad terms, it deaJs with the optimal assignment of a set of transportation orders to a fleet of vehicles, and t he sequencing of stops for each vehicle. The VRP has a large number of real-life applications and comes in many guises, depending on the type of operation, the time frame for decision making, the objective, and the types of constraint that must be adhered to. Outside of transportation logistics, the VRP has less intuitive but still important applications, e.g. in robotics and VLSI di«ign. Tbe VRP is a computationally hard, discret« optimization problem. It has been a main subject for thousfmds of rescarcbi-rs since it was introduced by Dantzig and Ramser in 1959. A large variety of optimization and approximation methods have been proposed and studied. Depending on variant and response requirements, exact VRP methods of today have a size limit of 50-100 orders. Hence, there has been much research on algorithms t liui are able to find high quality solutimis in limited time. Our ability to fmd good solutions to practical variants of i lie VRP in a reasonable resjwnse time has increased tremendously since this problem was introduced. Improvements are not only due to a general increase in computing power, but also to substantial advances, both in exact methods and heuristics. VRP research is regarded as one of the great successes of Operations Research. The results have lead to a tool industry in route design and fleet managianent, through which n search results have yielded huge economical and environmental savings. VRP research has often been criticized iar being too focused on idealized models with non-realistic assumptions for practical applications. The methodological evolution has lead to a situation where the classical problems are now more or less regarded as being solved from a pragmat ic point of view. As a result, the research community has turned to variants of the VRP which before were considered too difficult to handle. The variants include aspects of the VRP that are essential to the routing of vehicles in real-life. The family of these extended problems is often called Ricb Vehicle Routing Problems. In addition to the iuii rnal niotivation in the research community alluded to above, the growing tool industry and their end users provide external forces in the direction of richer VRP models. …