Vehicle routing and related problems 2 the vehicle routing problem the vrp is a combinatorial problem whose ground set is the edges of a graph gv. The vehicle routing problem covers both exact and heuristic methods developed for the vrp and some of its main. Request pdf on jan 1, 2002, paolo toth and others published the vehicle. Responsibility edited by paolo toth, university of bologna, bologna, italy, daniele vigo, university of bologna, bologna, italy. The vehicle routing problem vrp is a combinatorial optimization and integer programming problem which asks what is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers. J f cordeau et alguide to vehicle routing heuristics 5 metaheuristics are capable of consistently producing high. Although the vehicle routing problem with split deliveries vrpsd is a relaxation of the vrp, it is still nphard dror and trudeau, 1990, archetti et al. They studied a single vehicle darp, in which customer requests are trips from an origin to a destination that appear dynamically. Using congestion zones for solving the time dependent. The pickup and delivery vehicle routing problem, which has also been extensively studied, is covered in the transportation on demand chapter.
Models, relaxations and exact approaches for the capacitated. Lancomme, prins and ramdane 2001 have solved the problem using genetic algorithms. Capacitated vehicle routing and some related problems. The vehicle routing problem vrp is a hard and wellknown combinatorial optimization problem which calls for the determination of the optimal routes used by a fleet of vehicles, based at one or more depots, to serve a set of customers.
The vrp is static in the sense that vehicle routes are computed assuming that no new tasks arrive. Interest in vrp is motivated by its practical relevance as well as its considerable difficulty. The vehicle routing problem is a problem which calls for the determination of the optimal routes used by a fleet of vehicles, based at one or more depots, to serve a set of customers. Problems, methods, and applications, second edition 9781611973587. Problems, methods, and applications, second edition paolo toth, daniele vigo eds. Dec 01, 2001 the vehicle routing problem covers both exact and heuristic methods developed for the vrp and some of its main variants, emphasizing the practical issues common to vrp. The vehicle routing problem vrp is an hard and very wellknown combinatorial optimization problem.
Four variants of the vehicle routing problem chapter 10. Pdf the bees algorithm for the vehicle routing problem. Problems, methods, and applications, second edition. He is author of about 100 papers and book chapters, editor of several journal special issues, and coeditor, with paolo toth, of the vehicle routing problem 2002. Software tools and emerging technologies for vehicle routing and intermodal transportation chapter.
Vrp is a generic name given to a class of problems in which vehicles visit customers and deliver commodities to them, collect commodities from them, or both. The electric fleet size and mix vehicle routing problem with. The vehicle routing problem vrp calls for the determination of the optimal set of routes to be performed by a fleet of vehicles to serve a given set of customers, and it is one of the most important, and studied, combinatorial optimization problems. Over the past decades, the vehicle routing problem vrp and its. The vehicle routing problem request pdf researchgate. Heuristics for the vehicle routing problem part ii. Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts freight distribution and collection, transportation, garbage collection, newspaper delivery, etc. A number of other variants have been treated in recent articles and book chapters see, e. A combination of wellknown algorithms was adapted to the time dependent setting and used to solve the realworld problems. Laporte,o toth and vigo,1 laporte and semet,12 gendreau.
Exact solution of the vehicle routing problem springerlink. The vrp is an important research topic in the operations research community. Martinelli, poggi and subramanian 2011 have posed new bounds for large scale instances. A survey on the vehicle routing problem and its variants. The first part covers basic vrp, known more commonly as capacitated vrp. Defined more than 40 years ago, the problem involves designing the optimal set of routes for fleets of vehicles for the purpose of serving a given set of customers. One of the most often considered aspects of the dvrp is the availability of customers, in which a part or all of the customers are revealed dynamically. Static and stochastic problems are characterized by input partially known as random variables, which realizations are only revealed during the execution of. The vrp is an important combinatorial optimisation problem. He was awarded the first prize of faro competition organized by the italian railways in 1995 with alberto caprara, matteo fischetti, and paolo toth and was a finalist for the. Symmetry free fulltext dynamic vehicle routing problem.
The data are used to predict travel times during certain times of the day and derive zones of congestion that can be used by optimization algorithms. This is justified by the need to avoid the reorganization of the loads inside the vehicles, to reduce the return of the vehicles with empty load and to. The vehicle routing problem covers both exact and heuristic methods developed for the vrp and some of its main variants, emphasizing the practical issues common to vrp. Hence, the use of exact optimization methods may be difficult to. Paolo toth, daniele vigo in the field of combinatorial optimization problems, the vehicle routing problem vrp is one of the most challenging. Models, relaxations and exact approaches for the capacitated vehicle routing problem paolo toth, daniele vigo. Vehicle routing problem wikipedia republished wiki 2. Related work solving and optimizing tour assignments of vehicles is a well known and well studied eld of research, known as vehicle routing problem vrp toth and vigo 2001. The vehicle routing problem vrp formulation was rst introduced by dantzig and ramser 35, as a generalization of the traveling salesman problem tsp.
The electric fleet size and mix vehicle routing problem with time windows and recharging stations gerhard hiermann1, jakob puchinger1 and richard f. Siam monographs on discrete mathematics and applications. It first appeared in a paper by george dantzig and john ramser in 1959, in which first algorithmic. Vehicle routing problems, methods, and applications second edition society for industrial and applied mathematics philadelphia mathematical optimization society. More than 40 years have elapsed since dantzig and ramser introduced the problem in 1959. The vehicle routing problem edited by paolo toth, daniele vigo. The vehicle routing problem vrp, introduced by dantzig and ramserl in 1959, holds a central place in distribution. Feb 26, 2015 he is author of about 100 papers and book chapters, editor of several journal special issues, and coeditor, with paolo toth, of the vehicle routing problem 2002. The vehicle routing problem vrp dates back to the end of the fifties of the last. The basic problem variant is the capacitated vrp cvrp, where each customer has a given demand that has to be satis ed, with.
Toth, paolo and vigo, daniele, editors, vehicle routing. In the field of combinatorial optimization problems, the vehicle routing problem vrp is one of the most challenging. It is adapted from a fairly recent algorithm, the bees algorithm, which was developed for continuous optimisation problems. The vehicle routing problem monographs on discrete. The electric vehicle routing problem with backhauls. Related work solving and optimizing problems involving tour assignments of vehicles is a well known and well studied eld of research, known as vehicle routing problem vrp toth and vigo, 2014. This chapter focuses on some of the most important vehicle routing problem types.
We introduce a package service model where trucks as well as drones can deliver packages. It generalises the wellknown travelling salesman problem tsp. The vehicle routing problem society for industrial and applied. Paolo toth, daniele vigo, paolo toth, daniele vigo. The classical vrp can be formally defined as follows. Cumulative vehicle routing problems 87 q 0 is the initial value of flow from the origin to the first node of the tour in the case of collection, or the final value of flow from the last node of the tour to the origin in the case of the delivery, e. In the classical vehicle routing problem with backhauls vrpb the customers are divided into two sets. Toth and vigo 1999 a heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls see results downloads download dataset download result report template. Applications of the vehicle routing problem chapter 12. The dynamic vehicle routing problem dvrp is one of the most important problems in the area of enterprise logistics. Vigo, the granular tabu search and its application to the vehicle routing problem. Algorithms for the vehicle routing problem paolo toth, daniele vigo d.
The book is composed of three parts containing contributions from wellknown experts. The vehicle routing problem vrp is a combinatorial optimization and integer programming problem that seeks to nd the most e cient utilization and routing of a vehicle eet to service a set of customers subject to constraints. We show that the results obtained by the enhanced bees algorithm are competitive with the best metaheuristics available for the vehicle routing problem within 0. Society for industrial and applied mathematics in the field of combinatorial optimization problems, the vehicle routing problem vrp is one of the most challenging. The electric fleet size and mix vehicle routing problem. Toth, \optimal and canonical solutions of the change making problem, european journal of operational research 4, 1980. Dynamic vehicle routing problempredictive and unexpected. Therefore, the vrptwsd is nphard, since it is a combination of the vehicle routing problem with time windows vrptw and the vehicle routing problem with split delivery. In this thesis we present a new algorithm for the vehicle routing problem called the enhanced bees algorithm. The vehicle routing problem society for industrial and. We present a heuristic algorithm to solve the problem of finding a good schedule for all drones and trucks. The vehicle routing problem vrp is a challenging combinatorial optimization problem with great practical significance.
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