A python library with implementations of 15 classical heuristics for the capacitated vehicle routing problem. The cvrp is a variant of the vehicle routing problem characterized by capacity constrained vehicles. In the cvrp, a fleet of capacitated vehicles located at a central depot are used to deliver products to a set of geographically dispersed customers with known. That is, cvrp is like vrp with the additional constraint that every vehicles must have uniform capacity of a single commodity. The classical capacitated vehicle routing problem cvrp, as introduced by dantzig and ramser 1959, is concerned with the determination of routes for a. 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. In this paper, we study the capacitated vehicle routing problem and address it by the minmaxmin robust approach. Dynamic vehicle routing for relief logistics in natural disasters 071 chefu hsueh, hueykuo chen and hueywen chou 6. Previous work on exact solutions to the capacitated vehicle routing problem on trees is sparse. This difficult combinatorial problem contains both the bin packing problem and the traveling salesman problem tsp as special cases and conceptually lies at the intersection of these two. Pdf capacitated vehicle routing problem model for carriers. A matheuristic for the electric vehicle routing problem. Revised december 17, 2001 abstract we consider the vehicle routing problem, in which a. This paper presents an algorithm that combines both approaches.
It is a problem to design a set of vehicle routes in which a. The capacitated vehicle routing problem cvrp is one of the most popular routing problems. Instructions for each problem for this problem, you have five trucks. The vehicle starts from one of the depots and after visited the customers must return to the same depot. The vehicle routing problem vrp is a combinatorial optimization and integer programming problem seeking to service a number of customers with a fleet of vehicles. The algorithm is tested on a number of benchmark problems with encouraging results. The twoechelon capacitated vehicle routing problem 2ecvrp is a twolevel distribution system where the deliveries to customers from a depot are managed through intermediate capacitated depots, called satellites. Gis based solution of multidepot capacitated vehicle routing. The dynamic vehicle routing problem dtu research database. In the literature, many di erent variants of the vehicle routing problem were presented laporte 1992, toth and vigo 2014. The aim is to plan tours for vehicles to supply a given number. New benchmark instances for the capacitated vehicle routing. Modeling and solving the capacitated vehicle routing.
The vrp is concerned with the determination of the optimal routes used by a fleet of vehicles, based at one or more depots, to serve a set of customers. This chapter considers the cvrp on trees tcvrp, a problem that often naturally arises in railway, river, and rural road networks. Models, relaxations and exact approaches for the capacitated. It first appeared in a paper by george dantzig and john ramser in 1959, in which first algorithmic. This problem is modeled as a capacitated vehicle routing problem to improve the distribution efficiency and is extended to capacitated vehicle routing problem with time windows to increase customer service quality. Let ibe the set of customers that need to be served and fthe set of charging stations css at which the vehicles can stop to recharge their battery. Heuristic methods for capacitated vehicle routing problem priyanka lal, dr. On cvrp instances with up to 297 customers our approach signi. It is the most common studied combinatorial optimization problem in transport and logistics. The depot is the same for all vehicles and doesnt need to be serviced. On the capacitated vehicle routing problem springerlink. Introduction in the capacitated vehicle routing problem cvrp, we are given a eet of vehicles with identical capacity located at a depot and a set of customers with known demands located on the vertices of a graph. A hybrid solution method for the capacitated vehicle. Robust branchandcutandprice for the capacitated vehicle.
Introduction the capacitated vehicle routing problem cvrp is one of the variants of the classical vehicle routing problem vrp. The goal of many arc routing problems is to produce a route with the minimum amount of dead mileage, while also fully encompassing the edges required. Modeling and solving the capacitated vehicle routing problem. Human solutions to the capacitated vehicle routing problem. The capacitated vehicle routing problem, which is been consider in this research, is one of the variants of the vehicle routing problem. Solving the heterogeneous capacitated vehicle routing. Among the various types of vrps, capacitated vehicle routing problem. Draw five routes that visit each and every one of the sites starting from the depot the green dot, making sure that each truck returns to. Pdf capacitated vehicle routing problem abdullahi adinoyi. New benchmark instances for the capacitated vehicle.
The most important step was to find an intuitive way to map this optimization problem to a qubo problem that could then be embedded on the quantum annealer. Oct 12, 2005 the best exact algorithms for the capacitated vehicle routing problem cvrp have been based on either branchandcut or lagrangean relaxationcolumn generation. The objective is to design a set of minimum cost paths for each vehicle in order to serve a given set of customers. Both of these problems are deceptively simple to state, but are rather complex mathematically. Bertsimas garrett van ryzin t march, 1991 abstract in 9 we introduced and analyzed a model for stochastic and dynamic vehicle routing in which a single, uncapacitated vehicle traveling at a constant velocity in a. Gis based solution of multidepot capacitated vehicle. The capacitated vehicle routing problem with loading. The vehicle routing problem vrp is one of the most studied among the combinatorial optimization problems, due both to its practical relevance and to its considerable difficulty. This difficult combinatorial problem contains both the bin packing problem and the traveling salesman problem tsp as special cases and conceptually lies at the intersection of. Sambandam national institute of industrial engineering, mumbai, india dr. It generalises the wellknown travelling salesman problem tsp. In this version, all vehicles have the same capacity that cannot be exceeded on a tour and clients. Stochastic and dynamic vehicle routing in the euclidean. An exact algorithm for the twoechelon capacitated vehicle.
Capacitated vehicle routing problem with time windows. Neural large neighborhood search for the capacitated vehicle. Solving the capacitated vehicle routing problem with a. Introduction vehicle routing problem vrp has become an integral part in logistic operations which determines optimal routes for several vehicles to serve customers 1.
Our objective is to build highquality models that exploit the tree structure of the problem that can also be easily. Capacitated vehiclerouting problem model for scheduled solid. This paper presents solution techniques for capacitated vehicle routing problem cvrp using metaheuristics. In this article, a hybrid approach for solving the capacitated vehicle routing problem cvrp using dwaves quantum annealing hardware was provided. Furthermore, we show for the cvrp and the sdvrp that. Capacitated vrp cvrp is a vrp in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost. The vehicle routing problem vrp is one of the most optimized tasks studied and it is implemented in a huge variety of industrial applications. Pdf on the capacitated vehicle routing problem william. Sweep clustering and velocity tentative particle swarm optimization i.
The book is composed of three parts containing contributions from wellknown experts. The problem has potential practical applications in realworld routing problems where electric vehicles with fast recharging capabilities may be used for lessthantruckload ltl deliveries in urban areas. The capacitated vehicle routing problem with loading constraints. Capacitated vehicle routing problem solving using adaptive.
The general problem is introduced as a capacitated problem crvrp and a capacitated problem with customer time window constraints crvrp. Capacitated vehicle routing and some related problems. Capacitated vehicle routing problem is divided into set of customers called cluster, and find optimum travel distance of vehicle route. The performance of two simple batching strategies is examined in relation to. Introduction to vehicle routing 16 the vehicle routing problem the vrp is a combinatorial problem whose ground set is the edges of a graph gv,e. Problem descriptions and bat algorithm capacitated vehicle routing problem. Pdf solving the heterogeneous capacitated vehicle routing.
A hybrid solution method for the capacitated vehicle routing. This study proposes a modified particle swarm optimization pso algorithm in a capacitated vehicle routing problem cvrp model to determine the best waste collection and route optimization solutions. There is a total of 446 units to collect, averaging 89 per truck. The capacitated vehicle routing problem cvrp is the most common variant of the vehicle routing problem. Objective of this problem is to minimize the time and distance travelled. Neural large neighborhood search for the capacitated. Cost of transportation of goods and services is an interesting topic in todays society.
Capacitated vehicle routing problems cvrps form the core of logistics planning and are hence of great practical and theoretical interest. Our attention is focused on a variant of vrp, the capacitated vehicle routing problem when applied to natural gas distribution networks. A robust approach to the capacitated vehicle routing. We consider the vehicle routing problem, in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost. Contrary to normal routing problems, which usually involve mapping a route between nodes, arc routing focuses more heavily on the route itself. Multidepot capacitated vehicle routing problem with time window mdcvrptw vehicle routing problem vrp is an important problem in the fields of road transportation, distribution and logistics in the context of delivery of goods or materials located at the central distribution centre depot to geographically scattered customers stores. Applying monte carlo techniques to the capacitated vehicle. Thus, the more waste collection route is optimized, the more reduction in different costs and environmental effect will be. The vehicles have a limited carrying capacity of the goods that must be delivered. Stochastic and dynamic vehicle routing in the euclidean plane. The vehicle routing problem vrp concerns the distribution of goods between depots and customers toth and vigo 2002. Draw five routes that visit each and every one of the sites starting from the depot the green dot, making sure that each truck returns to the depot with no more than 100 units on board. Arc routing is the process of selecting the best path in a network based on the route. The best exact algorithms for the capacitated vehicle routing problem cvrp have been based on either branchandcut or lagrangean relaxationcolumn generation.
Heuristic methods for capacitated vehicle routing problem. Several heuristics are applied to solve these vehicle routing problems and tested in wellknown benchmark. A multistage algorithm for a capacitated vehicle routing. The first part covers basic vrp, known more commonly as capacitated vrp. Euclidean plane with multiple capacitated vehicles dimitris j. Next, the capacitated vehicle routing problem in the presence of time windows dvrptw is examined under varying levels of dynamism. The capacitated vehicle routing problem cvrp is a fundamental problem in combinatorial optimization with wideranging applications in practice 14. 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. Vehicle routing problem, chance constrained programming, stochastic programming with recourse, belief function. Using grey wolf algorithm to solve the capacitated vehicle. Solving the capacitated vehicle routing problem with a genetic algorithm satisfy the deterministic demand of customers from a single depot, such that the total cost is minimised and the capacity and distance restrictions are satisfied. Procedia social and behavioral sciences 62 2012 60 65 wcbem 2012 capacitated vehicle routing problem for multiproduct crossdocking with split deliveries and pickups asefeh hasanigoodarzia, reza tavakkolimoghaddama a.
Capacitated vehiclerouting problem model for scheduled. The capacitated vehicle routing problem a hybrid solution. This study proposes a modified particle swarm optimization pso algorithm in a capacitated vehiclerouting problem cvrp model to determine the best waste collection and route optimization solutions. Evolutionary multitasking in combinatorial search spaces. A matheuristic for the electric vehicle routing problem with. Solution to a capacitated vehicle routing problem using. The vehicle routing problem society for industrial and. 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. The goal of the vehicle routing problem is to find a set of routes for a fleet of vehicles where the.