This paper studies approximations to the average length of Vehicle Routing Problems (VRP) with time window, route duration, and capacity constraints. The approximations are valuable for the strategic and planning analysis of transportation and logistics problems. Using asymptotic properties of vehicle routing problems and the average probability of successfully sequencing a customer with time w...

The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes w...

In this paper, we present an intelligent solution system for a vehicle routing problem (VRP) with rigid time window in urban distribution. The solution has three stages. The first stage uses Clustering Analysis in Data Mining to classify all customers by a number of attributes, such as distance, demand level, the density of customer, and city layout. The second stage introduces how to generate ...

Abstract Suppose that one is given a Vehicle Routing Problem (VRP) on road network, but does not have access to detailed information about network. One could obtain heuristic solution by solving modified version of the problem, in which true distances are replaced with planar Euclidean distances. We test this heuristic, two different types VRP, using real network data for twelve cities across w...

Abstract: The Open Vehicle Routing Problem (OVRP) is one of the most important extensions of the vehicle routing problem (VRP) that has many applications in industrial and service. In the VRP, a set of customers with a specified demand of goods are given and a depot where a fleet of identical capacitated vehicles is located. We are also given the ‘‘traveling costs’’ between the depot and all th...

In this work the development and implementation of a Decision Support System is described. It will assist in the route calculation process and in optimizing the filling of the trucks that have to transport a considerably number of vehicles from near of 8 origins to more than 3,000 possible destinations spread over Spain and Portugal, and some in France, Germany, etc. The problem can be classifi...

Vehicle-routing problems (VRP), which can be considered a generalization of TSP, have been studied in depth. Many variants of the problem exist, most of them trying to find a set of routes with the shortest distance or time possible for a fleet of vehicles. This paper combines two important variants, the stochastic time-dependent VRP and the multi-objective VRP. A genetic algorithm for solving ...

Vehicle Routing Problem (VRP) is a key element of many transportation systems which involve routing of fleet of vehicles from a depot to a set of customers node. It is required that these vehicles return to the depot after serving customers’ demand. This paper investigates a relaxed version of VRP, in which the number of visits to the customer is not restricted to be at most one. The relaxed ve...

The vehicle routing problem (VRP) is a difficult and well-studied combinatorial optimization problem. We develop a parallel algorithm for the VRP that combines a heuristic local search improvement procedure with integer programming. We run our parallel algorithm with as many as 129 processors and are able to quickly find high-quality solutions to standard benchmark problems. We assess the impac...