We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, entire range of tour capacity. The result extends to splittable CVRP.

This paper presents a hybrid approach that aims at solving the Capacitated Vehicle Routing Problem (CVRP) by means of combining Constraint Programming (CP) with Lagrangian Relaxation (LR) and Probabilistic Algorithms. After introducing the CVRP and reviewing the main literature on this area, the paper proposes the use of a multistart hybrid Variable Neighbourhood Search (VNS) algorithm. This al...

This paper describes a new method for solving the Capacitated Vehicle Routing Problem (CVRP). The CVRP is defined as the problem of delivering goods from a depot to a number of customers with a fleet of capacitated vehicles, minimizing the cost of distributing the goods while respecting the capacity constraints of the vehicles. We have developed a method based on Monte Carlo Simulation (MCS) an...

The Capacitated Vehicle Routing Problem (CVRP) is a combinatorial optimization problem where a fleet of delivery vehicles must service known customer demands from a common depot at a minimum transit cost without exceeding the capacity constraint of each vehicle. In this paper, we present a meta-heuristic approach for solving the CVRP based on simulated annealing. The algorithm uses a combinatio...

The Vehicle Routing Problem (VRP) is an hard and very well-known combinatorial optimization problem which finds many practical applications in the design and management of distribution systems. The VRP is concerned with the design of the optimal routes used by a fleet of identical vehicles stationed at a central depot to serve a set of customers with known demands. In the basic version of the p...

This paper proposes a flexible solution methodology for solving the Vehicle Routing Problem with Stochastic Demands (VRPSD). The logic behind this methodology is to transform the issue of solving a given VRPSD instance into an issue of solving a small set of Capacitated Vehicle Routing Problem (CVRP) instances. Thus, our approach takes advantage of the fact that extremely efficient metaheuristi...

A well known transformation by Pearn, Assad and Golden reduces a Capacitated Arc Routing Problem (CARP) into an equivalent Capacitated Vehicle Routing Problem (CVRP). However, that transformation is regarded as unpractical, since an original instance with r required edges is turned into a CVRP over a complete graph with 3r + 1 vertices. We propose a similar transformation that reduces this grap...

This paper presents the SR-GCWS-CS probabilistic algorithm that combines Monte Carlo simulation with splitting techniques and the Clarke and Wright savings heuristic to find competitive quasi-optimal solutions to the Capacitated Vehicle Routing Problem (CVRP) in reasonable response times. The algorithm, which does not require complex fine-tuning processes, can be used as an alternative to other...

We investigate a robust approach for solving the capacitated vehicle routing problem (CVRP) with uncertain travel times. It is based on the concept of K-adaptability, which allows to calculate a set of k feasible solutions in a preprocessing phase. Once a scenario occurs, the corresponding best solution may be picked out of the set of candidates. The aim is to determine the k candidates such th...

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard...