The capacitated vehicle routing problem (CVRP) is an interesting combinatorial optimization task, which occurs frequently in real-world applications [28]. The problem deals with scheduling a fleet of vehicles to distribute goods between depots and customers. A set of routes for vehicles should be determined, which are in some sense optimal, e.g. the shortest or the cheapest. Certain constraints...

As unmanned aerial vehicle (UAV) technology improves, it will become increasingly efficient to use UAVs as part of package delivery networks. However, while the vehicle routing problem (VRP) is well studied, studying routing on a system of drones that can near-instantaneously transmit information about position, held packages, and destination while also able to near-instantaneously recieve new ...

The problem of finding a Capacitated Minimum Spanning Tree asks for connecting a set of client nodes to a root node through a minimum cost tree network, subject to capacity constraints on all links. This paper reports on our design, implementation and performance evaluation of a hybrid Ant Colony Optimization algorithm for finding Capacitated Minimum Spanning Trees. Our Ant Colony Optimization ...

The single vehicle routing problem with multiple routes is a variant of the vehicle routing problem where the vehicle can be dispatched to several routes during its workday to serve a number of customers. In this paper we propose a goal programming model for multi-objective single vehicle routing problem with time windows and multiple routes. To solve the model, we present a heuristic method wh...

This work deals with the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). We propose undirected and directed two-commodity flow formulations, which are based on the one developed by Baldacci, Hadjiconstantinou and Mingozzi for the Capacitated Vehicle Routing Problem. These new formulations are theoretically compared with the one-commodity flow formulation proposed by Dell...

The Capacitated m-ring-star Problem is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some Steiner point present in a route. We develop a new exact algorithm for this problem using a branch-and-cut-and-price approach and compare its performance with that of a branch-and-cut algorithm pro...

We consider the capacitated vehicle routing problem (VRP): a fixed fleet of delivery vehicles of uniform capacity must service at minimal transit cost from a common depot known customer demand for a single commodity. This problem is modeled as a side-constrained traveling salesman problem (TSP). Among the additional constraints are the vehicle capacity restrictions, analogous to TSP subtour eli...

This article introduces a new exact algorithm for the capacitated vehicle routing problem with stochastic demands (CVRPSD). The CVRPSD can be formulated as a set partitioning problem and it is shown that the associated column generation subproblem can be solved using a dynamic programming scheme. Computational experiments show promising results. © 2007 Elsevier B.V. All rights reserved.

This article introduces a new exact algorithm for the Capacitated Vehicle RoutingProblem with Stochastic Demands (CVRPSD). The CVRPSD can be formulated as a SetPartitioning Problem and it is shown that the associated column generation subproblemcan be solved using a dynamic programming scheme. Computational experiments showpromising results.

The most studied combinatorial optimization problem in transport and logistics is the vehicle routing problem (VRP). The goal of the vehicle routing problem is to nd a set of routes for a eet of vehicles which optimises the objective function (e.g. total distance, routing costs). Every demand needs to be ful lled and vehicle capacities need to be respected. Many solution methods exist for the '...