Branch-and-price algorithms for the Bi-Objective Vehicle Routing Problem with Time Windows
Résumé
This paper presents generic exact methods for the bi-objective vehicle routing problems (BOVRP). The first part explains the BOVRP. Then, an efficient mono-objective solution method used as a component of bi-objective methods is introduced. After that, the methods are presented. The computational evaluation is performed on a specific variant of the VRP, the VRP with time windows (VRPTW). 1 Context The Vehicle Routing Problem was first introduced in 1959 by Dantzig and Ramser [3] which aimed to minimize the cost of gasoline transportation between a bulk terminal and several service stations. The bi-objective VRP with time windows (BOVRPTW) is a variant of the VRP. Let G = (V, E) be a non-oriented graph. A node i ∈ V \v 0 is called a customer and has a demand q i. These demands are satisfied by a fleet of K vehicles of capacity Q. A vehicle k starts and returns at a node v 0 called the depot and performs a route r k by passing through a set of customers. The route r k is said to be feasible if each customer i served by the route is visited between the due time dt i and the end time et i and if the total capacity of a vehicle is not exceeded.
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