Exact Solution of the Capacitated Vehicle Routing Problem

Abstract

Vehicle routing problem (VRP) is a generic name given to a whole class of problems concerning the optimal design of routes to be used by a fleet of vehicles to serve a set of customers. The VRP generalizes one of the most famous and important combinatorial optimization problems: the traveling salesman problem (TSP). Since it was first proposed by Dantzig and Ramser in 1959, hundreds of papers in the areas of operations research were devoted to the exact and approximate solution of a member of the VRP class, known as the capacitated vehicle routing problem (CVRP), where a homogeneous fleet of vehicles is available and the only constraint considered is the vehicle capacity constraint. Real‐world applications of the VRP are, for instance, delivery and collection of goods, solid waste collection, street cleaning, school bus routing, dial‐a‐ride systems, transportation of handicapped persons, and routing of salesmen and of maintenance units. This article provides a review of the developments that had a major impact in the current state‐of‐the‐art of exact algorithms for the CVRP. The paper also reports a comparison of the computational performances of the recent exact methods.

Linear Programming Optimization Techniques for Addis Ababa Public Bus Transport

“…The VRP problem is a combination of the two well-known optimization problems: the Bin Packing Problem (BPP) and the Traveling Salesman Problem (TSP) [15][16][17]. The BPP is a problem given a finite set of numbers (the item sizes) and a constant K, specifying the capacity of the bin, what is the minimum number of bins needed?…”

Stochastic Vehicle Routing Problem: A Literature Survey

“…Dantzig and Ramser (1959) proposed VRP for the¯rst time under the title \Truck dispatching problem" with the objective to design optimum routing of a°eet of gasoline delivery trucks between a bulk terminal and a large number of service stations. VRP is a generic name given to a whole class of problems in which a set of routes for a°eet of vehicles based at one or several depots must be determined for a number of geographically dispersed cities or customers (Laporte et al, 1989Calvete et al, 2004;Baldacci et al, 2010). It is de¯ned by a depot, a set of geographically dispersed customers with demands, and a set of vehicles with capacity.…”