An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation

• Published in: Operations research Vol. 52; no. 5; pp. 723 - 738
• Main Authors: Baldacci, R, Hadjiconstantinou, E, Mingozzi, A
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.09.2004; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; branch-and-cut algorithm; Bridge/routers; capacitated vehicle routing; Commodities; Cost efficiency; cutting plane; integer; Integer programming; Integers; Japanese encephalitis viruses; Linear programming; Mathematical inequalities; Optimal solutions; programming; Routing; Studies; Technology application; Transportation; Transportation industry; two-commodity formulation; Vehicle capacity; Vehicle operation; Vehicles
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1040.0111

The capacitated vehicle routing problem (CVRP) is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. In this paper, we describe a new integer programming formulation for the CVRP based on a two-commodity network flow approach. We present a lower bound derived from the linear programming (LP) relaxation of the new formulation which is improved by adding valid inequalities in a cutting-plane fashion. Moreover, we present a comparison between the new lower bound and lower bounds derived from the LP relaxations of different CVRP formulations proposed in the literature. A new branch-and-cut algorithm for the optimal solution of the CVRP is described. Computational results are reported for a set of test problems derived from the literature and for new randomly generated problems.