Stronger multi-commodity flow formulations of the capacitated vehicle routing problem

Letchford, Adam and Salazar Gonzalez, Juan Jose (2015) Stronger multi-commodity flow formulations of the capacitated vehicle routing problem. European Journal of Operational Research, 244 (3). pp. 730-738. ISSN 0377-2217

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The Capacitated Vehicle Routing Problem is a much-studied (and strongly NP-hard) combinatorial optimization problem, for which many integer programming formulations have been proposed. We present two new multi-commodity flow (MCF) formulations, and show that they dominate all of the existing ones, in the sense that their continuous relaxations yield stronger lower bounds. Moreover, we show that the relaxations can be strengthened, in pseudo-polynomial time, in such a way that all of the so-called knapsack large multistar (KLM) inequalities are satisfied. The only other relaxation known to satisfy the KLM inequalities, based on set partitioning, is strongly NP-hard to solve. Computational results demonstrate that the new MCF relaxations are significantly stronger than the previously known ones.

Item Type:
Journal Article
Journal or Publication Title:
European Journal of Operational Research
Additional Information:
The final, definitive version of this article has been published in the Journal, European Journal of Operational Research 244 (2), 2015, © ELSEVIER.
Uncontrolled Keywords:
?? vehicle routingmulti-commodity flowsinteger programmingcombinatorial optimisationmodelling and simulationmanagement science and operations researchinformation systems and managementdiscipline-based research ??
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Deposited On:
13 Feb 2015 13:39
Last Modified:
17 Dec 2023 01:29