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  • 2015-mcf-cvrp-source

    Rights statement: The final, definitive version of this article has been published in the Journal, European Journal of Operational Research 244 (2), 2015, © ELSEVIER.

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

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/08/2015
<mark>Journal</mark>European Journal of Operational Research
Issue number3
Volume244
Number of pages9
Pages (from-to)730-738
Publication statusPublished
Early online date18/02/15
Original languageEnglish

Abstract

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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, European Journal of Operational Research 244 (2), 2015, © ELSEVIER.