Valid Inequalities for the Fleet Size and Mix Vehicle Routing Problem with Fixed Costs

Roberto Baldacci, Maria Battarra, Daniele Vigo

Research output: Contribution to journalArticle

18 Citations (Scopus)


In the well-known vehicle routing problem (VRP), 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. An important variant of the VRP arises when a mixed fleet of vehicles, characterized by different capacities and costs, is available for distribution activities. The problem is known as fleet size and mix VRP with fixed costs FSMF and has several practical applications. In this article, we present a new mixed integer programming formulation for FSMF based on a two-commodity network flow approach. New valid inequalities are proposed to strengthen the linear programming relaxation of the mathematical formulation. The effectiveness of the proposed cuts is extensively tested on benchmark instances.

Original languageEnglish
Pages (from-to)178-189
Issue number4
Publication statusPublished - 2009


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