Premium
Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs
Author(s) -
Baldacci Roberto,
Battarra Maria,
Vigo Daniele
Publication year - 2009
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20331
Subject(s) - vehicle routing problem , benchmark (surveying) , integer programming , mathematical optimization , linear programming , computer science , flow network , set (abstract data type) , linear programming relaxation , relaxation (psychology) , routing (electronic design automation) , fixed cost , operations research , branch and cut , mathematics , economics , computer network , psychology , social psychology , accounting , geodesy , programming language , geography
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. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009