Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs

• Published in: Networks Vol. 54; no. 4; pp. 178 - 189
• Main Authors: Baldacci, Roberto, Battarra, Maria, Vigo, Daniele
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.12.2009; Wiley
• Subjects: Applied sciences; branch-and-cut; Exact sciences and technology; fleet management; Flows in networks. Combinatorial problems; Logistics; Mathematical programming; Operational research and scientific management; Operational research. Management science; vehicle routing; Fleet; Network flow; Fleet management; branch-and-cut; Fixed cost; Vehicle routing problem; Linear programming; Mixed integer programming; Routing; Multicommodity flow problem; Branch and cut method; vehicle routing; Capacity constraint; Mixed problem; Logistics
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.20331

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