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Pricing in Dynamic Vehicle Routing Problems

Faculty of Economics and Business, Institute of Transport and Logistics Studies, University of Sydney, Sydney, NSW 2006, Australia
Department of Civil and Environmental Engineering, Martin Hall, University of Maryland, College Park, College Park, Maryland 20742
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
miguel{at}itls.usyd.edu.au
masmah{at}umd.edu
jaillet{at}mit.edu

The principal focus of this paper is to study carrier pricing decisions for a type of vehicle routing problems defined in a competitive and dynamic environment. This paper introduces the vehicle routing problem in a competitive environment (VRPCE) as an extension of the traveling-salesman problem with profits (TSPP) to a dynamic competitive auction environment. In the VRPCE, the carrier must estimate the incremental cost of servicing new service requests as they arrive dynamically. The paper presents a rigorous and precise treatment of the sequential pricing and costing problem that a carrier faces in such an environment. The sequential pricing problem presented here is an intrinsic feature of a sequential auction problem. In addition to introducing the formulation of this class of problems and discussing the main sources of difficulty in devising a solution, a simple example is constructed to show that carriers’ prices under first-price auction payment rules do not necessarily reflect the cost of servicing transportation requests. An approximate solution approach with a finite rolling horizon is presented and illustrated through numerical experiments, in competition with a static approach with no look-ahead.

Key Words: freight transportation; dynamic vehicle routing; carrier fleet management strategies; pricing; carrier profitability; bidding strategies; auctions; electronic commerce
History: Received: April 2006; revised: February 2007; accepted: February 2007.