Pricing in Dynamic Vehicle Routing Problems

  • Authors:

  • Miguel Andres Figliozzi;Hani S. Mahmassani;Patrick Jaillet

  • Affiliations:

  • 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

  • Venue:
  • Transportation Science
  • Year:
  • 2007

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Abstract

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.