Pricing in Dynamic Vehicle Routing Problems

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.