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Pricing strategies for the site-dependent vehicle routing problem

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  • Silvia Schwarze

    (University of Hamburg)

Abstract

The vehicle pricing game (VPG) which addresses the vehicles’ viewpoints within a vehicle routing problem (VRP) is introduced. Each vehicle acts as a player who demands a price per kilometer. That is, vehicles represent decentralized actors in transport systems, e.g., carriers under subcontracts. Based on these prices, a VRP is solved and profits are generated. Which price should a vehicle choose to maximize its own profit, considering the competition among vehicles? To answer this question, site dependencies leading to inhomogeneous vehicles are included. More detailed, skill-levels, e.g., relating to the size of a vehicle, are used to indicate a vehicle’s ability to carry out particular services. Moreover, penalty options are added. The VPG serves as an element of a vertical collaboration in a transport scenario and thus provides decision support for cooperative models. Theoretical results for the VPG are provided for a particular case of a two-player ring network game, for which the full set of equilibria is described and their uniqueness is discussed. It is shown that the uniqueness of the higher-skilled vehicle’s payoff is guaranteed even for multiple equilibria. The competition ratio is defined; it restricts a vehicle’s price to keep its competitiveness. Moreover, the acceptance ratio gives a lower bound on prices such that a loss of market share is still accepted. Experimental results are provided for general networks including the analysis of penalty options. It is demonstrated that strict site dependencies by tendency lead to monopolistic structures. In addition, particular penalty types show a positive effect regarding load imbalances caused by universally skilled vehicles.

Suggested Citation

  • Silvia Schwarze, 2016. "Pricing strategies for the site-dependent vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 137-173, January.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:1:d:10.1007_s00291-015-0399-6
    DOI: 10.1007/s00291-015-0399-6
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    References listed on IDEAS

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    1. Miguel Andres Figliozzi & Hani S. Mahmassani & Patrick Jaillet, 2007. "Pricing in Dynamic Vehicle Routing Problems," Transportation Science, INFORMS, vol. 41(3), pages 302-318, August.
    2. Yaron Hollander & Joseph Prashker, 2006. "The applicability of non-cooperative game theory in transport analysis," Transportation, Springer, vol. 33(5), pages 481-496, September.
    3. Stefan Engevall & Maud Göthe-Lundgren & Peter Värbrand, 2004. "The Heterogeneous Vehicle-Routing Game," Transportation Science, INFORMS, vol. 38(1), pages 71-85, February.
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    Cited by:

    1. Alf Kimms & Herbert Kopfer, 2016. "Collaborative planning in transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 1-2, January.
    2. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.

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