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Dynamic pricing in an urban freight environment

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  • Friesz, Terry L.
  • Mookherjee, Reetabrata
  • Holguín-Veras, José
  • Rigdon, Matthew A.

Abstract

In this paper, we propose a dynamic, game theoretic model of dynamic pricing in an urban freight environment with three main entities: sellers, transporters and receivers. The sellers and transporters are modelled as non-cooperative Cournot-Nash agents. The sellers compete to capture receiver input factor demands, while the transporters compete to capture the transportation demand generated by the seller/receiver transactions. Each competing agent's extremal problem is formulated as an optimal control problem and the set of these coupled optimal control problems is transformed into a differential variational inequality representing the general Nash equilibrium problem. A nonlinear complementarity problem is also formulated and used to solve a numerical example.

Suggested Citation

  • Friesz, Terry L. & Mookherjee, Reetabrata & Holguín-Veras, José & Rigdon, Matthew A., 2008. "Dynamic pricing in an urban freight environment," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 305-324, May.
    • Handle: RePEc:eee:transb:v:42:y:2008:i:4:p:305-324
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    References listed on IDEAS

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    Cited by:

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    2. Stein, Oliver & Sudermann-Merx, Nathan, 2018. "The noncooperative transportation problem and linear generalized Nash games," European Journal of Operational Research, Elsevier, vol. 266(2), pages 543-553.
    3. Nilesh Anand & Ron van Duin & Hans Quak & Lori Tavasszy, 2015. "Relevance of City Logistics Modelling Efforts: A Review," Transport Reviews, Taylor & Francis Journals, vol. 35(6), pages 701-719, November.
    4. Saberi, Sara, 2018. "Sustainable, multiperiod supply chain network model with freight carrier through reduction in pollution stock," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 421-444.
    5. Friesz, Terry L. & Han, Ke, 2019. "The mathematical foundations of dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 309-328.
    6. Chung, Sung H. & Weaver, Robert D. & Friesz, Terry L., 2012. "Oligopolies in pollution permit markets: A dynamic game approach," International Journal of Production Economics, Elsevier, vol. 140(1), pages 48-56.
    7. David Escuín & Carlos Millán & Emilio Larrodé, 2012. "Modelization of Time-Dependent Urban Freight Problems by Using a Multiple Number of Distribution Centers," Networks and Spatial Economics, Springer, vol. 12(3), pages 321-336, September.
    8. Sagratella, Simone & Schmidt, Marcel & Sudermann-Merx, Nathan, 2020. "The noncooperative fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 373-382.
    9. Gerard Jong & Inge Vierth & Lori Tavasszy & Moshe Ben-Akiva, 2013. "Recent developments in national and international freight transport models within Europe," Transportation, Springer, vol. 40(2), pages 347-371, February.
    10. Li, Li & Zhang, Rachel Q., 2015. "Cooperation through capacity sharing between competing forwarders," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 115-131.
    11. Varun Raturi & Ashish Verma, 2019. "Competition between High Speed Rail and Conventional Transport Modes: Market Entry Game Analysis on Indian Corridors," Networks and Spatial Economics, Springer, vol. 19(3), pages 763-790, September.
    12. Saberi, Sara & Cruz, Jose M. & Sarkis, Joseph & Nagurney, Anna, 2018. "A competitive multiperiod supply chain network model with freight carriers and green technology investment option," European Journal of Operational Research, Elsevier, vol. 266(3), pages 934-949.
    13. Avinash Unnikrishnan & Varunraj Valsaraj & Steven Waller, 2009. "Stochastic and Dynamic Shipper Carrier Network Design Problem," Networks and Spatial Economics, Springer, vol. 9(4), pages 525-550, December.

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