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Network equilibrium of production, transportation and pricing for multi-product multi-market

Author

Listed:
  • Jiuping Xu

    (Sichuan University)

  • Guomin Fang

    (Sichuan University
    Chengdu University of Information Technology)

  • Zezhong Wu

    (Chengdu University of Information Technology)

Abstract

In this paper, we consider a production, transportation and pricing problem for multi-product multi-market (PTPMM) as a system, and develop a PTPMM network equilibrium model. After allocating each product’s production cost and revenue to each path, we establish a profit network graph. An equilibrium PTPMM matrix and a $$\lambda $$ λ -combination equilibrium are proposed based on a generalization of the well-known Wardrop’s equilibrium principle. The necessary and sufficient conditions for the $$\lambda $$ λ -combination equilibrium are proposed using a linear scalarized profit function. We prove that solving the PTPMM network equilibrium problem can be reduced to the solving of the weak vector variational inequality problem, which proposes an algorithm for the PTPMM problem. Finally, an illustrative example is given to demonstrate an application of these theoretical results.

Suggested Citation

  • Jiuping Xu & Guomin Fang & Zezhong Wu, 2016. "Network equilibrium of production, transportation and pricing for multi-product multi-market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 567-595, December.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:3:d:10.1007_s00186-016-0557-x
    DOI: 10.1007/s00186-016-0557-x
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