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A Multiproduct, Multicriterion Supply-Demand Network Equilibrium Model

Author

Listed:
  • T. C. E. Cheng

    (Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

  • Y. N. Wu

    (Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China, and Department of Mathematics, Chongqing Normal University, Chongqing, China)

Abstract

We consider a multiproduct supply-demand network equilibrium model on the basis of Wardrop’s equilibrium principle. We prove that such a network equilibrium model with both a single criterion and multiple criteria are each equivalent to a vector variational inequality. For the case with multiple criteria, we derive the necessary and sufficient conditions for network equilibrium in terms of a vector variational inequality by Gerstewitz’s function when the cost function is vector valued. This result is derived based on conditions that are weaker than those for many existing results. We follow with an example to illustrate the application of the theoretical results.

Suggested Citation

  • T. C. E. Cheng & Y. N. Wu, 2006. "A Multiproduct, Multicriterion Supply-Demand Network Equilibrium Model," Operations Research, INFORMS, vol. 54(3), pages 544-554, June.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:3:p:544-554
    DOI: 10.1287/opre.1060.0284
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    References listed on IDEAS

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    1. Nagurney, Anna & Dong, June, 2002. "A multiclass, multicriteria traffic network equilibrium model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 445-469, June.
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    3. G. Y. Chen & C. J. Goh & X. Q. Yang, 1999. "Vector network equilibrium problems and nonlinear scalarization methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 239-253, April.
    4. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
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    Cited by:

    1. Zhaobo Chen & Chunying Tian & Ding Zhang & Dongyan Chen, 2020. "Dynamic model of a supply chain network with sticky price," Operational Research, Springer, vol. 20(2), pages 649-670, June.
    2. 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.

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