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A Multiproduct, Multicriterion Supply-Demand Network Equilibrium Model

Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China, and Department of Mathematics, Chongqing Normal University, Chongqing, China
lgtcheng{at}polyu.edu.hk
lgtnwu{at}polyu.edu.hk

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.

Subject classifications: network equilibrium; variational inequality; Wardrop’s equilibrium principle; supply-demand network.
History: Received July 2003; revision received January 2004; revision received March 2004; revision received September 2004; accepted March 2005.