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A multiproduct, multicriterion supply-demand network equilibrium model. (English) Zbl 1167.90533
Summary: 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.

MSC:
90B50Management decision making, including multiple objectives
90C29Multi-objective programming; goal programming
90C47Minimax problems
90B10Network models, deterministic (optimization)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)