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

Cheng, T. C. E.; Wu, Y. N.

Oper. Res. 54, No. 3, 544-554 (2006); erratum ibid. 59, 1309-1210 (2011).

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:

90B50	Management decision making, including multiple objectives
90C29	Multi-objective and goal programming
90C47	Minimax problems in mathematical programming
90B10	Deterministic network models in operations research
90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)