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.
- Network equilibrium
- Supply-demand network
- Variational inequality
- Wardrop's equilibrium principle
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research