A vector network equilibrium problem with a unilateral constraint. (English) Zbl 1229.90187

Wu, Yunan; Chen, Guangya; Cheng, T. C. Edwin

J. Ind. Manag. Optim. 6, No. 3, 453-464 (2010).

Summary: We formulate a network equilibrium model with a unilateral constraint based on Wardrop’s principle and establish that the model is equivalent to a quasi-variational inequality. For the case with vector cost functions, we use Gerstewitz’s function to derive two equivalence relations between the vector network equilibrium model with a unilateral constraint and quasi-variational inequalities without any convexity assumptions.

MSC:

90C29	Multi-objective and goal programming
90C35	Programming involving graphs or networks
90B06	Transportation, logistics and supply chain management
90B10	Deterministic network models in operations research

Keywords:

network equilibrium; variational inequality; Wardrop’s equilibrium principle