American Institute of Mathematical Sciences

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July  2009, 5(3): 615-628. doi: 10.3934/jimo.2009.5.615

Classical duality and existence results for a multi-criteria supply-demand network equilibrium model

Yunan Wu 1, and  T. C. Edwin Cheng 2,

1. 

School of International Business, Beijing Foreign Studies University, Beijing 100089, China
2. 

Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Received  July 2008 Revised  January 2009 Published  June 2009

We propose a dual model of a multi-criteria network equilibrium model and establish a primal-dual relationship between the network model and its dual model under certain generalized monotonicity assumptions. By using Gerstewitz's function, we obtain the primal-dual relationship without any convexity assumptions. As an application of the dual model, we derive an existence result for the network model.
Keywords: Wardrop's equilibrium principle, Variational inequality, Network equilibrium, Duality..
Mathematics Subject Classification: Primary: 90C29, 90C35; Secondary: 90B06, 90B1.
Citation: Yunan Wu, T. C. Edwin Cheng. Classical duality and existence results for a multi-criteria supply-demand network equilibrium model. Journal of Industrial and Management Optimization, 2009, 5 (3) : 615-628. doi: 10.3934/jimo.2009.5.615
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