Journal of Industrial and Management Optimization (JIMO)

A nonlinear complementarity model for supply chain network equilibrium

Pages: 727 - 737, Volume 3, Issue 4, November 2007      doi:10.3934/jimo.2007.3.727

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Liping Zhang - Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China (email)

Abstract: We study a nonlinear complementarity formulation of the supply chain network equilibrium problem, which is parallel to the variational inequality model established by Dong et al. (2004). In this setting, we obtain weaker conditions to guarantee the existence and uniqueness of the equilibrium pattern for a supply chain. A smoothing Newton method that exploits the network structure is proposed and convergence results are presented. Numerical examples show that the algorithm is more applicable than the modified projection method presented by Dong et al. (2004).

Keywords:  Supply chain, Nonlinear complementarity problem, Network equilibrium.
Mathematics Subject Classification:  Primary: 90B20; Secondary: 90C30.

Received: September 2006;      Revised: July 2007;      Available Online: October 2007.