American Institute of Mathematical Sciences

Advanced
October  2007, 3(4): 727-737. doi: 10.3934/jimo.2007.3.727

A nonlinear complementarity model for supply chain network equilibrium

Liping Zhang 1,

1. 

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  September 2006 Revised  July 2007 Published  October 2007

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: Network equilibrium., Supply chain, Nonlinear complementarity problem.
Mathematics Subject Classification: Primary: 90B20; Secondary: 90C3.
Citation: Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial & Management Optimization, 2007, 3 (4) : 727-737. doi: 10.3934/jimo.2007.3.727
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