Journal of Industrial and Management Optimization (JIMO)

Sample average approximation method for stochastic complementarity problems with applications to supply chain supernetworks

Pages: 317 - 345, Volume 7, Issue 2, May 2011      doi:10.3934/jimo.2011.7.317

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Mingzheng Wang - School of Management Science and Engineering, Dalian University of Technology, Dalian 116023, China (email)
M. Montaz Ali - School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag-3, Wits-2050, Johannesburg, South Africa (email)
Guihua Lin - School of Mathematical Science, Dalian University of Technology, Dalian 116024, China (email)

Abstract: We consider a class of stochastic nonlinear complementarity problems. We propose a new reformulation of the stochastic complementarity problem, that is, a two-stage stochastic mathematical programming model reformulation. Based on this reformulation, we propose a smoothing-based sample average approximation method for stochastic complementarity problem and prove its convergence. As an application, a supply chain super-network equilibrium is modeled as a stochastic nonlinear complementarity problem and numerical results on the problem are reported.

Keywords:  Stochastic nonlinear complementarity problem, two-stage stochastic mathematical programming, sample average approximation, super-network, convergence.
Mathematics Subject Classification:  Primary: 90C33, 90C30, 90C15.

Received: November 2009;      Revised: January 2011;      Available Online: April 2011.