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

Mingzheng Wang; M. Montaz Ali; Guihua Lin

doi:10.3934/jimo.2011.7.317

Article Contents

2011, Volume 7, Issue 2: 317-345. Doi: 10.3934/jimo.2011.7.317

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

1.
School of Management Science and Engineering, Dalian University of Technology, Dalian 116023
2.
School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag-3, Wits-2050, Johannesburg
3.
School of Mathematical Science, Dalian University of Technology, Dalian 116024

Received: October 31, 2009

Revised: December 31, 2010

Published: March 2011

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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.

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