A Benders Decomposition Method for Solving Stochastic Complementarity Problems with an Application in Energy

Authors:
S. A. Gabriel;J. D. Fuller
Affiliations:
Department of Civil and Environmental Engineering, University of Maryland, College Park, USA 20742-3021;Department of Management Sciences, Faculty of Engineering, University of Waterloo, Waterloo, Canada N2L 3G1
Venue:
Computational Economics
Year:
2010

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Abstract

In this paper we present a new Benders decomposition method for solving stochastic complementarity problems based on the work by Fuller and Chung (Comput Econ 25:303---326, 2005; Eur J Oper Res 185(1):76---91, 2007). A master and subproblem are proposed both of which are in the form of a complementarity problem or an equivalent variational inequality. These problems are solved iteratively until a certain convergence gap is sufficiently close to zero. The details of the method are presented as well as an extension of the theory from Fuller and Chung (2005, 2007). In addition, extensive numerical results are provided based on an electric power market model of Hobbs (IEEE Trans Power Syst 16(2):194---202, 2001) but for which stochastic elements have been added. These results validate the approach and indicate dramatic improvements in solution times as compared to solving the extensive form of the problem directly.