On the Solution of Bi-level Large Scale Quadratic Programming Problem with Stochastic Parameters in the Constraints
O. E. Emam *
Department of Information Systems, Faculty of Computers and Information, Helwan University, P.O. Box 11795, Egypt.
S. A. Kholeif
Department of Information Systems, Faculty of Computers and Information, Helwan University, P.O. Box 11795, Egypt.
S. M. Azzam
Department of Information Systems, Faculty of Computers and Information, Helwan University, P.O. Box 11795, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the bi-level large scale quadratic programming problem with stochastic parameters in the constraints (SBLLSQPP) is solved. Randomness is assumed only on the right-hand side of the constraints and the random variables are assumed to be normally distributed. The main features of the proposed solution procedure are based on convert the probabilistic nature of this problem into an equivalent deterministic, Taylor transformation and decomposition algorithms. An illustrative numerical example is given to clarify the main results developed in the paper.
Keywords: Large scale problems, stochastic programming, quadratic programming, bi–level programming.