Robust preliminary analysis of large-scale linear model for optimal industrial investments

Which equipment should be bought for a given sum to increase the profit of an industrial enterprize with a known specification of production within given limits? This problem is described as a large-scale linear program (LP) of a specific structure. An effective preliminary analysis for this structure was proposed in Ioslovich and Makarenkov [On methods of dimensionality reduction in linear programming, Econ. Math. Methods Moscow (in Russian) 11(3) (1975) 316–324] which aimed to reduce the size of the problem by detection of the redundant and active constraints. In this paper a robust system is considered, dealing with box-constrained uncertainties in the input coefficients. The analysis is based on robust evaluations of bounds for primal and dual constraints. A robust evaluation of uncertain duals presented in [I. Ioslovich, P.-O. Gutman, Robust redundancy determination and evaluation of the dual variables of linear programming problems in the presence of uncertainty, 1, in, V. Kucera, M. Sebek (Eds.), Proceedings of 3rd IFAC Symposium on Robust Control Design (ROCOND 2000), IFAC, Prague, Czech Republic, Elsevier Science, Amsterdam, 2000, paper 115] is essentially used.