Constructing Sets of Uniformly Tighter Linear Approximations for a Chance Constraint

The aim of this paper is to construct sets of uniformly tighter linear constraints to replace a chance constraint, in order to be able to solve the chance-constrained programming problem by the simplex method. The chance constraints are first diagonalized by a linear orthonormal transformation. Uniformly tighter linear constraints can then be formed to replace the chance constraint. The developed multistage linear programming problem can also be solved using the Dantzig-Wolfe decomposition technique. Approximation errors of our method and one of Hillier's [8] are compared.