Dissection Methods for Solutions in Chance Constrained Programming Problems Under Discrete Distributions

Under the assumption of discrete distributions for the random variables involved, deterministic equivalent problems are derived for a general class of chance constrained (but not necessarily linear) programming problems. These permit the explicit solution of such problems for all or most types of optimal stochastic decision rules which are of interest, including optimal multistage rules and not restricted to the class of linear rules. The formulation given encompasses certain cases of stochastic programming with recourse, and the deterministic equivalents derived for these reduce to well-known versions available in the literature.