Chance Constrained Programming with one Discrete Random Variable in Each Constraint

Abstract

Stochastic programming problems in which there are linear constraints containing one discrete random variable among either the technical coefficients or the resource (which are all positive), and non-negativity constraints for the variables, are studied. First, the case of just one linear constraint with stochastic resource is presented. Next is the case of just one linear constraint where one of the technical coefficients is a random variable. In both cases, initially the case of two decision variables is studied, which permits us to solve the problems taking advantage of the corresponding graphical representations. The corresponding generalizations for the case of n decision variables follow. The general case of several of such constraints is also presented. All the specific solution methods obtained are based on the chance constrained method. Each of the cases is illustrated with an example taken from Economics.