AbstractIn usual stochastic programming problems involving randomly distributed "resources" and chance constraints, decision variables are taken as deterministic. With the help of simple illustrations involving a single decision variable, Vajda and Greenberg showed that minimum expected values could be made smaller by treating the decision variable as random. This idea has been extended here to the case of two decision variables. The difficulty of finding an optimal mixed strategy in the case of an infinite-range distribution of the decision variable(s) has also been shown.