A Class of stochastic programs with decision dependent uncertainty

The standard approach to formulating stochastic programs is based on the assumption that the stochastic process is independent of the optimization decisions. We address a class of problems where the optimization decisions influence the time of information discovery for a subset of the uncertain parameters. We extend the standard modeling approach by presenting a disjunctive programming formulation that accommodates stochastic programs for this class of problems. A set of theoretical properties that lead to reduction in the size of the model is identified. A Lagrangean duality based branch and bound algorithm is also presented.