ABSTRACT Ambiguous Chance Constrained Programs: Algorithms and Applications

Chance constrained problems are optimization problems where one or more constraints ensure that the probability of one or more events occurring is less than a prescribed thresh-old. Although it is typically assumed that the distribution defining the chance constraints are known perfectly; in practice this assumption is unwarranted. We study chance con-strained problems where the underlying distributions are not completely specified and are assumed to belong to an uncertainty set Q. We call such problems “ambiguous chance constrained problems. ” We focus primarily on the special case where the uncertainty set Q of the distributions is of the form Q = {Q: ρp(Q,Q0) ≤ β}, where ρp denotes the Prohorov metric. We study single and two stage ambiguous chance constrained programs. The single stage ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure Q0. We show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem. We also show that the robust sample