Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications

In this paper, we consider a Kullback-Leibler divergence constrained distributionally robust optimization model. This model considers an ambiguity set that consists of all distributions whose to empirical distribution is bounded. Utilizing the fact measure has exponential cone representation, obtain counterpart problem as dual program under mild assumptions on underlying problem. The resulting conic reformulation original can be directly solved by commercial programming solver. We specialize our generic formulation two classical problems, namely, Newsvendor Problem and Uncapacitated Facility Location Problem. Our computational study in out-of-sample analysis shows solutions obtained via approach yield significantly better performance terms dispersion cost realizations while central tendency deteriorates only slightly compared stochastic programming.