A decomposition algorithm for distributionally robust chance-constrained programs with polyhedral ambiguity set

In this paper, we study a distributionally robust optimization approach to chance-constrained stochastic programs to hedge against uncertainty in the distributions of the random parameters. We consider a general polyhedral ambiguity set under finite support. We develop a decomposition-based solution approach to solve the model and use mixing inequalities to develop custom feasibility cuts. In addition, probability cuts are also developed to handle the distributionally robust chance constraint. Finally, we present a numerical study to illustrate the effectiveness of the proposed decomposition-based algorithm and showcase the results for Wasserstein ambiguity set, total variation distance ambiguity set, and moment-based ambiguity set as special cases of the polyhedral ambiguity set.