Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs

We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we revisit the so-called Dawson and Sankoff bound that provided one of the best approximations of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality employed previously is a very relaxed approximation with assumptions that do not generally hold. Computational results demonstrate on average over a 43% improvement in the bounds. As a byproduct, we provide an exact reformulation of the floor function in optimization models.