  We study the polyhedral structure of the static probabilistic lot-sizing
problem and propose valid inequalities that integrate information from the
chance constraint and the binary setup variables. We prove that the proposed
inequalities subsume existing inequalities for this problem, and they are
facet-defining under certain conditions. In addition, we show that they give
the convex hull description of a related stochastic lot-sizing problem. We
propose a new formulation that exploits the simple recourse structure, which
significantly reduces the number of variables and constraints of the
deterministic equivalent program. This reformulation can be applied to general
chance-constrained programs with simple recourse. The computational results
show that the proposed inequalities and the new formulation are effective for
the the static probabilistic lot-sizing problems.
