IIS Cuts for Stochastic Programs with Joint Chance-Constraints

We present a new method for solving stochastic programs with joint chance constraints with discretely distributed random data. The problem can be reformulated as a large-scale mixed 0-1 integer program. We derive a new class of optimality cuts based on irreducibly infeasible subsets (IIS) of an LP defined by requiring that all scenarios be satisfied and propose a method for improving the upper bound of the problem when no cut can be found. We describe an implementation of a branchand-cut algorithm and report on computational results with several test instances from optimal vaccine allocation as well as from the literature. The computational results are very promising as the proposed method gives significantly better results than the state of the art commercial solver.