IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation

We present a new method for solving stochastic programs with joint chance constraints with random technology matrices and 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 called IIS cuts and apply them to our problem. The cuts are based on irreducibly infeasible subsystems (IIS) of an LP defined by requiring that all scenarios be satisfied. We propose a method for improving the upper bound of the problem when no cut can be found. We derive and implement a branch-and-cut algorithm based on IIS cuts, and refer to this algorithm as the IIS branch-and-cut algorithm. We report on computational results with several test instances from optimal vaccine allocation. The computational results are promising as the IIS branch-and-cut algorithm gives better results than a state-of-the-art commercial solver on one class of problems.