A Counterexample to “Threshold Boolean form for joint probabilistic constraints with random technology matrix”

Recently, in the paper “Threshold Boolean form for joint probabilistic constraints with random technology matrix” (Math. Program. 147:391–427, 2014), Kogan and Lejeune proposed a set of mixed-integer programming formulations for probabilistically constrained stochastic programs having random constraint matrix and finite support distribution. We show that the proposed formulations do not in general correctly model such problems. In particular, we characterize the structure of the feasible region defined by the proposed formulations, and provide an example of a probabilistically constrained stochastic program that has a feasible region that does not match this structure.