Risk-averse production planning

We consider a production planning problem under uncertainty in which companies have to make product allocation decisions such that the risk of failing regulatory inspections of sites - and consequently losing revenue - is minimized. In the proposed decision model the regulatory authority is an adversary. The outcome of an inspection is a Bernoulli-distributed random variable whose parameter is a function of production decisions. Our goal is to optimize the conditional value-at-risk (CVaR) of the uncertain revenue. The dependence of the probability of inspection outcome scenarios on production decisions makes the CVaR optimization problem non-convex. We give a mixed-integer nonlinear formulation and devise a branch-and-bound (BnB) algorithm to solve it exactly. We then compare against a Stochastic Constraint Programming (SCP) approach which applies randomized local search. While the BnB guarantees optimality, it can only solve smaller instances in a reasonable time and the SCP approach outperforms it for larger instances.