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-atrisk (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.