Exact methods for a facility location problem with risk

In this work we consider an unconstrained facility location problem where we assume the customers demands to be probability distributions. Moreover we opt to penalize the total cost variance, this leading to study a second-order cone program. After, we tackle this non-linear program via two exact methods: a cutting plane approach exploiting "perspective cuts" and a Logic-Based Benders Decomposition method. Finally we implement the first approach in Python and discuss the results.