On a bi-level formulation to protect uncapacitated p-median systems with facility recovery time and frequent disruptions

We consider an uncapacitated p-median system that is subject to external manmade or natural disruptions and formulate the problem of protecting against the worst-case losses when taking into account facility recovery issues. The model is a mixed integer bi-level problem with integer variables controlled by both the upper and lower level. To solve it, we apply two exact decomposition methods: a decomposition algorithm based on a special type of valid inequalities and Benders decomposition coupled with variable reduction and some heuristic rules to speed up the resolution of the master problems. Although we compare the performance of the two decomposition approaches, for brevity, we only show here the Benders decomposition.