An implicit enumeration algorithm for the hub interdiction median problem with fortification

Hubs are intermediate facilities that play a pivotal role in efficient functioning of transportation and telecommunication systems. Like any other service infrastructure, hub facilities can be subject to natural or man-made disruptions after installation. In this paper, we address the problem of optimally allocating protective resources among a set of p existing hub facilities in such a manner that the damage inflicted by an intentional strike against the service system is minimized. Casting the problem as a Stackelberg game, the leader (i.e., the network protector or defender) fortifies q of the p operating hubs in order to minimize the impact of the upcoming strike, whereas the follower (i.e., the attacker) tries to identify and interdict r of the p−q unprotected hubs that their loss would diminish the network performance the most. A bilevel programming formulation is presented to model the problem and using a min-max approach the model is reduced to a single level mixed integer programming (MIP) model. Furthermore, an efficient exact solution algorithm based on implicit enumeration is proposed for solving the problem. Extensive computational experiments show the capability of the proposed algorithm to obtain the optimal solutions in short computational times. Some managerial insights are also derived based on the obtained numerical results.