Critical supply network protection against intentional attacks: A game-theoretical model

A crucial issue in today's critical supply chains is how to protect facilities against intentional attacks, since it has become unacceptable to ignore the high impact of low probability disruptions caused by these attacks. This article develops a game-theoretical model to deal with the protection of facilities, in the context of the uncapacitated fixed-charge location problem. Given a set of investment alternatives for protecting the facilities against identified threats, the objective is to select the optimal defence strategy. The attacker is considered as a player who tries to maximise the expected damage while weighing against the attacks expenditures. The conflict on facilities vulnerability is modelled using the concept of contest. The vulnerability of a facility is defined by its destruction probability. Contest success functions determine the vulnerability of each facility dependent on the relative investments of the defender and the attacker on each facility, and on the characteristics of the contest. A method is developed to evaluate the utilities of the players (i.e., the defender and the attacker). This method evaluates many expected costs, including the cost needed to restore disabled facilities, the backorder cost, and the cost incurred because of the increase in transportation costs after attacks. In fact, when one or several facilities are unavailable, transportation costs will increase since reassigned customers may receive shipments from facilities which are farther away. The model considers a non-cooperative two-period game between the players, and an algorithm is presented to determine the equilibrium solution and the optimal defence strategy. An illustrative example is presented. The approach is compared to other suggested strategies, and some managerial insights are provided in the context of facility location.