Risk Management for Leontief-Based Interdependent Systems

When stricken by a terrorist attack, a war, or a natural disaster, an economic unit or a critical infrastructure may suffer significant loss of productivity. More importantly, due to interdependency or interconnectedness, this initial loss may propagate into other systems and eventually lead to much greater derivative loss. This belongs to what is known as a cascading effect. It is demonstrated in this article that the cascading effect and the derivative loss can be significantly reduced by effective risk management. This is accomplished by deliberately distributing the initial inoperability to other systems so that the total loss (or inoperability) is minimized. The optimal distribution strategy is found by a linear programming technique. The same risk management can also be applied to situations where objectives need to be prioritized. A case study featuring 12 economic sectors illustrates the theory. The result suggests that using the same amount of resources, minimizing risk (inoperability) of infrastructures will generally give rise to highest payoff, whereas overlooking it may result in greatest total loss. The framework developed in this work uses a steady-state approach that applies primarily to managing situations where the attack is catastrophic resulting in very long recovery time.