Using hazard networks to determine risk reduction strategies

In many cases, the interdependencies among the hazards in a system can be expressed by means of a hazard network, in which the nodes correspond to the hazards and the links indicate how they depend on one another. We formulate a set of mathematical optimization models which apply in such circumstances and can be used to determine the best protection or prevention strategy based on the estimated costs of mitigation. We illustrate how the model works in three different situations: (1) when total mitigation of any hazard eliminates all the hazards that follow it, (2) when a number of hazards must be totally mitigated to achieve the same effect, and (3) when partial mitigation helps to reduce the risks associated with subsequent hazards. The models developed and illustrated are readily scalable and should apply to a wide range of risk management problems.