Cost–benefit functions for the allocation of security sensors for air contaminants

In this paper, we study various functional forms of the cost–benefit function in a context of risk analysis and multi-objective decision-making for the allocation of hazard protection. An approach of benefit–cost analysis under uncertainty is used. The study identifies measures of hazard intensity and population exposure as well as additional parameters that influence assessments of benefits and costs. Parameter uncertainties are propagated by numerical interval analysis. Several tiers of the uncertainty of the benefit-to-cost ratio are generated to compare hazard intensity and population exposure in multi-objective tradeoff analysis. We develop an example application with the allocation of chemical, biological, and radiological air contaminant sensors throughout a region. The sensors provide local protection to non-identical sectors of the population that are exposed to non-identical intensities of the hazard. The results illuminate the significance of the cost–benefit function for the allocation of sensors. The paper has implications for anti-terrorism, disaster preparedness, transportation safety, and other areas of public safety.