Risk Adjusted Budget Allocation Models with Application in Homeland Security∗

This paper presents and studies models for multi-criterion budget allocation problems under uncertainty. The proposed models incorporate uncertainties in decision maker’s weights using a robust weighted sum approach. The risk averseness of the decision maker in satisfying random risk related constraints is ensured by using stochastic dominance. A sample average approximation approach together with a cutting surface method is used to solve this model. An analysis for the computation of statistical lower and upper bounds is also given. We use the proposed models to study the budget allocation to ten urban areas in the United States under the Urban Areas Security Initiative (UASI). Here the decision maker considers property losses, fatalities, air departures, and average daily bridge traffic as separate criteria. The properties of the proposed modeling and solution methodology are discussed using a RAND Corporation proposed allocation policy and the current government budget allocation as two benchmarks. The budget results are discussed under several parameter scenarios.