This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample Average Approximation approach to solve these models, and provide an analysis with computation of statistical lower and upper bounds. A homeland security budget allocation problem is used as a case study to illustrate the properties of the proposed modeling and solution methodology. 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 models are studied with a RAND Corporation proposed allocation policy and the current government budget allocation as two benchmarks. The results from these models are discussed under several parameter scenarios. These results indicate that, in some cases, recent government budget allocations are consistent with those suggested by our models. In other settings, our models provide solutions that are less costly and less risky than the benchmarks, which indicates that the proposed models can be very effective.
IE/MS Dept. Northwestern University, 2010