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The Analytic Hierarchy Process (AHP) enables the measurement (on a ratio scale) of benefits that include both quantitative and qualitative factors. The AHP hierarchy should include every objective to which the funding alternatives under consideration contribute. The objectives are structured into homogeneous clusters that fit the organization's vision of its strategies and tactics. Elements in each cluster should be within approximately an order of magnitude of importance of one another, so that reasonable pairwise comparisons can be made. A problem arises, however, when alternatives under consideration differ in cost by several orders of magnitude. Unless the ratio of alternative benefits are commensurate with the ratio of their costs, a resource allocation optimization will tend to select the lower cost alternatives. This paper will present approaches for deriving ratio scale measures of alternative benefits that can span the same orders of magnitude as the alternative costs.

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