Note on incremental benefit/cost ratios in analytic hierarchy process

Scholars have frequently applied benefit-cost analysis to policy issue decisions. They hope to measure the relative importance among alternatives and provide systematical decision-making information using the benefit and cost factors. In this paper, the work of Bernhard and Canada [1] is studied based on incremental benefit/cost ratios with a cutoff ratio to analyze and extend the benefit/cost problem. This note has three purposes. First, we derive some theoretical properties for the incremental benefit/cost ratios with the cutoff ratio and a corrected method to show that the previous results are incomplete. Second, we provide an efficient method for solving the incremental benefit/cost ratios with cutoff ratio problems. Third, Bernhard and Canada [1] assumed that the desired incremental benefit/cost ratios could be derived using a comparison matrix under the perfectly consistent condition. We offer a counter-example to highlight the difference between the normalized benefit from the benefit and the normalized benefit vector from the AHP. We hope these findings will be useful for decision makers in applying benefit/cost analysis.