Some Problems in Using Benefit'cost Ratios With the Analytic Hierarchy Process

For Analytic Hierarchy Process applications having separate benefit and cost output vectors, Saaty has recommended choosing a solution using a simple benefit/cost ratio procedure. But, even when benefits and costs are known with certainty and measured in dollars, it is shown that this procedure does not, in general, yield an optimal solution. An incremental analysis, with further specification of an appropriate cutoff rate, is shown to be required. Saaty's procedure is also shown to be sensitive to arbitrary semantic changes in benefit and cost labelling, while proper procedures, such as the one proposed herein, do not have that sensitivity.