A sensitivity analysis algorithm for the constant sum pair-wise comparison judgments in hierarchical decision models

Every hierarchical decision modeling process starts with quantifying the contributions of decision elements through pair-wise comparisons. As subjective values, the pair-wise comparison judgments are seldom provided at a 100% confidence level and are subject to variations. To increase the model's validity and ensure requisite decision making, it is important to know how sensitive the model result is to these inputs. In this paper, a sensitivity analysis algorithm is developed to test a hierarchical decision model's robustness to the pair-wise comparison judgment inputs acquire from the constant sum method. It defines the allowable region of perturbation(s) induced to a judgment matrix at any level of a decision hierarchy to keep the current ranking of decision alternatives unchanged. An example will be presented to demonstrate the application of this algorithm in technology selection.