A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP

Abstract

The Analytic Hierarchy Process (AHP) is a decision analysis technique used to evaluate complex multiattribute alternatives among one or more decision makers. It imposes a hierarchical structure on any complex multicriterion problem. However, a major drawback of the AHP is that a large number of pairwise comparisons is needed to calibrate the hierarchy. When there are a few levels and sublevels, the AHP can be applied in a straightforward manner to derive the weights (relative preference for each alternative). As the size of the hierarchy increases, the number of pairwise comparisons increases rapidly. It is well established in the marketing and consumer behavior literature that in a very long interview, even under the best circumstances, the respondent is likely to suffer from information overload. Recognition of this problem was the motivation which led to the investigation of a modification of AHP which required less data collection, i.e., a reduction in the threat of information overload. The first question to be answered is the effect on AHP weights due to different patterns of missing data likely to result from reallife data collection. In this study, a Monte Carlo simulation was conducted, which uses the Incomplete Pairwise Comparisons (IPC) algorithm [14], to investigate the effect of reduced sets of pairwise comparisons in the AHP. Data for the study were generated with known structure and comparisons made between complete and incomplete matrices. The results of the simulation suggest that incomplete sets of pairwise comparison matrices can capture the attribute level weights without significant loss of accuracy and independent of decision model (form and amount of error) considered.