A MONTE-CARLO INVESTIGATION OF INCOMPLETE PAIRWISE COMPARISON MATRICES IN AHP

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 m ulticriterion problem. However, a major drawback of the AHP is that a large number of pairwise comparisons is needed to calibrate the hierar chy. When there are a few levels and sublevels, the AHP can be applied in a straightforward manner to derive the weights (relative preferenc e for each alternative). As the size of the hierarchy increases, the n umber of pairwise comparisons increases rapidly. It is well establishe d in the marketing and consumer behavior literature that in a very lon g interview, even under the best circumstances, the respondent is like ly to suffer from information overload. Recognition of this problem wa s the motivation which led to the investigation of a modification of A HP which required less data collection, i.e., a reduction in the threa t of information overload. The first question to be answered is the ef fect on AHP weights due to different patterns of missing data likely t o result from reallife data collection. In this study, a Monte Carlo s imulation was conducted, which uses the Incomplete Pairwise Comparison s (IPC) algorithm [14], to investigate the effect of reduced sets of p airwise 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 o f pairwise comparison matrices can capture the attribute level weights without significant loss of accuracy and independent of decision mode l (form and amount of error) considered. (C) 1997 Elsevier Science B.V .