One of the most widely used methods in decision-making is the Analytic Hierarchy Process (AHP). With its technique of comparing the alternatives by means of a sequence of pairwise comparison matrices, the AHP is both easy to understand and very versatile. This research aims at contributing some insights on this method, in particular, regarding to what is known as the incomplete AHP. The core of this research is to investigate whether the initial comparisons used to extract the data for a multi-criteria decision making problem, will play a role in producing a relatively accurate estimation of the ranking of the alternatives. Three problems are investigated in this work. The first problem is to determine the optimal number of the initial comparisons. As the number of initial comparisons increases, a complete pairwise comparison matrix will more likely be estimated accurately. Consequently, the time required to calculate these initial comparisons will also increase. These conflicting goals will be investigated further in this thesis.
The second problem of this research is to determine which initial comparisons should be asked as the starting point. Using the minimal number of initial comparisons (i.e., comparisons), five different strategies will be investigated. Lastly, the final problem is to determine if the method that we use to estimate the missing comparisons will also affect the accuracy of the weight vector. Two methods will be compared in this thesis, namely the Least Squares, and the Geometric Mean methods.
In order to determine whether a matrix is accurately estimated, two methods are used to compare the estimated and the original weight vectors. One method is to compare the ranking order of the alternatives, while the other is to compute the average difference between the two vectors. The smaller the average difference, the better the corresponding selection strategy is.
Furthermore, the two methodologies will be compared based on their computation requirements. The methodology with less computational time and better accuracy will be considered better than the other. The final results of this thesis will provide more insight into the incomplete AHP in general, thus hopefully providing the decision maker a reliable tool to optimally use this method.