I used this video to gain good insight ..
The best way to learn AHP is through a good example, this case of purchasing an automobile ...
Click here for the AHP example problem link ..
AHP Car buying example ..
AHP has two steps,
step one, doing the paired comparisons and finding the average weights for each criteria and
step two, finding the consistency ratio (to check whether your paired comparisons made any sense, for eg. if A is better than B and B is better than C , definitely A should be better than C, if not there is inconsistency in the paired comparisons). This consistency (or inconsistency) is what we are trying to assess and determine.
Once we get the average (row) weights from the normalised matrix, get the dot product of the normalised matrix and the average weights, (this gives lamda, the eigen value). To get the consistency index., use the formula (lamda-N)/(N-1), where N is the number of alternatives or suppliers or candidates etc...
Once you get the CI (Consistency Index) for an alternative, divide by the random index (RI) to get Consistency Ratio (CR) = CI/RI which should be less than 0.1 (alpha value), which means it is accepted ..
Similarly repeat the calculation of Consistency Ratio for each of the criteria and get a Final Ratings Matrix. Take the transpose of this "Final Ratings Matrix" for all the criteria (parameters) and multiply it with the average weights (from the different criteria in the first computation sheet)
ie. Multiply the NxJ matrix with the Jx1 matrix to get an Nx1 matrix (column matrix)
Please do not forget, N stands for the different alternatives (suppliers etc) and J stands for the different criteria or parameters on which the alternatives are evaluated.
Comparing the values from the Nx1 matrix will tell us which of the different alternatives or suppliers or candidates or manufacturing processes or transporters etc should be chosen.
Analytic Hierarchy Process (AHP) is a very efficient process, given our paired comparisons between the different alternatives is consistent, (though we establish the consistency by the help of the Consistency Ratio.)