Analytical Hierarchy Process (AHP) is a well known method for making qualitative decisions. AHP provides formal technique for evaluating alternatives in presence of different criteria or attributes.

Satty’s (1980) AHP technique is a pairwise comparison method which tries to capture relative judgements about attributes and alternative in a matrix form that ensure consistency. The simplicity of AHP technique makes it wonderful method to be widely used in operations management, decision making, project management, and various other fields where decisions need to be taken with accuracy and without human intuition. AHP provides mathematical framework for decision making.

In this lecture we discuss AHP technique for multi-criteria decision making problem with an example of University selection problem. I have discussed about this problem in another lecture Things to consider when selecting a University for higher education.

Three steps are involved:

Step 1: Creation of hierarchy with final Goal at top level of hierarchy, e.g. say Level1. List the criteria or attributes which we have to consider with respect to Goal, at second level, say Level2, and at bottom level, say Level 3 we list the alternatives among which one alternative we need to choose. Sometime we may need to choose more than one, in those scenario we can order the alternatives based on their final score after matrix computation during AHP process.

Step 2: Pairwise comparison matrix for criteria with respect to Goal and alternatives with respect to each criteria.

Step 3: Calculate the normalized weights of criteria and then use these weights in computation of calculating final score for alternatives.

Sounds like complex, actually it is not that difficult either, do not worry we look at computation with the help of an example.

Natural question arises, how we get confidence that our results are good. There have been different solutions and variants proposed over period of time however they all have base AHP in them. We create consistency matrix, calculate consistency index (C.I.), consistency ratios (C.R.). Typically consistency ratio less than 0.1 is recommended but in many circumstances higher C.R. are also accepted. One can also change the scale values in pairwise comparison matrices if C.R. is too far-off then accepted limits and fine-tune their decisions.

In the discussed example we come up with final score and select the alternative with highest value. When one have many alternatives one can plot them in descending order which can help to determine next best alternative if best chose alternative is not available.

We discuss University selection problem, however same AHP technique which is discussed can be applied to various other real world problems, such as 1) There are many good car in the market, each car has tons of attributes, how do we choose better car for us? difficult ? it is difficult one, for example family person may like to buy bigger car which can fit easily 6-7 people, however single person like to buy fancy two-door sporty car – fun to drive. Each car will have different cost to own, different fuel consumption, different horse power, torque, and many many more attributes. 2) Another real world problem can be for human resource managers that they get many equally competent candidates for same job posting, how do we choose best one without any personal bias? Is there any mathematical framework which can help managers to make better decisions.

Similarly there are many different real world problems where we have many criteria, many alternatives, and we need to make a choice. Analytical Hierarchy Process technique is a very good tool to use which helps us in such situations.

More complex methods such as Fuzzy AHP and variants have been evolved with time. You may further like to check one of my publication on fuzzy-AHP technique with time variance: H.C.Rajput et al., Including time dependency and ANOVA in decision-making using the revised fuzzy AHP: A case study on wafer fabrication process selection, Applied Soft Computing, Volume 11, Dec 2011, Pages 5099-5109.

ERRARA:

In the discussed example, the calculation of consistency ratio, C.R is 0.828/1.44 based on R.I. table discussed

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