What is Analytical Hierarchy Process (AHP) ?

Analytical Hierarchy Process (AHP) is a mathematical tool of problem solving that has become popular amongst management personnel in the late 1990’s and early 2000’s. The AHP method has been created after understanding the structure of a problem and the real hindrance that managers face while solving it. This structure has been explained in this article.

The Logic behind AHP

The AHP method looks at the problem in three parts. The first part is the issue that needs to be resolved, the second part are the alternate solutions that are available to solve the problem. The third and the most important part as far as the AHP method is concerned is the criteria used to evaluate the alternative solutions.

The AHP method understands that although there are several criteria, the magnitude of each criterion may not be equal. For instance if you have to choose between two restaurants, the taste and the waiting time are two factors, however both of them may not have equal importance in your perception. The taste may ne far more important than the waiting time and so on. Therefore if you assign weightage of 2 to taste and 1 to waiting time, you are more likely to arrive at a restaurant that will best meet your need.

Hence, while evaluating alternative solutions, weights need to be attached to the criteria to ensure reaching the correct conclusion. This may seem obvious. However, until very late management scientists have been facing issues as to how to assign weights. In the above example, our assignment of weights was arbitrary. Also the example had only two criteria. As the number of criteria (factors) multiplies, the assignments become more and more arbitrary.

The AHP method has inbuilt checks and balances. These checks and balances, therefore ensure that you reach logically consistent solutions when you compare the relative importance of the criteria in the process of assigning weights to them.

It is for this reason that AHP is one of the most sought after technicques in management science today. Managers in mega corporations like General Electric, Ford Motors, Motorola etc, use it in their six sigma projects.

The Connection Between AHP and Six Sigma

AHP is a separate technique. It is not a part of the standard Six Sigma methodology. In fact, it was developed many years after the Six Sigma methodology was developed. However it has found large scale application in six sigma projects. Managers use AHP to assign numerical weights to factors. These factors could be the ones used by the customers while evaluating a product or they could be the ones used by the management to evaluate alternative solutions.

Drawbacks of AHP

The AHP method has its own issues. The method involves higher level mathematics. It is based on the concept of eigen vectors. It is for this reason that performing the calculations pertaining to AHP on an Excel sheet are an ordeal. However, of late software tools have been developed that can perform the calculations. The managers therefore just need to be aware of the AHP process, the calculations are automated.

How to Use the Analytical Hierarchy Process (AHP)

Although the AHP is one of the most advanced methods available in the field of management science and operations research, the complexity involved in using this tool makes it difficult to apply. Thankfully software tools have been built which automate the mathematics intensive part. The user has to follow a simple methodology of data collection which is then fed into the tool to get the results.

Here is the procedure for doing the same:

Step 1: Define Alternatives

The AHP process begins by defining the alternatives that need to be evaluated. These alternatives could be the different criteria that solutions must be evaluated against. They could also be the different features of a product that need to be weighted to better understand the customers perception. At the end of step 1, a comprehensive list of all the available alternatives must be ready.

Step 2: Define the Problem and Criteria

The next step is to model the problem. According to AHP methodology, a problem is a related set of sub problems. The AHP method therefore relies on breaking the problem into a hierarchy of smaller problems. In the process of breaking down the sub-problem, criteria to evaluate the solutions emerge. However, like root cause analysis, a person can go on and on to deeper levels within the problem. When to stop breaking the problem into smaller sub problems is a subjective judgement.

Example: A firm needs to decide on the best investment option amongst stocks, bonds, real estate and gold. If the AHP method is used, the problem of best investment will be broken down into smaller problems like protection from downfall, maximum chance of appreciation, liquidity in the market and so on. Each of these sub problems can then be broken into smaller problems till the management feels that the appropriate criteria has been reached.

Step 3: Establish Priority amongst Criteria Using Pairwise Comparison

The AHP method uses pairwise comparison to create a matrix. For example the firm will be asked to weigh the relative importance of protection from downfall vs. liquidity. Then in the next matrix, there will be a pairwise comparison between liquidity and chance of appreciation and so on. The managers will be expected to fill this data as per the expectations of the end consumer or the people who are going to use the process.

Step 4: Check Consistency

This step is inbuilt in most software tools that help solve AHP problems. For instance if I say that liquidity is twice as important as protection from downfall and in the next matrix I say that protection from downfall is half as important as chance of appreciation, then the following situation emerges:

Liquidity = 2 (Protection from downfall)

Protection from downfall = ½ (Chance of appreciation)

Therefore, Liquidity must equal chance of appreciation.

However, if in the pairwise comparison of liquidity and chance of appreciation, if I have given a weight of more or less than 1, then my data is inconsistent. Inconsistent data gives inconsistent results, hence prevention is better than cure.

Step 5: Get the Relative Weights

The software tool will run the mathematical calculation based on the data and assign relative weights to the criteria. Once the equation is ready with weighted criteria, one can evaluate the alternatives to get the best solution that matches their needs. 

EXAMPLE OF HOW IT WORKS

We've mentioned how AHP is unique because it can quantify criteria and alternatives, but what does that really look like? As an end user of Prioritization Helper, you won't see the calculations going on behind the scenes. Here is a quick look of the calculations behind a result.

Let's pretend the Smith family wants to decide the best city to live in - City A, B, C, or D. The goal is to determine which city is best, given the criteria - Culture, Close to Family, Jobs, Housing, and Transportation. They weigh the criteria, and compare the four city alternatives to the criteria. The following tables illustrate the derived data based on their input. In general, all of the decimals will add up to 1, and higher decimals equals a higher priority.

Table 2 shows how the criteria were rated against each other. Looking at the top row, Culture scored a "3" above Housing and a "5" above Transportation, while Family scored a "5" above Culture, and Jobs scored a "2" above Culture. This gives Culture 15.2% of the criteria priority, with the most important criteria being Family, at 43.3%.

The next table demonstrates the weights of each alternative against the criteria Family. Here, City C was the closest to family, while City D was the furthest. This would be repeated for every criteria.

Finally, the weighed importance of each criteria is then multiplied against the score of each alternative to get the weighed score (For City A's weighted Cultural score: .152 x .163 = .024776). Add all new criteria numbers together to get the Overall Priority score (For City A: .024776 + .09093 + .018864 + .085095 + .009462 = .229)

Bahurmoz, Asma. "The Analytic Hierarchy Process: A Methodology for Win-Win Management " JKAU: Econ. & Adm., Vol. 20, No. 1, 2006.

The Smith's best decision based off of their priorities, is City C. In Prioritization Helper, the final results would look like "City C - 38.5% City B - 27.5% City A - 22.9% City D - 11.1%"

As you can see, there's a lot going on, and it can be tricky to understand. That's why we've created Prioritization Helper! You can gain the benefits of an unbiased decision in minutes, without the hard work.