The AHP Method: Definition and Example

The Analytic Hierarchy Process (AHP) is a method for organizing and analyzing complex decisions, using math and psychology. It was developed by Thomas L. Saaty in the 1970s and has been refined since then.

Analytic Hierarchy Process (AHP)

What are the steps in the AHP method?

Here are the steps to consider in the AHP method:

1. Define the goal and alternatives

Start by defining what you need to assess. Your goal can be for example:

Once you’ve determined what you want to evaluate, you can specify potential comparisons to make.

2. Define the problem and decision criteria

According to the AHP methodology, a problem is a collection of related issues. Its method entails segmenting the issue into more manageable subproblems or requirements. For instance, a company might want to find its next investment It needs to choose between stocks, real estate and gold. It can be divided into smaller issues like the ability to generate cash flow, market liquidity, and a growth perspective. These can serve as criteria to further analyze the solutions.

3. Assess the relative value or priority of each decision criterion

It is time for the evaluation. Create a pairwise comparison matrix that allows you to contrast elements in the top row with elements in the left column. Building a matrix to compare the ability to generate cash flow against liquidity, the growth perspective against liquidity, and other factors would be done in the example of the company choosing an investment.

You can enter a number to represent the dominance of one element over another in the matrix. It will show how participants perceive that some factors are more important to the project’s success than others.

4. Gather groups of judgments

Obtain all the judgments from participants. If there are numerous participants, you can combine their evaluation using the means of their numbers.

5. Calculate the weights of the criteria and alternatives priorities

Each value is multiplied by the sum of the columns, and the average of each criterion is calculated to give it a weight that can be compared.

Take the sum over all weighted priority entries. To aid in decision-making, you are provided with a hierarchy of priorities. The option with the higher score is the one that is closest to your objective.

6. Analyze the inconsistency of judgments

You can evaluate the consistency of the hierarchy. For instance, if a participant in one matrix indicated that the perspective on growth was more important than liquidity The weight of that other criterion must be consistent with that judgment.

If liquidity=3 x growth perspective

And growth perspective=1/3 ability to generate cash flow

In the comparison matrix, liquidity should have the same value as the capacity to produce cash flow and display a weight of 1. If it displays a different value, the information is inconclusive, and you should review it before drawing any conclusions.

What is the AHP method?

You can choose and prioritize your projects by using the AHP method, which stands for Analytic Hierarchy Process. AHP is a mathematical model that also incorporates psychology to aid in the organization and analysis of difficult choices. It differs from other decision-making techniques in that it suggests quantifying your evaluation criteria.

It consists of three parts:

AHP requires you to quantify the criteria and alternative solutions to your issue in order to connect them to your ultimate objective. Let’s say, for illustration, that the issue is that you need to relocate and find a new home. Your options in this instance are various houses that are on the market. You may want to consider factors like garden size, proximity to family and work.

You start by comparing the criteria two by two. To assess the relative importance of the criteria, AHP lets you give the evaluation criteria a numerical value. You give the one that means more to you a higher rating.

The method of weighing criteria makes it simpler to evaluate and contrast the alternatives. In our example, you might give the criteria that are close to your place of employment a higher score, but the other family members also gave it a numerical value. The AHP process ensures that everyone’s opinions are taken into consideration.

You receive a list of projects or solutions with scores ranging from 0 to 100 at the conclusion of the process. That result demonstrates how closely your project adheres to your strategic objective. The highest number is the most desired solution. You can choose your project based on that ranking and decide how to distribute your resources.

Ways to use the AHP method

whenever you meet one or more of the following criteria, you can use the AHP method. When your decision:

The AHP method can be applied to a wide range of decisions, including:

Benefits to using the AHP method

The AHP method presents the following benefits:

The AHP method is easy to use

AHP is intuitive. When using AHP, it is simple to comprehend what you are doing. You divide a difficult decision into objectives, standards, and options. After that, you weigh factors and compare your choices based on these factors. It is more challenging to comprehend the model’s recommendation for a particular course of action using other mathematical techniques. Because you can explain how you arrived at the result with AHP, you are more likely to believe it.

AHP makes it easier to reach a consensus

The AHP method provides a method for supporting the weighing of the criteria. Participants don’t question why one was given priority over the other as a result, and they can concur on the outcome. This simpler priority setting is made possible by the pairwise comparison from AHP. Each participant is asked which criterion is more crucial and by how much. After that, everyone discusses and reviews the comparisons to determine their merit. If the group is divided, you can proceed using the average value. Finally, an algorithm converts all of the comparisons that were agreed upon by the group into a score.

AHP works with multiple criteria

Important decisions often come with conflicting criteria. You may have seen situations in which goals were contradictory. For instance, a project that seeks to combine the best quality and the lowest price Additionally, everyone on a team may have a different perspective and priority when working together. With AHP, you can take into account all the factors that are significant to you and rank them in order of importance.


AHP uses its algorithm to check that your input is consistent. Even identifying these contradictions with the aid of AHP software can help you deal with them.

AHP reduces decision bias

AHP structures the decision. By requiring that each participant contribute, it lessens decision bias and promotes teamwork to arrive at a consensus.

The first step is to determine the criteria. Each organization is free to select its own standards, but for the purpose of this illustration, let’s use the standards Team commitment, Return on investment, and profit.

Examples of the AHP method in action

The organization in this instance wants to know which project to give priority to.

The Goal

Decide which project to prioritize among these 3:

Determine the most important criteria

Finding the criteria comes after knowing the objective. Every organization is free to select its own standards, but for this illustration, let’s use the following standards:

Then, you determine the relative weight between the criteria. You create a comparison matrix and give each item a score to show how important it is in relation to the overall objective.

Divide each value by the sum of the column totals to normalize the numbers.

Add up all of the criteria values to determine the priority, then compute the average.

These values demonstrate that, with 73 participants, the return on investment is the most crucial factor. 5%.

Compare the alternatives

Now that the return on investment criteria have been established, we can compare the various alternatives. The same calculation used in the step before is used to determine the priority score.

We repeat that step for each criterion.

Obtain the overall priority score

Finally, we multiply each criterion’s weighted priority by each alternative’s score.

For instance: Weighted score for return on investment times weighted score for new ERP equals zero. 735 x 0. 20 = 1. 46.

To determine the overall priority score for each alternative, we add up the results of all the newly weighted criteria. Your highest score is the option to prioritize.


How do you use the AHP method?

How to Use the Analytical Hierarchy Process (AHP)
  1. Step 1: Define Alternatives. …
  2. Step 2: Define the Problem and Criteria. …
  3. Step 3: Establish Priority amongst Criteria Using Pairwise Comparison. …
  4. Step 4: Check Consistency. …
  5. Step 5: Get the Relative Weights.

How do you calculate AHP?

The AHP method is a reliable and adaptable MCDM tool for handling complicated decision-making issues. This technique breaks down a complex system into a hierarchy of elements, which typically includes goals, standards for evaluation, and potential solutions.

Why is the AHP method good?

The comparisons, which are typically empirical, are transformed by AHP into numerical values for further processing and comparison. Each factor’s weight enables evaluation of each element within the defined hierarchy.

What is the purpose of the AHP table?

The comparisons, which are typically empirical, are transformed by AHP into numerical values for further processing and comparison. Each factor’s weight enables evaluation of each element within the defined hierarchy.

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