What is the Analytical Hierarchy Process? And How Does it Work?

In this video, I answer the question, ‘What is the Analytical Hierarchy Process?’ and look at how we carry it out, with a worked example.

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The Analytical Hierarchy Process

Basic Definition of the Analytical Hierarchy Process

The Analytical Hierarchy Process (AHP) is a structured decision-making framework that helps individuals and organizations evaluate complex choices.

A common use-case in the projects world is in determining which projects and programs to include in a wider portfolio.

The Analytical Hierarchy Process was developed by Thomas Saaty. It breaks the problem into a hierarchy of:

• Goal
• Evaluation Criteria
• Options

It then uses pairwise comparisons and mathematical calculations to weight the evaluation criteria.

With this infrastructure in place, AHP allows users to prioritize options based on 

• Their relative scores against each criterion
• Weighted by the criterion weighting

This ranks the relative options to allow for consistent decision-making. 

The Basic Analytical Hierarchy Process Process

Step 1: Define the Problem and Goal

• Clearly state the decision you need to make.
• Identify the overall goal of the decision-making process.

Step 2: Structure the Hierarchy

Break the decision down into a hierarchy with three levels:

1. Goal (the overall objective).
2. Criteria (factors influencing the decision).
3. Alternatives (the options being considered).

Step 3: Determine the criteria for evaluation

What matters most in making your prioritization among the alternative options? When you have your list of criteria, you will need to allocate weights.

Step 4: Conduct Pairwise Comparisons of Criteria

What distinguishes the AHP from other, simpler, processes is the sophistication of how we calculate the weightings for each evaluation criterion. We do this by comparing each criterion against the others, using a pairwise comparison matrix.

We use Saaty’s 1-9 scale to assign numerical values to these comparisons. (put on screen).

Step 5: Calculate the Priority Weights

The mathematical methods for calculating and testing the weights for your evaluation criteria is beyond the scope of this video. But, in summary:

• Convert comparison values into numerical scores.
• Normalize the matrix and compute priority weights for each criterion, to determine the relative importance of each factor.

Step 6: Check for Consistency

Calculate a Consistency Ratio (CR) for the weights, to ensure logical and consistent comparisons. A CR ≤ 0.1 indicates acceptable consistency; if higher, review the comparisons.

PLEASE NOTE: The number on the screen is incorrect and should be 0.1 (not 1).

Step 7: Evaluate the Alternatives

Once again, whilst a simpler approach will just score each alternative against each criterion, AHP uses a pairwise comparison in a similar way to how you assessed the relative importance of your criteria.

• We compare each pair of alternatives against each evaluation criterion.
• We ask a question like: ‘With respect to criterion A, how much more do you prefer option X to option Y?’

Step 8: Aggregate the Results to Rank the Alternatives

• Multiply the priority weights of criteria by the scores of alternatives.
• Sum up the weighted scores to determine the best alternative.

Step 9: Make the Decision

• Select the alternative with the highest overall priority score.
• Validate the results and refine the analysis if needed.

An Example of the Analytical Hierarchy Process

Scenario: Selecting the Best Project

A company must choose among four potential projects (Project A, B, C, and D). The decision is based on four key criteria:

1. Net Present Value (NPV) – The financial return of the project. Higher is better.
2. Alignment with Corporate Strategy – How well the project supports the company’s long-term goals.
3. Implementation Risk – The likelihood of encountering significant challenges (lower is better).
4. Integration Complexity – The difficulty of integrating the project into existing systems (lower is better).

So, our Decision Hierarchy looks like this:

• Goal: Select the Best Project
  • Criteria: NPV, Alignment with Corporate Strategy, Implementation Risk, Integration Complexity
    • Alternatives: Project A, Project B, Project C, Project D

Conduct Pairwise Comparisons

The decision-makers compare each criterion against the others. To do it properly, we would use Saaty’s 1-9 scale. Here, we’ll simplify, and use a scale of 1 to 4. Let’s assume they prioritize NPV as the most important factor, followed by Alignment with Strategy, while Implementation Risk and Integration Complexity are somewhat less important.

Example of Pairwise Comparison for Criteria

(Higher values indicate a stronger preference over the other criterion.)

Normalisation

After normalizing this matrix and calculating priority weights, we get approximately:

• NPV: 47%
• Strategy Alignment: 28%
• Implementation Risk: 16%
• Integration Complexity: 10%

How I calculated these is beyond the scope of this video.

Compare the Four Projects Under Each Criterion

Now, we compare Project A, B, C, and D under each criterion. Below are the assumed pairwise comparisons and final weights for each alternative.

Compute the Final Scores

To calculate the overall score for each project, multiply the criteria weights by the respective project scores:

Make the Decision

The project with the highest score wins!

Final Ranking:

1. Project A (0.317) → Best choice
2. Project B (0.265)
3. Project C (0.234)
4. Project D (0.184)

Conclusions about the Analytical Hierarchy Process

In our example, using AHP, Project A emerges as the best option because it has the highest weighted score based on NPV, strategy alignment, and risk factors.

The Analytical Hierarchy Process has some moderately complex maths in calculating and validating the weights and scores. But, it is valuable where:

• significant implications rest on the decisions you make and where
• you want to take account of more than just financial implications – for which we can use the Discounted cash Flow method

In such scenarios, this is, perhaps, the most robust approach available to us.

Recommended Videos and Articles to Help with the Analytical Hierarchy Process

Carefully curated recommendations for you:

• Your Essential Guide to How to Make Robust Project Decisions (article)
• Rapid Project Decisions: Do You Know How to Make them with Confidence? (article)
• Better Decision-making and More Robust Choices – Top 10 Tips (video)
• Decision-Making AI for Project Portfolios – with Stuart Easton (video interview)
• What is a Discounted Cash Flow – DCF? | Video
• How to Create a Discounted Cash Flow – DCF Made Easy

What Kit does a Project Manager Need?

I asked Project Managers in a couple of forums what material things you need to have, to do your job as a Project Manager. They responded magnificently. I compiled their answers into a Kit list. I added my own. 

Check out the Kit a Project Manager needs

Note that the links are affiliated.

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