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# Analytic Hierarchy Process

Updated on May 31, 2024
Article byPrakhar Gajendrakar
Edited byAaron Crowe
Reviewed byDheeraj Vaidya, CFA, FRM

## What Is Analytic Hierarchy Process (AHP)?

The analytic hierarchy process (AHP) is a rational decision-making technique. The process integrates quantitative data, calculation, qualitative data, and human psychology. This method accounts for all possible alternatives to derive the best possible solution.

For eg:
Source: Analytic Hierarchy Process (wallstreetmojo.com)

AHP comprises three important steps: the problem is identified, the decision maker analyzes possible alternatives, and the analyst finds a criterion to choose the best option. Project prioritization and selection frequently involve its use. When evaluating projects, AHP enables one to codify the strategic objectives as a list of weighted criteria.

### Key Takeaways

• The analytic hierarchy process addresses problems by evaluating every alternative approach to determine the best possible solution. It comprises three main steps: the problem, the alternatives, and the criterion that suits the desired outcome.
• The method is applied to both advanced analytical solutions and day-to-day decision-making. It even accounts for psychological factors.
• AHP is used to transform intangible or psychological factors into comparable values. Decision makers assign a quantitative value to intangible or psychological factors.

### Analytic Hierarchy Process Explained

The term analytic hierarchy process (AHP) refers to rational decision-making. While using this method, managers run through every possible alternative and choose the most prudential option. But not just managers; every individual makes decisions daily; the decision is based on data and psychological factors.

In the 1970s, Thomas L Saaty proposed the analytic hierarchy decision-making technique. Professor Saaty taught at the University of Pittsburgh. In addition to being a theorist, he was an inventor and architect.

AHP follows a three-part process; first, the problem is identified. Then, the decision maker analyzed possible alternatives. Finally, the decision maker finds a criterion to choose the best option among the alternatives. This decision-making method can be used to select a stock or even for a mundane daily life decision, say, choosing a menu for breakfast.

AHP is used to transform intangible or psychological factors into comparable values. To achieve that, AHP converts intangible or psychological factors into values and then helps compare and eliminate inconsistencies with the result to offer the best suitable solution. The decision maker then eliminates inconsistencies between the particular factor and the outcome.

Fuzzy AHP is a variation of AHP that integrates qualitative and quantitative methods. In this variation, the researcher classifies factors into target levels.

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### Steps

Analytic hierarchy process steps are as follows:

#### #1 – Defining The Problem Or Objective

Professor Thomas L. Saaty believed that a problem always contains sub-problems. Hence, the AHP method breaks down the problem into sub-parts and implements the root cause analysis. A root cause analysis identifies the fundamental reason behind any problem or situation. It helps to arrive at an optimum solution by bridging the cause-and-effect relationship for an event.

For eg:
Source: Analytic Hierarchy Process (wallstreetmojo.com)

This approach is applied across different industries, from healthcare and software to environment and manufacturing.

#### #2 – Stating The Alternatives

In step two, the decision maker gathers all possible solutions (alternatives). In a trial-and-error process, each criterion is checked against the outcome. The performance of each alternative is recorded elaborately.

#### #3 – Setting Priorities And Criteria

Then, the decision maker creates a matric. They compare alternatives in pairs and sets. Using set criteria, the decision maker eliminates alternatives that do not coincide with the desired outcome.

#### #4 – Check Consistency

By step 4, the decision maker has big data. If a comparison yields inconsistent results, the analyst traces their steps and double-checks calculations. This way, errors can be prevented.

#### #5 – Determining Relative Weights

In the final step, the software is used to conduct quantitative calculations. This step outputs relative weights that support the given criteria. This result is expressed in the form of an equation.

Thus, the decision maker applies the equation to arrive at the best possible solution for the particular scenario.

### Examples

Let us look at analytic hierarchy process examples to understand the method better.

#### Example #1

Let us assume that Miranda wants to move to a new country; she can either move to Canada for a new job or stay where she is (New York). This example is a psychological hierarchy process; comfort and standard of living are the main criteria.

Here, the main problem is further broken down into multiple smaller problems. Canada can be expensive; Miranda just got promoted at her New York job, so she can easily move to and from Canada and New York. Also, Miranda’s mother lives in New York.

In addition, there are other criteria like cost, comfort, safety, and growth. Miranda can turn each criterion into a tangible factor by assigning a value and performing a pairwise comparison.

First, Miranda compares factors using three criteria—cost, comfort, and safety. Miranda compares alternatives in pairs. Miranda assigns a quantifiable value to each factor and compares them against the desired outcome. Then she checks the results for consistency.

By the end of the decision-making process, Miranda concludes that the cons of relocating to Canada outweigh the pros. So she decides to stay put.

#### Example #2

Phyton is commonly used in AHP. AHP selects a leader based on multiple criteria—charisma, age, education, and experience. Each criterion is assigned a quantifiable value—say, 1 point for charisma, 1 for education, and 1 for experience.

Using the AHP scales, criteria are compared to each other. The analyst checks every step for inconsistencies. In case of inconsistency, the step is repeated using different parameters.

• The whole concept of AHP is simple and easy to use.
• AHP outcomes are very easy to comprehend.
• Most cases, AHP results fare well in real-world scenarios based on multiple criteria.
• The AHP process checks the results for consistency. This way, errors are prevented.
• AHP is the solution for personal bias in decision-making, whether in day-to-day or corporate decision-making.

Disadvantages of the hierarchy process are –

• AHP programs use advanced mathematics and eigenvectors.
• To automate the process, the analyst must know the calculation process.
• This process quantifies intangible factors and emotions into quantitative data. Despite being an objective method, this step is entirely subjective. If different analysts undertake the same process, they might quantity factors differently.
• AHP requires robust computing capabilities.
• This process consumes a lot of time and effort.

1. How is the analytic hierarchy process used?

The AHP framework is built on rational factors. It is a popular decision-making method—the best possible solution is determined based on quantitative and qualitative factors. It is used in many coding languages.

2. What is the analytic hierarchy process in GIS?

GIS is a Geographic Information System used to create and manage map data. GIS is integrated with an AHP to determine the suitability of land using multiple criteria.

3. Is the analytic hierarchy process qualitative?

The AHP is already applied in day-to-day decision-making—many individuals rely on their rationale and critical thinking for everyday decisions. Thus., AHP is an amalgamation of qualitative and quantitative attributes. It accounts for both tangible and intangible factors. Ultimately the process narrows down to the best possible solution for the given scenario.