Analytic Hierarchy Process (AHP)

Analytic Hierarchy The Analytic Hierarchy Process (AHP) is a method developed to solve multi-criteria decision making problems. It was first introduced by Thomas L. Saaty in the 1970s. AHP helps quantify comparisons between criteria and alternatives by transforming complex decision processes into a hierarchical structure. This method is particularly preferred in decision problems based on uncertainty or subjective judgments.

Basic Principles of AHP

The AHP method is based on three fundamental principles:

Hierarchical Structuring: Organizing the problem into a hierarchy consisting of the goal, criteria, subcriteria, and alternatives.

Pairwise Comparisons: Determining priority weights through pairwise comparisons between criteria and alternatives.

Consistency Analysis: Calculating the consistency ratio (CR) to evaluate the consistency of the decision maker’s comparisons.

Steps of AHP

The following steps are followed to apply the AHP method:

Modeling the Problem Hierarchically

The decision problem is transformed into a hierarchical structure comprising the goal, criteria, and alternatives. For example, assuming a company needs to select the best supplier, the hierarchy might look like this:

Goal: Select the best supplier

Criteria: Price, quality, delivery time, service quality

Alternatives: Supplier A, Supplier B, Supplier C

Constructing Pairwise Comparison Matrices

Decision makers create comparison matrices by performing pairwise comparisons for each criterion and alternative. Preference intensities are determined using Saaty’s 1–9 scale:

For example, if the criterion “Price” is considered three times more important than “Quality,” the comparison matrix will assign (Price, Quality) = 3 and (Quality, Price) = 1/3.

Calculating Weights and Priorities

Criterion weights are calculated using the eigenvector method or the average weight method from the comparison matrix. The same process is repeated for alternatives to determine their priority values.

Performing Consistency Analysis

The consistency ratio (CR) is calculated to assess the consistency of comparisons. A CR value less than 0.10 indicates that the judgments are consistent. If CR > 0.10, the comparisons must be reviewed.

The consistency ratio is calculated using the following formula:

Where:

CI: Consistency Index

RI: Random Index (obtained from tables)

Comparing Alternatives and Reaching the Final Decision

The weights calculated for criteria and alternatives are combined to derive the final ranking of alternatives. The alternative with the highest overall weight is the decision maker’s optimal choice.

Advantages and Disadvantages of AHP

Advantages

• Systematizes complex decisions
• Transforms subjective judgments into a mathematical model
• Controls consistency in the decision process
• Allows simultaneous evaluation of multiple criteria

Disadvantages

• Can be time-consuming due to the large number of pairwise comparisons
• May produce biased results due to the decision maker’s subjectivity
• The computational process can become complex in large-scale problems

Application Areas of AHP

The AHP method has a wide range of applications. Some common application areas include:

Business and Management: Supplier selection, investment decisions, risk analysis

Engineering and Industry: Product design, production planning

Healthcare: Hospital management, selection of treatment methods

Public Administration and Urban Planning: Politics determination, infrastructure projects

Education: University preferences, academic performance evaluations

AHP provides decision makers with a systematic and analytical frame to help them make more informed and consistent decisions.