AHP Analytical Hierarchy process

By Shashikant Nishant Sharma

The Analytic Hierarchy Process (AHP) is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. It was developed by Thomas L. Saaty in the 1970s and has been extensively studied and refined since then. AHP helps decision-makers set priorities and make the best decision by reducing complex decisions to a series of pairwise comparisons, and then synthesizing the results.

Key Steps in AHP

1. Define the Problem and Goal: Clearly state the decision problem and identify the goal to be achieved.
2. Structure the Hierarchy: Break down the problem into a hierarchy of more easily comprehended sub-problems, each of which can be analyzed independently. The hierarchy typically has three levels:
   • Goal: The overall objective of the decision.
   • Criteria: Factors or attributes that will be used to evaluate the alternatives.
   • Alternatives: The different options or choices available.
3. Pairwise Comparisons: Compare the elements at each level of the hierarchy pairwise in terms of their impact on an element above them. This involves asking how much more one element is important or preferred over another with respect to the criterion above them. This comparison can be done using a scale of relative importance, typically ranging from 1 (equal importance) to 9 (extreme importance of one over the other).
4. Priority Calculation: Use the pairwise comparison matrix to calculate the weight or priority of each element. This is often done using eigenvalue methods or other techniques to derive ratio scales.
5. Consistency Check: Evaluate the consistency of the judgments to ensure that the pairwise comparisons are reliable. A Consistency Ratio (CR) is calculated, and if it is within an acceptable range (usually CR < 0.1), the judgments are considered consistent.
6. Synthesize the Results: Combine the priorities of the elements to determine the overall ranking of the alternatives. This is done by aggregating the weights through the hierarchy to arrive at the overall priorities for the decision alternatives.

Applications of AHP

AHP is versatile and can be applied in various fields, including:

• Business and Management: For strategic planning, resource allocation, and performance measurement.
• Engineering: For selecting the best engineering design or technology.
• Healthcare: For evaluating treatment options or healthcare policies.
• Education: For selecting academic programs or assessing teaching methods.
• Government and Public Policy: For policy analysis and decision-making in public projects.

Example

Consider a simple example where a company needs to choose a new software package. The goal is to select the best software package. The criteria might include cost, ease of use, functionality, and support. The alternatives are Software A, Software B, and Software C.

1. Define the Problem and Goal: Select the best software package.
2. Structure the Hierarchy:
   • Goal: Select the best software package.
   • Criteria: Cost, Ease of Use, Functionality, Support.
   • Alternatives: Software A, Software B, Software C.
3. Pairwise Comparisons: Compare each criterion pairwise and each software alternative under each criterion pairwise.
4. Priority Calculation: Calculate the weights for each criterion and for each software alternative under each criterion.
5. Consistency Check: Ensure the consistency ratio is acceptable.
6. Synthesize the Results: Combine the weights to determine the overall ranking of the software packages.

By following these steps, the decision-makers can arrive at a rational and justifiable decision based on a structured and quantifiable method.

Advantages of AHP

• Structured Approach: Provides a clear and systematic framework for decision-making.
• Flexibility: Can be applied to a wide range of decision problems.
• Consistency: Ensures consistency in judgments through the consistency ratio.
• Quantitative and Qualitative: Combines both quantitative data and qualitative judgments.

Disadvantages of AHP

• Subjectivity: The process relies on the subjective judgments of the decision-makers.
• Complexity: Can become complex and time-consuming for large-scale problems with many criteria and alternatives.
• Pairwise Comparison Limitations: The number of comparisons grows rapidly with the number of criteria and alternatives, which can be overwhelming.

In summary, AHP is a powerful tool for decision-making that helps break down complex problems into manageable parts, allowing for a rational and comprehensive analysis of the alternatives.

References

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