An Introduction to the Analytic Hierarchy Process (AHP)
AHP standing for the Analytic Hierarchy Process is considered as a decision-making tool that can assist both a person and an organization to make the complicated decisions via breaking down a problem into smaller parts which are more manageable. In the 1970s, Thomas Saaty developed AHP, and also it has since become a popular tool employed in the different areas, such as project management, engineering, and economics. including
In the AHP, utilizing a pairwise comparison method, decisions are made by assessing and comparing a set of criteria and alternatives against each other. The criteria and alternatives are then are ranked in order of the relative importance to each other, enabling the decision-maker to make informed choices according the analysis results.
In general, AHP presents a structured systematic approach to decision-making, which can assist both people and organizations to make informed decisions and feel more confident in their abilities. It can assist you to navigate the complicated problems and make the best decisions in a situation Whether you’re performing a personal project or making the decisions for a big company.
The AHP provided by Thomas Saaty in the 1970s is considered as a method to make complicated decisions arranged in a systematic way. Saaty as an expert in both the mathematics and operational research wanted to create a tool that would assist individuals to make the decisions according to an organized analysis of both the criteria and the alternatives
History of AHP
The AHP method was first published by Thomas Saaty in 1977 and was rapidly identified as a powerful tool that can assist us to make the decisions. Since then, it has been commonly employed in the different areas, including project management, engineering, and economics, as well as making the personal decisions.
The AHP has been changed by the continuous refinement and improved over the years, and is therefore one of the most popular decision-making tools employed in the world. AHP‘s popularity is due to its simplicity, versatility, and capability to manage complex problems in a systematic and organized manner. AHP can be employed to make the governmental, organizational and personal decisions. The AHP method is focused on the continuous evolution and has been applied to support decision-making in a wide variety of areas, making it one of the most popular decision-making methods used in the world.
AHP method steps
The AHP is comprised of a number of steps:
1- Recognizing the problem: The first step in the AHP method is to recognize the problem or decision to be made, and to define the analysis objectives in a clear manner. .
2- Breaking down the problem: The next step in the AHP method is to break down the problem into smaller parts which are more manageable, including criteria and alternatives.
3- Developing a hierarchy: The criteria and alternatives are then arranged in a hierarchical fashion with the most desirable criteria at the top and the least desirable at the bottom.
4- Performing pairwise comparisons: In this step, the criteria are compared to each other, and also alternatives are compared to each other. This is performed by a pairwise comparison method, where the decision-maker rates each pairwise comparison on a 9-point scale.
5- Arranging the criteria and alternatives in order of importance relative to each other: The results obtained from the pairwise comparisons are employed to assess the relative importance of both the criteria and the alternatives. This allows the decision-makers to arrange the criteria and alternatives in order of importance relative to each other and focus their attention on the most desirable ones.
6- Synthesizing the data: The last step in the AHP method is to synthesize the data and make a decision. The decision-maker can employ the criteria and alternatives ranked in order of importance relative to each other in order to make informed decisions and select the best course of action.
Generally, the steps in the AHP method present an organized and systematic approach to decision-making, enabling both people and organizations to make well-informed decisions and feel more confident in their abilities.
A simple example of AHP method
In the following, there is a simple example of how the AHP can be employed to make a decision:
Let’s say you’re attempting to make a decision which city go on your next vacation. You’ve reduced the number of your choices to three cities, including Paris, New York, and Tokyo. Cost, attractions, food, and safety can be considered as your criteria in order to select a city.
Step 1: Recognizing the problem –Selecting a city for your next vacation
Step 2: Breaking down the problem – Criteria for selecting a city includes cost, attractions, food, and safety, and also the alternatives are the cities, including Paris, New York, and Tokyo.
Step 3: Creating a hierarchical structure –A hierarchical structure contains both the criteria (including cost , attractions, food and safety) and the alternatives (including Paris, New York, and Tokyo) : ,, safety :
Step 4: Performing pairwise comparisons: The criteria are compared to each other, and also a 9-point scale is employed to rate their relative importance.
. For instance, a score of 9 indicated that cost is more important than attractions, a score of 7 implies that attractions are more important than food, and also a score of represents that food is more important than safety.
Step 5: Ranking the criteria and alternatives in order of importance relative to each other: The results obtained from the pairwise comparisons are employed to rank the criteria and alternatives in order of the relative importance to each other. For instance, cost followed by attractions, food, and safety, can be considered as the most important criterion,
Step 6: Synthesizing the data – The last step in AHP method is to synthesize the data and make a decision. You would employ the criteria ranked in order of their importance relative to assess the alternatives and identify the best city to go on your vacation. For instance, using your pairwise comparisons, you found that Paris can be selected as the best city for your vacation because it the best combination of cost, attractions, food, and safety is provided by this city. .
In this example, AHP method presents an organized and systematic approach to decision-making, which can assist you to make an informed decision according to your priorities and preferences.
The consistency ratio in AHP method
The CR representing consistency ratio is considered as a major concept in the AHP method employed to assess the consistency of the pairwise comparisons made between elements inthe hierarchical structure. The CR can be computed as a ratio of the CI standing for consistency index and the RCI representing the random consistency index (based on the size of a pairwise comparison matrix (PCM).
A value of CR lower than 0.1 indicates that a pairwise comparison has an acceptable consistency level, while a value of CR higher than 0.1 indicates that the inconsistency is observed in the pairwise comparisons , and also there is a need to revise it . Higher CR values indicate that the pairwise comparisons made between elements in the hierarchical structure may be unable to reflect their relative importance accurately, and also the results obtained from AHP method may not be reliable.
The CR is considered as an important tool for ensuring that both the quality and reliability of the AHP method are achieved, and also its value should be computed as the AHP method is used for decision-making.
AHP formula
The eigenvalue method is considered as the formula employed in the AHP is. It is a mathematical technique employed to assess the relative importance of various elements in the hierarchical structure.
In AHP method, creating a PCM is applied to determine the relative importance of both the criteria and the alternatives. The PCM is then employed to find the eigenvector, indicating the relative importance of each element in the hierarchical structure.
The following formula can be used to compute the eigenvalue:
Let A be the PCM of size n x n, then the eigenvalue λ is obtained from the following formula:
A * v = λ * v
Where v represents the eigenvector, and also λ denotes the eigenvalue.
The eigenvector serving as a column vector indicates the relative importance of each element in the hierarchical structure, and also the eigenvalue represents that there exits the consistency in the PCM. The higher the eigenvalue, the more consistent the PCM would, and also the more reliable the results would be.
The eigenvalue method is considered as a powerful tool used for making the complicated decisions, and also it is placed at the core of the (AHP).
Applications of AHP method
AHP is applied in a wide variety of areas, such as operational research, management, engineering, and environmental science, in order to support decision-making process and problem-solving via assessing and prioritizing and the complex data.
Supply chain management (SCM): AHP method can be employed to assess and prioritize the suppliers with respect to the criteria, including quality, delivery, and cost.
Project management: AHP method can be utilized for the prioritization of in a tasks project and the assignment of resources based on criteria, including cost, time, and risk.
Marketing: AHP method can be used for assessing and prioritizing both the strategies and the tactics related to marketing based on criteria like cost, reach, and impact.
Human resource management (HRM): AHP method can be used for assessing and prioritizing people who applies for a job according to criteria, including experience, education, and fit.
Financial management: AHP method can be employed to assess and prioritize a range of opportunities related to investment based on criteria like risk, return, and diversification.
Healthcare: AHP method can be applied to assess and prioritize the therapies according to criteria, including efficiency, side effects, and cost.
Environmental management: AHP method can be utilized for assessing and prioritizing environmental initiatives according to criteria like effect, practicality, and cost.
Education: AHP method can be applied to assess and prioritize the both programs and initiatives related to education based on criteria like cost, effect, and practicality.
Construction: AHP method can be used for assessing and prioritizing the projects related to construction according to criteria, including cost, a plan of procedure for a project, and quality.
Customer service: AHP method can be applied to assess and prioritize the initiatives related to customer service based on criteria like cost, effect, and practicality.
These are just a few examples of how AHP method can be employed in the different areas. The AHP process is characterized by the flexibility and will be truly tailored to tailored to meet the specific requirements and archive the goals of each situation.
AHP papers
Studies conducted on AHP process are research articles or academic papers evaluating the use of AHP method in the different areas and applications. The papers usually explain the steps involved in the AHP method, the results of using AHP method for a given problem or case study, and the advantages and limitations of utilizing the AHP.
The field of activity of AHP papers can differ considerably, including procurement, sustainability, efficient energy use, transportation, water systems, and selecting the vendor. . The papers may utilize AHP method in combination with other approaches related to decision-making, including the TOPSIS standing for Technique for Order Preference by Similarity to Ideal Solution (), fuzzy logic, grey relational analysis, and VIKOR method representing the VlseKriterijumska Optimizacija I Kompromisno Resenje.
The objectives of AHP papers are to contribute to better understanding of the AHP process and its usage, and to provide practical insights for decision-makers working in the different areas. .
Studies conducted on the AHP process published in 2020 are as follows:
- “Supplier selection using the AHP-TOPSIS integrated method: An empirical study in the automobile industry” focuses on using AHP and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select suppliers in the automobile industry.
- “Green procurement evaluation using AHP and grey theory: A case study in the iron and steel industry” examines the use of AHP and grey relational analysis to evaluate green procurement practices in the iron and steel industry.
- “Prioritizing sustainable development goals using AHP: A case study in Iran” uses AHP to prioritize the United Nations Sustainable Development Goals (SDGs) in Iran.
- “AHP-based assessment of university sustainability: A case study in Iran” applies AHP to evaluate the sustainability of universities in Iran.
- “AHP-based evaluation of energy-efficient building projects: A case study in Turkey” utilizes AHP to assess energy-efficient building projects in Turkey.
- “Integrating the AHP and grey relational analysis methods for vendor selection in supply chain management” combines AHP and grey relational analysis to select vendors in supply chain management.
- “Applying the AHP and Fuzzy AHP methods to evaluate the environmental impact of manufacturing processes: A case study in the automotive industry” uses AHP and fuzzy AHP to evaluate the environmental impact of manufacturing processes in the automotive industry.
- “Evaluating the sustainability of urban transportation systems using AHP and fuzzy AHP: A case study in Iran” applies AHP and fuzzy AHP to evaluate the sustainability of urban transportation systems in Iran.
- “Using the AHP and VIKOR methods to evaluate the sustainability of urban water systems: A case study in Iran” employs AHP and the VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method to evaluate the sustainability of urban water systems in Iran.
- “Applying the AHP and grey relational analysis methods for vendor selection in the aerospace industry” combines AHP and grey relational analysis to evaluate and select vendors in the aerospace industry.
- These articles demonstrate the versatility of the AHP method and its application in various fields, including procurement, sustainability, energy efficiency, transportation, water systems, and vendor selection.
AHP software
Both Microsoft Excel and MATLAB can be used to implement the AHP method. It is essential to note, however, that there are some limitations on both Excel and MATLAB have when they are applied to implement the AHP method, including a lack of standardization, restricted functionality mode, and the potential for results which are not consistent or correct. It is therefore recommended to utilize a specialized AHP application or consult with an a specialized expert who works in in the field of complicated or high-stakes decision-making.
Limitations of implementing the AHP process in Excel
Microsoft Excel is considered as the most frequently used spreadsheet program that can be employed to calculate the AHP process, but there are some obvious drawbacks to using it:
Restricted functionality mode: Excel is mainly developed as a spreadsheet program and may not have all the regular features and functions which are essential to perform the complex calculations related to AHP process.
Time-consuming: conducting the calculations related to AHP method in Excel can be time-consuming, particularly if the problem hierarchy is created from a large scale or the pairwise comparisons are complex.
Inconsistent data: As both the assessment and the validation are inappropriate, it is therefore possible to obtain inconsistent or incorrect data when conducting the calculations related to AHP process implemented in Excel.
Lack of standardization: There exists no standardization of method employed to carry out calculations associated with AHP process implemented in Excel, resulting in the confusion or misinterpretation of the findings.
Inadequate documentation: It can be tough to document and communicate the results obtained from the calculations related to AHP process implemented in Excel as both the methodology and calculations are not capable of being understood by other users easily.
Limited support: There exists limited support available for the calculations related to AHP process performed in Excel, and also users may need to rely upon online resources or forums for the assistance.
It is therefore recommended to utilize a specialized AHP application or consult with an expert working in this field if the calculations related to AHP process are necessary for the complicated or high-stakes decision-making.
Limitations of implementing AHP process in MATLAB
The implementation of AHP process in MATLAB includes some limitations that should be considered:
Complexity: Implementing the AHP method can be complex, particularly for users who have limited experience in MATLAB used for in programming.
Restricted functionality mode: MATLAB is mainly developed as a software used for technical computing, and may not have all the regular features and functions which are required for the complex calculations related to AHP process.
Time-consuming AHP process: Implemented in MATLAB can be time-consuming, particularly if the problem hierarchy is created from a large scale or the pairwise comparisons are complex.
Lack of standardization: There exists no standardization of the approach utilized for AHP process Implemented in MATLAB, leading to confusion or misinterpretation of the data.
Inadequate documentation: It can be hard to document and communicate the results obtained AHP process implemented in MATLAB, as the methodology and calculations related to AHP are not capable of being understood by other users.
Limited support: There exits limited support available for AHP process implemented in MATLAB, and also users may need to rely upon online resources or forums for helping.
Error-prone: Given the complex nature of AHP process and the need for exact calculations; therefore, making mistakes in implementing the AHP process is easy, and also this can influence the accuracy of the results.
It is therefore recommended to utilize specialized AHP application or c consult with an expert working in this field if the calculations related to AHP process are necessary for complicated or high-stakes decision-making.
AHP onlie software:
AHP online software is really easy to use. :
- Create a chart with a hierarchical structure
- Fill tables of the pair comparison method
- Obtain the complete output
What is AHP?
AHP, or the Analytic Hierarchy Process, is a decision-making method used to evaluate and prioritize complex information based on a hierarchy of criteria and alternatives.
How is AHP used in decision-making?
AHP is used in decision-making by breaking down a complex problem into a hierarchy of criteria and alternatives, and then making pairwise comparisons between the elements to determine their relative importance.
What are the advantages of using AHP?
The advantages of using AHP include its ability to handle complex problems, incorporate multiple criteria, and provide a systematic and transparent approach to decision-making.
What are the steps of the AHP method?
Step 1: Define the decision problem and create a hierarchy of criteria and alternatives.
Step 2: Make pairwise comparisons between the elements of the hierarchy to determine their relative importance.
Step 3: Calculate the weights of the elements based on the pairwise comparison results.
Step 4: Evaluate the alternatives based on their performance against the criteria.
Step 5: Determine the overall rankings of the alternatives based on their weighted scores.
How can the consistency of AHP results be evaluated?
The consistency of AHP results can be evaluated using the consistency ratio, which compares the consistency of the pairwise comparisons to a random consistency index.
What types of problems can AHP be used to solve?
AHP can be used to solve a wide range of problems, including project selection, product design, resource allocation, risk management and …
How can AHP be implemented using software?
AHP can be implemented using specialized AHP software, such as AHP Online software, or through custom-built software or Excel spreadsheets.