MCDM-AHP method in decision making
Developed by Mansoor Samadi
The MCDM-AHP (Multi-Criteria Decision Making - Analytic Hierarchy Process) is a tool that makes complex decisions. MCDM is a systematic approach that evaluate conflicting criterias in decision making, one of these approaches is AHP which uses a mathematic method to derive a relative importance of criteria in a decision problem.
The method was developed in the 1970s by Thomas Saaty , AHP is a mathematical method that is used to derive the relative importance of criteria in a decision problem. The idea behind the method is that a decision problem can be represented as a hierarchical structure, with the most important criteria at the top followed by the lesser important criteria at the bottom.
Decision-making is at the core of project management and yet it can be a daunting task, especially when the projects are complex and multi-facted projects. The pressure of making decisions in a timely and informed manner can be compounded when the criteria for success is not defined clearly, At time like this it not unusual that project managers may feel overwhelmed and unable to determine the most important factors to consider. This is where the AHP-decision-making method provides a systematic approach to this challenge. This approach is addressing the complexity of decision making by Segmenting the process into manageable chunks. By following these steps the project manager can get a obtain a holistic view of the project's key performance indicators and success factors.
AHP for Project management
A project manager in the current day is faced with a dynamic environment, where making the right choices based on fitting objective is a crucial factor for weather a organization is profitable or not. Simply completing a project and hope for the best outcome is no longer enough, as the projects are more complex with more risks and dynamic challenges this means that there is a higher demand for a strategic approach.
In order to accomplish this, organizations are using more resources in portfolio management which helps them structurize the projects so they are in alignment with the organizations strategic goals. One of the main part of portfolio management is cost-benefit, where projects with high benefits is given higher priority. The analysis takes into account the benefits of completing a project as well as the cost, as projects become more complex the cost-benefit analysis becomes as complex and hectic.
Here are three exampels on where the AHP method is applied for project, portfolio and program management.
In project sellection the AHP method can be used in various of ways such as financial return, strategic alignment, resource avaliblility, risk. As the projects become more complicated so does the project selection process, companies uses a lot of resources and money on projects that at the end does not fulfill the customers needs and demands. The AHP metod can solve this dellemma by improving the process of developing project proposals, and it could also remove some of the biasis that managers have. The weakness in project selection using AHP is that if some criterias are ignored, it will give some bad results, The AHP cannot fortune tell so it is exepcted to give all the criterias at the beginning of the selection process and as all other processes a powerfull member can promote their project and introduce more bias in the project selesction..
Across industries the AHP method have been used in selecting suppliers such as the automotive industry, construction and green supply chain management  . There have been multiple papers that demonstrate the effectiveness of the AHP method in supplier selection. With the AHP method it becomes easier to minimize supplier-related risks such as financial stability, quality control, and delivery reliability. The method can also be used to rank the supplier performance over time and adjust changes.
There are a multitude of risks that an orginisation have to account for and from there they can preform some risk management strategies and mitigate said risk based on the likelihood. For example a project manager in a construction company is about to build a commercial building, there are many ways that the project could be delayed such as weather, cost overruns, delays and safety hazards. The PM can weight each of the criterias based on the impact on the project and the likelihood of it happening. When the risks are in order the PM can make risk management strategies to mitigate the risks.
The analytic hierarchy process
Assuming that we have multiple criterias and alternatives, the weight of the criterias is first weighted using pairwise comparison, using saatys scale:
|The foundation scale of absolute numbers|
|Intensity of importance||Definition||Explanation|
|1||Equal importance||Two activities contribute equally to the objective|
|2||Weak or slightly|
|3||Moderate importance||Experience and judgment slightly favor one activity over another|
|5||Strong importance||Experience and judgment strongly favor one activity over another|
|7||Very strong||An activity is favored very strongly over another, its dominance demonstrated in practice|
|8||Very, very strong|
|9||Extreme importance||The evidence favoring one activity over another is of the highest possible order of affirmation|
|Table 1: Saatys scale. |
The AHP method makes use of the hiracy approach, where the objective is at the top and criteria is below it and the alternatives are at the bottom.
Example for AHP
There are many ways to preform the AHP analysis by making it more complex or less depending on the needs of the PM, here is an example:
- Identify the objectives
- Assign weights to the criteria by performing pairwise comparisons
- Evaluate the performance of each alternative with respect to each criterion
- Preform Consistancy test
- Calculate the global priority of each criteria and ranking
Idenrify the objective
A company is in the process of implementing a PMO system and is considering 3 providors. The company have come up with three specific criteria, which are considered highly important when determining which product they should buy. These criteria are cost, technical support, and flexibility.
Assign weights to the criteria by performing pairwise comparisons
When the objective is identified and relevent emperical information is gathered, the next step is to determin the relative importance among the criteria that is under consideration. This process involves giving a specific weight to each criteria based on its percieved importance. This step establish a hierachy, it ensures that the most significant criteria is given appropriate attention. This is done by giving each criteria a relative importance in the Saatys scale 1-9 as shown in table 1, which a person decides. It should be noted that the sum of each row is computed, this is used for later calculations.
Evaluate the performance of each alternative with respect to each criterion
The alternatives are assesed by making a pariwise comparision, just like the previous step. For this step the alternatives are compared against eachother with respect to each criterion the, where they are given a relative importance just like earlier, which a person decides. they are then compiled into tabels, shown below:
|Alternatives with respect to cost|
|Company 1||Company 2||Company 3|
|Alternatives with respect to support|
|Company 1||Company 2||Company 3|
|Alternatives with respect to flexibility|
|Company 1||Company 2||Company 3|
In order to give a relative weight to each criterium, the matrices are normalised. This is done by dividing each value with the sum of the column value. Afterwards the priority is calculated, this is done by taking the sum and dividing with the number of elements, 3 in this case:
The values calculated under priority have a meaning in AHP, the values represent the relative importance of the criteria to the overall goal. In this case the company have decided that flexibility have a importance of 16% (this is the priority calculated in the above table).
Preform consistancy test
When preforming the consistancy the following is computed:
- The largest eigenvalue, λ_max, of the matrix is calculated
- The Consistency index (CI) and the consistency ratio (CR) is calculated
Math software, like maple, was used to find the largest eigenvalue of the matrix. The consistency index is calculated with the following formula:
where n is the number of elements. RI is is called the random consistency index, to finx the consistency ratio the CI is divided by the RI. The consistency ratio can be calculated with the following expression:
The values for RI is presented below:
|Consistency of random matrices|
The consistancy test is preformed for the criterum matrix,cost matrix, support matrix and flexibility matrix:
Calculate the global priority of each criteria and ranking
|The AHP ranking|
After the AHP method calculations are completed the comapany that provides the best services compared to your needs is shown as company #1. This method can be scaled to larger organisation such as NASA, seen in the "implementation of AHP method in organisations".
Limitation of the AHP method
While AHP is a have been implemented in many cases and it is an effective method for decision-making in project management, it is not without limitations. Some of the limitations of the AHP method are listed below:
- complexity As the projects becomes larger the complexity increases exponentially, the large number of criterias becomes less manageable as it becomes more dificult to evaluate each criteria's reletive importance which can result to inconsistency in the decision making process, the criterias in the example above have only 3 criterias which is manageable but imagine if there were 500 criterias. Lets say the danish goverment had to decide the locations of the super hospitals, there are many criterias where some of them are political, economic, and so on, it becomes difficult to evaluate each criteria's reletive importance. 
- Time dependency in project and portfolio management
It takes a large sum of time for the decision makers to select alternatives. In the time where the DMs are selecting alternatives the project might have changed where a alternative is added or deleted, which then results in that the DMs have to make the entire process over again. In complex projects like govermental ones where the DM is excecuting a pairwise comparison to govermental policies, when the DM have finished the process, the goverment implements a new policy. The AHP method is great tool for small projects where there arent too many criterias and alternatives.
- Subjectivity It is fair to assume that all the DMs are knowledgeable in the subject and that they are unbias but each person have their own preferences and experence. When DMs confront an issue they will tackle the issue differentely dipending on their perefences. These preferences have no ground in mathematic formula or reasoning, the stakeholders are relying on the preferences of the DMs which can change depending on their mood and feeling. 
Implementation of AHP method in organisations
US China conflict
The process was used when back in the 1995 when US and china was in conflict regardin intellectural property rights, the conflict was regarding chineses civilians copying music, video without paying the owners. To see wether it was benefitial for the US to sanction China, an AHP analysis was made where benefit, cost and risk was taken into account and from the analysis it would be much more benefitial to not sanction China, in the references many more applications can be seen. 
When National Aeronautics and Space Administration (NASA) had to decide which power source to be used for the lunar outpost a AHP analysis was conducted where the criterias were safety, performance, reliability and flexibility and many more. NASA have since then used it to many other projects such as the lunar landing propulsion system, their Computer aided systems engineering tool set (CEASETS), and many more. 
As the AHP method is widely used method in the industry, there are multiple papers that are very intersting and informative that i was not able to incorpriate in this wiki but future AHP nerds may implement it:
This paper implents the AHP method for a building project where they use a software named 'Expert choise', it would be intersting to see what the commerical programs can do and how they solve some of the limitations of the AHP methods
- Kamal M.Al-Subhi A., "Application of the AHP in project management", 2001, ResearchGate.
- Erick L., Ewerton G., et. al."Applying machine learning to AHP multicriteria decision making method to assets prioritization in the context of industrial maintenance 4.0", 2019, ResearchGate
This paper goes deep into project delivery method and descripes the importance for the project owners to have a delivery method, they have developed a methodology that incorporates the AHP method:
- Mohammed K., "Selecting the appropriate project delivery method using AHP", 2002, ResearchGate
Even tho this source was used in the wiki, i higly reccormed that it is studied more because the source descripes in detatail and in a rational way the limitations that the AHP method have, it uses real life examples and some things to be aware of as project managers.
- Nolberto M., Eloy H., "Uses and Limitations of the AHP Method - A Non-Mathematical and Rational Analysis", 2021, Springer.
- ↑ Saaty, T. L. How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 48(1), 9-26, 1990. https://www.sciencedirect.com/science/article/pii/037722179090057I
- ↑ Palcic, I.; Lalic, B. Analytical Hierarchy Process as a tool for selecting and evaluating projects. Int. J. Simul. Model. (IJSIMM) 2009, 8, 16–26 https://www.researchgate.net/publication/238195934_Analytical_Hierarchy_Process_as_a_tool_for_selecting_and_evaluating_projects
- ↑ Wang, Y., Dong, Y., & Hao, J. (2018). AHP-based supplier selection for an automotive manufacturer in China. Journal of Manufacturing Systems, 46, 63-70.
- ↑ Chan, A. P., Chan, D. W., & Ho, K. S. (2016). Application of AHP in selecting suppliers for a construction project in China. Journal of Construction Engineering and Management, 142(6), 04016012.
- ↑ Chai, J., Liu, J., & Lu, Y. (2017). An AHP-based evaluation method for supplier
- ↑ 6.0 6.1 6.2 Saaty, Int. J. Services Sciences, Vol. 1, No. 1, 2008 https://www.rafikulislam.com/uploads/resourses/197245512559a37aadea6d.pdf
- ↑ 7.0 7.1 7.2 Hontoria, E., el al. "Uses and limitations of the AHP method, a Non-Mathematical and Rational Analysis", Springer, https://link.springer.com/chapter/10.1007/978-3-030-60392-2_5