Tag: AHP

AHP and the Magical Number Seven Plus or Minus Two

In the analytic hierarchy process you define a set of criteria and sub-criteria arranged in a hierarchy, to do pairwise comparisons and find the weights of criteria or decision alternatives. In my AHP excel template the number of criteria is limited to ten, in my AHP online software to 15. Still sometimes I am asked to extend and allow for more criteria.

Why the number of criteria should not exceed the magical number seven plus or minus two?

There are three reasons not to exceed the number of 9 criteria in any AHP project. Two of them are quite clear and published in the literature:

  • The first has to do with the human limits on our capacity for processing information, and was published by George A Miller, as well as in the context of AHP by Saaty and Ozdemir.
  • The second is related to the first one. The number of pairwise comparisons increases with the number of criteria, it is (n2 – n)/2. For example, 9 criteria require 36 comparisons. For a  high number of comparisons easily logical inconsistencies occur, and the consistency ratio CR exceeds values of 10% to 20%, making the basic assumption of near consistent matrices invalid and the AHP results questionable.

See also my post here.

The third reason is not so obvious and not so well known. It is based on the limited 1 to 9 AHP ratio scale for the judgment. The maximum preference you can give to one criterion is 9, i.e. this criterion is 9 times more important than all other criteria. Assume, you have only two criteria, then – if you fully prefer one over the other – the preferred one will result in a weight of 90%, the other gets a weight of 10%. The weights depend on the number of criteria, the maximum weight or maximum priority wmax is always

wmax = M/(n + M – 1)

with M = 9, the maximum of the AHP scale and n the number of criteria. The below diagram shows wmax as a function of the number of criteria.

ahp-crit

Clearly you can see that for 10 criteria the maximum possible weight reduces to 50%, or in other words, although you give full preference to one criterion, it only gets a weight of 50%! For more than ten criteria the weight will be below 50%. This is the reason, why the number of criteria should never exceed the magical number seven plus or minus two.

Updated AHP Excel Template Version 2014-05-09

Thanks to feedback from Benedikt, this latest update contains a minor change, to show the convergence of the power method, when calculating the eigenvalue. In the summary sheet a threshold (squared Euclidean distance d2) can be set, to show how many iterations it takes, until the change of the approximated eigenvector is below the given threshold. By default the value is set to Thresh: 1E-07:

thrh

In the above example it takes 7 iterations until d2 is below 1E-07. The actual difference is  3.5E-08 (EVM check). As the number of iterations in the template is fixed to 12, care should be taken if the value reaches 12.

You might download the latest version from my AHP template download page.

Welcome to BPMSG – May 2014

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

The latest beta version of my AHP online software (AHP-OS) has now additional features to manage complete AHP projects. AHP stands for Analytic Hierarchy Process, and is a decision support tool.  To use the full functionality, please register and log in; it’s all free.

You can store complete decision hierarchies, use them to estimate the weights of criteria and sub-criteria and evaluate up to seven decision alternatives.

AHP is also helpful to support group decision making; participants can input their individual judgments and a consolidated group result is calculated. I have prepared a practical example, where you can participate, input your judgments and view the overall group results and consensus. Just click on the link and try it out.

The development is still continuing. I am further optimizing the handling and plan to implement additional analysis, especially for group decision making. Bookmark the page and revisit from time to time to get the latest updates.

Now please enjoy your visit on the site and feel free to give me feedback – it is always appreciated.

Klaus D. Goepel,

Singapore, May 2014

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use. Please give credit or a link to my site, if you use parts in your website or blog.

About the author

AHP-OS online software – Frequently Asked Questions

Note: All answers assume that you are a registered user and logged in.

Q: How do I save a new AHP hierarchy definition?

A: In the Session Administration Menu click on New.

The hierarchy window is displayed. Define a new hierarchy in the text input field and click on Submit new hierarchy, then Save in the Hierarchy Input Menu.

The group session window will open. Optionally provide a project short description and  click Go, and the defined hierarchy is stored and shown as type “H” (Hierarchy) in the project table of the Session Administration Menu.

Q: How can I define and store a project for the evaluation of alternatives?

A: Start with a hierarchy definition, save and resume from the project table by clicking on the session code link. Complete all pairwise comparisons (Click on AHP in the hierarchy) to define the weights of criteria. (Before alternatives can be evaluated, criteria weights need to be defined.) Submit for group evaluation and view the result. In the group result page click on Use consol. priorities.

Then click on Evaluate Alternatives in the decision hierarchy display. Provide number and names of your alternatives and save a new project. It will be saved as type “A” (Alternative Evaluation). From there you can resume and start the alternative evaluation.

Q: How can I use a defined and stored hierarchy definition as template for a new project or new group session?

A: Click on the session code link of the project, you want to use, in the Stored AHP project session table.

a)      If the project has no participants, the project will be opened in the group session input mode. Click on Leave, then Close in the Active Session Menu.

b)      If the project has participants, the project will be opened in the AHP Group result window. Click on the Resume link at the bottom of the page, then Leave and Close in the Active Session Menu as in a).

You can now re-use the hierarchy definition and save as a new project.

Participate in an AHP group session – AHP practical example

This is a practical example of an AHP group session, using AHP-OS, where you can input your judgment and see the consolidated group result of all participants.

Imagine, you plan to buy a tablet computer. Decide on the importance of criteria, like display size, battery life etc. Click on the image below, input your name, click on AHP and start the pairwise comparisons.

What feature is more important and how much on a scale from 1 to 9? Once finished,  submit your input for group evaluation and see the results.

[php snippet=15]

View the detailed group results.

AHP Projects

With the latest update of my free web based AHP software you can now manage complete projects and group sessions. To use the full functionality, register a new account (It’s all free!) I had to implement the registration in order to manage and protect the data.

After login the project session page will be shown. Here your AHP projects are listed in a table, each of them with a unique session code.

A click on the session code will then open the project, either in the hierarchy display mode (the project has yet no participants),  where you can modify and update the hierarchy structure,  or in the group result mode, where you get the consolidated group result of all participants with a breakdown by categories and individual participants.

The project menu allows you to view project details, start a new hierarchy or delete existing projects.

After you have defined a new hierarchy, click on Save/Start new Group session. Enter a project short description, click Go, Ok and done, and the new project is saved in you project list.

Let me know in case you face any problems. A short description of the program as pdf can be found on the AHP-OS start page.

AHP group decision making

The figure below shows, how a group session is conducted to determine group priorities using BPMSG’s AHP online system. The group session chair initiates a group session (You need to be registered and logged in). A six character session code is generated. Participants can use this session code to log into the group session and provide their judgments. Try out a practical example, where you can participate and input your judgments

Example showing the result for two participants. See also my post about group decision making.

Welcome to BPMSG – Feb 2014

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

the development of my AHP online software is still continuing. Most of the recent changes were structural, and not so obvious to users, as I use the software on two different platforms and in two different designs. On the entry page you will now find a short introduction to the analytic hierarchy process, and links to further examples and documentation. From there you can go to the online priority calculator, or the AHP online solution to handle complete projects.

Overall the functionality is complete and the program is stable. Except for group inputs, the priority calculator includes all functions of my AHP excel template. With the AHP online system you can even define complete AHP hierarchies and evaluate alternatives. For both programs the results can now be exported as csv files for further processing in spreadsheet programs in two versions: using either dot or comma as decimal separator.

The next big step would be the implementation of group decision making. My idea is to implement web sessions for different users  on different computers, and an online consolidation of all judgments, to get the consolidated group result. This could be very useful when you are in a meeting and have group discussions, then all participant could do their judgment online, seeing the consolidated group result in real time.

It will still take some more time, so bookmark the page and revisit  from time to time to get the latest updates.

Now please enjoy your visit on the site and feel free to give me feedback – it is always appreciated.

Klaus D. Goepel,

Singapore, Feb 2014

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use. Please give credit or a link to my site, if you use parts in your website or blog.

About the author

AHP Online System

As I was asked by many visitors, how to evaluate priorities and alternatives for a whole project in AHP, I have realized an online solution, where you can define a hierarchy, get the priorities for all categories and evaluate alternatives. The project is realized in PHP.

AHP OS Example

Links

AHP Online System – BPMSG
AHP-OS software Implementation (paper 2018)
Short description (pdf) for download.

Please rate the software at the end of this post!

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