Welcome to BPMSG – March 2019

Dear Friends, dear Visitors,

here is the link to the ISAHP 2018 papers and authors. From there you might download my presentation Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). It is a short conference paper about my free AHP online software, the complete article – showing was published as

Goepel, K.D. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Journal of the Analytic Hierarchy Process, Vol. 10 Issue 3 2018, pp 469-487


My second contribution was a presentation about  Judgment Scales of the Analytical Hierarchy Process –The Balanced Scale. As above, it is a short part of a pubication about AHP scales:

Goepel, K.D. (2018). Comparison of Judgment Scales of the Analytical Hierarchy Process — A New Approach. International Journal of Information Technology & Decision Making, published Dec 11, 2018


Over the last couple of months my AHP excel template was updated to show errors for the resulting weights based on the work of Tomashevskii (2014, 2015). You find more details in my post from September 2018. I still have to implement the same calculation into AHP-OS.

Many thanks to all donors, supporting this website. Unfortunately, over the last months I didn’t receive many donations. The annual invoice from my hosting provider is expected to come soon, therefore, please continue to support my effort with a small donation, especially when you use my free template or online software.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated. And keep in mind: Better to be approximately right than precisely wrong.


Klaus D. Goepel, Singapore, March 2019

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.

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Author: Klaus D. Goepel, BPMSG, Contact

AHP Excel Template Update Version 2018-09-15

A new version of of the AHP Excel template with some major updates is now available for download. Based on the work of Tomashevskii (2014, 2015), errors for the resulting priorities/weights are shown.

Calculated weights with error indication

In addition the overall dissonance (ordinal inconsistency) according to Sajid Siraj (2011) is indicated. The zip file for download also contains the updated manual, showing the calculations and references.

Continue reading AHP Excel Template Update Version 2018-09-15

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AHP Excel Template Update Version 2018-08-22

In this latest version of the template, the balanced scale was replaced by the generalized balanced scale (balanced-n), and the adaptive scale was added. The maximum number of iterations for the power method was increased from 12 to 20.

If you need inputs for more than 20 participants, please contact the author. A version for up to 225 participants is available.

Go to download page.

For more information about AHP scales, please read my paper Comparison of Judgment Scales.

AHP Group Consensus Indicator – how to understand and interpret?

BPMSG’s AHP excel template and AHP online software AHP-OS can be used for group decision making by asking several participants to give their inputs to a project in form of pairwise comparisons. Aggregation of individual judgments (AIJ) is done by calculating the geometric mean of the elements of all decision matrices using this consolidated decision matrix to derive the group priorities.

AHP consensus indicator

In [1] I proposed an AHP group consensus indicator to quantify the consensus of the group, i.e. to have an estimate of the agreement on the outcoming priorities between participants. This indicator ranges from 0% to 100%. Zero percent corresponds to no consensus at all, 100% to full consensus. This indicator is derived from the concept of diversity based on Shannon alpha and beta entropy, as described in [2].  It is a measure of homogeneity of priorities between the participants and can also be interpreted as a measure of overlap between priorities of the group members.

Continue reading AHP Group Consensus Indicator – how to understand and interpret?

Incoming search terms:

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AHP Frequently Asked Questions

Over the year I receive many questions about AHP, my AHP excel template and my AHP online Software. Here a selection of frequently asked questions:

General Questions

Q: I have 15 criteria and 20 alternatives, can you extend your template/software?
A: The excel template can handle up to 10 criteria, my online software is limited to 12 criteria (in one hierarchy level) and 10 alternatives. In principle it could be extended, but the limitation is inherit to the AHP method. Please read my explanations here.

Q: I have more than 10 alternatives, can I use AHP for priority evaluation of criteria and a different method for the evaluation of alternatives?
A: Yes, you can combine AHP for criteria evaluation with another method for alternative evaluation. Alternative evaluation could be done for example using a simple table with a yes/no or applicable/not applicable scale, or any other scale, e.g. Likert scale, how good the individual alternative matches the specific criterion.

Q: I have 150 participants, can I use your excel template/software?
A: My AHP excel template is limited to 20 inputs, my AHP online software can handle a (practically) unlimited number of participants. Use the AHP online software.

Q: How can I resolve the inconsistency (CR>0.1), when participants are done with their pairwise comparisons.
A: Once the pairwise comparison is done and submitted, data can not be changed and consistency ratio is what it is. Ask your decision makers to adjust their judgments  in direction of the most consistent input during the pair-wise comparisons for the highlighted three most inconsistent comparisons. Please see also my posting here.

Q: Can I use the Likert scale instead of the AHP scale?
A: No, AHP is based on the rational scale 1/9 … 1 … 9. It cannot be replaced by the Likert scale.

Q: Do you support Fuzzy AHP?
A: No, I have made no provisions to support Fuzzy AHP, neither in Excel, nor in my online software.

Q: How is the computation done, where do I find the description and formulas?
A: Please download the manual for the excel template, or the description about the  Software Implementation of AHP-OS.

Q: How can I cite your work, can you give me a reference?
A: Please cite my paper: Implementing the analytic hierarchy process as a standard method for multi-criteria decision making in corporate enterprises–a new AHP excel template with multiple inputs (Excel template) or my paper Software Implementation of AHP-OS.

AHP Excel template

Q: Can I extend the number of participants to more than 20?
A: Though it is possible in principle, the better way is to use my AHP online software with (practically) unlimited number of participants. I will not do a further extension of the template.

Q: Do you have a version of the Excel template w/o multiple inputs?
A: Yes, a simplified version is available on request from the author.

Q: How can I do alternative evaluation using your Excel template.
A: It is not possible. The template can only handle one category of a hierarchy and calculate the priority of one set of criteria.

AHP Online software

Q: If I have a group of decision makers, do they need to register for the online software?
A: No, they don’t need to register. As the owner of a project you get a link for group decision inputs. Simply send them the link, and they can start the pairwise comparisons.

Q: Can I erase/delete inputs from individual participants from the group results?
A: Yes, you can select and delete individual participants from a project .

Q: The alternative evaluation is not working?
A: Criteria evaluation (priorities) and alternative evaluation have to be handled as two different projects. Only when you have a decision hierarchy with completed comparisons and evaluated priorities, you can define the alternatives from the group result page clicking on Use consol. priorities. Define number and name of alternatives from there and save as new project. Hierarchy evaluation and alternative evaluation projects appear as type “H” for the first and type “A” for the latter in your project list.

Q: Can I get the source code of your online software?
A: Sorry, it is not an open source project.

Improving AHP consistency

In the implementation of both, AHP excel template as well as AHP online software, inconsistent judgments are highlighted and recommendations for consistent judgments are given.  How it is done, and what is the method behind?

The method is based on Saaty’s article “Decision-making with the AHP: Why is the principal eigenvector necessary“. European Journal of Operational Research 145 (2003) 85–91. He describes three methods how to transform a positive reciprocal matrix to a near consistent matrix.

In my implementation I construct the matrix εij = aij wj/wi to identify the three judgments for which εij is farthest from one. In Saaty’s paper it is shown as table 3, in my excel template it is called Consistency Error Matrix.  As I have to do it on each individual input sheet using as an approximation the RGMM (row geometric mean method) results, before calculating the eigenvector solution in the summary sheet.

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AHP Excel Template Version 2015-04-09

In this version I changed the minimum number of criteria from three to two; the number of criteria  ranges now from 2 to 10.

It seems in the Turkish language version of Excel the selection of the consolidated matrix (“0”) gives an error. I did some minor modifications, but I am not sure whether it is now working. Please give me your feedback.

Download the latest version of the AHP Excel Template.