## Updated AHP Excel Template Version 8.5.2013

In this latest update I followed the several requests to extend the number of participants (decision makers); you now can use the template for up to 20 participants. In addition the weight of individual participants can be adjusted for the aggregation of individual judgments (AIJ). For example, if you have one expert in the group, you might want to give him/her evaluation a  x-time higher importance than the rest of participants. Then you simply change the weight in the input sheet from 1 to x. The calculation is done using the weighted geometric mean:

with cij = element of the consolidated decision matrix, aij(k) element of the decision matrix of participant k.

Kindly let me know in case you find any problem with this new version. Feedback is appreciated always! You can download this latestes version from my AHP template download page.

## Welcome to BPMSG – May 2013

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

time for an update on my BPMSG welcome page! Being quite busy the last half year, I didn’t work so much on major articles or videos, but at least I tried to keep my site current with some regular updates.

Related to the analytical hierarchy process (AHP), you might find information about the consistency ratio (CR). CR is one of the most critical issue in the practical application of AHP, as it seems to be difficult for many decision makers to fulfill Saaty’s “ten-percent rule-of thumb”. The way out: either you accept higher ratios (up to 0.15 or even 0.2), modify the judgements in the pair-wise comparisons, or you use the balanced scale instead of the standard AHP 1 to 9 scale. All three can be done in my updated AHP template from Februar 2013.

As I received many requests to extend the number of participants to more than 10, here the detailed procedure, how you can do it by yourself. Extending the number of criteria beyond 10 is more complex and not recommended by me. If you actually have more than 10 criteria please try to group in sub-groups. At the moment I don’t have any planes to extend the number of criteria to more than ten.

I also started a new topic: Diversity. Triggered by some business related questions, I found out that the concept of diversity – as applied in ecology – is very universal, and can be applied in many business areas. You can watch my introduction as video:

I already applied the concept in several areas, and even developed a new consensus indicator for group decision making based on the partitioning of the Shannon entropy.  A paper is submitted for the ISAHP conference in June, and after the event I will place a copy of the paper on my site for download.

For those of you, interested in the topic of diversity and the partitioning in alpha (within group) and beta (in-between group) components my free BPMSG Diversity Calculator could be a useful tool.

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

Klaus D. Goepel,
Singapore, May 2013

## Updated AHP Excel Template Version 08.02.13

An updated version of my AHP Excel template for multiple inputs is now available as version 08.02.13. Beside the extension from 8 to 10 criteria and from 7 to 20 participants some new features have been added. In the past it was sometimes difficult for participants to achieve a low consistency ratio. Now inconsistent comparisons in the input sheet will be highlighted, if the required consistency level is exceeded.  The level of consistency needed (“alpha” in the summary sheet) can also be changed from 0.1 (standard rule of thumb from Saaty) to higher values, for example 0.15 or 0.2. In addition another scale for the judgment can be chosen. For my projects I made good experience with the balanced scale.

A new feature is the consensus index. If you have more than 1 participant and do the group aggregation (select participant “0”), the consensus index is an indicator, how homogenous the judgment within the group was done. Zero percent means no consensus, all participants put their preference on different criteria;  100% means full consensus. Here the changes in detail:

## Summary sheet

• Number of criteria increased from 8 to 10
• Number of participants increased from 7 to 20
1. Linear standard scale
2. Log
3. Sqrt
4. InvLin
5. Balanced
6. Power
7. Geom.
• Alpha – allows to adjust consistency threshold (0.1 default)
• Consensus indicator for group aggregation added
• Geometric Consistency Index CGI added

## Input sheets

• Consistency ratio is calculated on each input sheet.
• Priorities are calculated and shown based on RGMM (row geometric mean method)
• Top three inconsistent pairwise comparisons highlighted (if CR>alpha)

## Known Issues

Thanks to feedback from Rick, sometimes there seems to be a problem with the correct display of weights beside the criteria in the summary sheet. If you face this problem, unprotect sheet summary. Select weigths (O18:O27). Click “conditional formating”, “clear rules”,”clear rules from selected cells”. Then the values will be displayed correctly, and you can format them in the way you want. It is a strange effect; it only appears on one of my PCs, on the other it works fine. I uploaded a modified version, but not sure whether it works for everyone.

## Updated AHP Excel Template Version 11.12.12

Due to feedback from several users, I revised the implementation of the power method for the calculation of the Eigenvector and Eigenvalue to improve the accuracy of my AHP excel template. The calculation sheet ‘8×8 in the workbook was completely reworked. My tests show a significant increase in accuracy. As an example see my updated post AHP template – numerical accuracy.

By default the number of iterations is now set to 12.  The check value in sheet ‘8×8 cell B33 shows the sum of all matrix elements solving the Eigenvalue equation (AI*λ) x = 0 with A the Decision matrix, λ = estimated principal Eigenvalue and x = estimated Eigenvector. The ideal check value is zero. With the example numbers given in the template the result is 5E-08.

Please let me know, if  you find any problems in the new version.

## Update AHP Excel Template Version 16.10.12

Thanks to the feedback from Pascal a bug is corrected, when you select the results of individual participants in the summary sheet. Selection/display  of results from participant 4 to 7 was not shown correctly.

## News from BPMSG

I’m really getting lazy …
No update of my web site since May 2012; page rank down from 3 to 2. What is going on?

It seems less questions coming up regarding my AHP excel template, though the number of downloads is quite stable. I am still curious to know about your applications; so please kindly feedback, if you are using the template for your study or work.

In between I upgraded my video equipment, using a Canon XA10 video camera and Adobe Premier Elements for editing. I produced a couple of videos for work and on holidays. Very satisfied with the results, brilliant quality in HD. Hopefully I will find some time to share my experience here or on  my Youtube channel,  so just stay connected.

Thanks so far!

Klaus

September 2012

P.S. Update Nov 8th, 2012 – Now having  problems with my XA-10 Camcorder

## Update AHP Excel Template Version 9.5.12

This update corrects a bug in the calculation of the consistency ratio CR. In the 8×8 sheet the correct random index is now selected from the table depending on the actual number of criteria.

## New AHP Excel template with multiple inputs

The AHP Excel template works under Office Libre and Excel version MS Excel 2013. The workbook consists of 20 input worksheets for pair-wise comparisons, a sheet for the consolidation of all judgments, a summary sheet to display the result, a sheet with reference tables (random index, limits for geometric consistency index GCI, judgment scales) and a sheet for solving the eigenvalue problem when using the eigenvector method (EVM). Latest version: 2022-07-08.

Alternative for complex AHP projects: AHP free online software.

### Excel Template

• Within the input worksheets (questionnaires) priorities are calculated using the row geometric mean method (RGMM).
• Three consistency indices (the consistency ratio CR, the geometric consistency index GCI and overall dissonance Psi) are calculated. The level of consistency needed (α) is implemented as a variable input field in the summary sheet, and can be set between zero and one.
• If CR exceeds α, the top 3 inconsistent pair-wise comparisons on the input sheets are highlighted, to allow the participants an adjustment of their judgments. The judgment resulting in lower inconsistency is proposed.
• Final priorities are shown in a summary sheet; their calculation is based on the eigen vector method (EVM). For the solution of the eigenvalue problem the power method algorithm is applied with a fixed number of 20 iterations.
• Different judgment scales are implemented.
• Errors of the EVM and RGMM are show beside the calculated priorities.
• Either individual participants, or an aggregation of individual judgments (AIJ) based on the weighted geometric mean of all participants’ judgments can be selected.

Limitations

• The template does not include the hierarchy of the decision problem and the final aggregation of weights, i.e. it is only suitable for finding the weights in each category or sub-category. For the definition of a hierarchy and evaluation of alternatives see here.
• Sensitivity analysis of the final result is not included.

### Reference

When you use the template for your research, please make a reference to the author’s paper.

```Klaus D. Goepel, (2013). 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, Proceedings of the International Symposium on the Analytic Hierarchy Process, Kuala Lumpur 2013. DOI: https://doi.org/10.13033/isahp.y2013.047```