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.
Thanks to a comment from Patric, I corrected a wrong reference in the multInp sheet. The matrix of participant 13 was referring to the matrix of participants 12. Download the latest version of the AHP Excel Template.
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:
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.
In this latest update of my AHP excel template, input sheets were modified to show the proposed ideal judgments for the three most inconsistent inputs, resulting in a lower consistency ratio CR.
Example
On the left side judgment A9, A7 and A6 are highlighted as inconsistent, CR is 32%. The consistent judgment is shown as A4, A9 and A3. After correction with the proposed intensities (right side) the consistency ratio decreases to 7% below the required threshold of 10%.
You might download the latest version from my AHP template download page.
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.
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
As I received many requests to extend the number of participants in my AHP excel template, here a short information how to use it for more than 20 participants. There are two possibilities
As the template is quite complex, I strongly recommend to use the first possibility. But if you really want to modify the template itself, follow the step-by-step instruction below. This instruction does not include the AHP consensus indicator calculation.
Note: {} is the Excel array function: mark cell area, and use Ctrl-Shift-Enter.
All matrices in the input sheets are named Matrixn, n = 1 to max. number of participants. (Matrix1, Matrix2, etc.)
The matrices in the multInp sheet are named “m_pn” (m_p1, m_p2, etc.)
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:
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.
I appreciate any feedback! Please download the latest version from my AHP template download page.
Question: I know how AHP is working, but what I’m struggling with is, how to resolve the inconsistency (CR>0.1), when participants are done with their pairwise comparisons. It is time consuming if they go through the matrix and re-evaluate all their inputs. Do you have any suggestions?
Answer: Yes, CR often is a problem. Also my projects show that, making the pair-wise comparisons, for many participant CR ends up to be higher than 0.1. Based on a sample of nearly 100 respondents in different AHP projects, the median value of CR is 16%, i.e. only half of the participants achieve a CR below 16% in my projects; 80-percentile is 36%. There seems also to be a tendency of increasing CR with the number of criteria, i.e. the median value significantly increases for more than 5 criteria.
From my experience, CR > 0.1 is not critical per se. I get reasonable weights for CR 0.15 or even higher (up to 0.3), depending on the number of criteria. The acceptance of a higher CR also depends on the kind of project (the specific decision problem), the out coming priorities and the required accuracy (what is the actual impact on the result due to minor changes of criteria weights?).
In my latest AHP excel template and AHP online software AHP-OS the three most inconsistent judgments will be highlighted. The ideal judgment (resulting in lowest inconsistency) is shown. This will help participants to adjust their judgments on the scale to make the answers more consistent.
The first measure to keep inconsistencies low is to stick to the Magical Number Seven, Plus or Minus Two, i.e. keep the number of criteria in a range between 5 and 9 max. It has to do with the human limits on our capacity for processing information, originally published by George A. Miller in 1956, and taken-up by Saaty and Ozdemir in a publication in 2003. Review your criteria selection, and try to cluster them in groups of 5 to 9, if you really need more.
Another possibility to improve consistency is to select the balanced-n scale instead of the standard AHP scale. In my sample, changing from standard AHP scale to balanced scale decreases the median from 16% to 6%. You might select different scales in my template.
George A. Miller, The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information, The Psychological Review, 1956, vol. 63, pp. 81-97
Saaty, T.L. and Ozdemir, M.S. Why the Magic Number Seven Plus or Minus Two, Mathematical and Computer Modelling, 2003, vol. 38, pp. 233-244
Goepel, K.D., Comparison of Judgment Scales
of the Analytical Hierarchy Process - A New Approach, Preprint of an
article submitted for consideration in International Journal of
Information Technology and Decision Making © 2017 World Scientific
Publishing Company http://www.worldscientific.com/worldscinet/ijitdm
(2017)
Dear Friends, dear Visitors,
yesterday I realized 10000 visits on my website since April 2012, when I implemented the Piwik web statistics. Over the last couple of months the daily visitor frequency was actually increasing, doubling within the last 3 months. On my youtube channel http://www.youtube.com/bpmsg I am now slowly reaching 100,000 video views.
So first to all of you a big thank you, showing interest in the topics of bpmsg.com, and especially to those of you, giving me feedback, as I can learn and progress from there. For me it also means to stay committed and keep the content interesting and updated.
The topic with the highest interest is AHP – the analytic hierarchy process, and many of you downloaded my AHP excel template. Actually, here I would really like even more feedback about your applications, just to get an idea, in what other areas my template is used. Some of them, as I received, are:
In my last update of the template I improved the accuracy of calculation significantly, so please always use the latest version, and revisit the site from time to time, to get the latest update. Alternatively you might subscribe to the bpmsg newsfeed; the link is given in the footer of the page.
My latest topic “Diversity index as business KPI – the concept of diversity” seems also to gain some interest. My video on youtube got in a short time more viewers than the previous video about operational and strategic business performance. For me it was intersting to apply the diversity concept in business performance, as I haven’t seen this before, and the mathematical concept, to measure diversity of species in a habitat (biodiversity), is quite well established . I am thinking to publish a second video, showing more practical applications of the diversity concept in a business context.
After starting my youtube channel in 2009, I gained more and more experience in making videos. You can clearly see the difference, comparing one of my older videos with the latest ones. Now my camcorder – a Canon XA10 – is with me most of the time on my business trips or vacations. Therefore you also find some video travel impressions on this web site under the topic “others”. My last trip was to the Philippines showing the nice island of Bohol, as well as one of the world’s largest crater lakes on a lake on an island – Lake Taal.
Klaus Goepel,
Singapore, Dec 2012
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.
