## AHP Excel Template Version 2015-06-07

Thanks to feedback from Frank, this updated version got some minor modifications for the case of two criteria only.

## 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:

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.

## Updated AHP Excel template Version 2013-12-24

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%.

## 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

## How to extend the AHP Excel Template for more Participants?

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

• Use my AHP online Software.
• Use several templates, each  of them for up to 20 participants, and then combine the consolidated results in an additional summary template.
• Modify the template.

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.

1. Unprotect sheet In20; create a copy of the sheet In20 and rename to In21.
2. Go to “Formulas – Name Manager” and delete name Matrix20 with scope In21.
Mark matrix cells of the decision matrix in In21 (C79:L88), and define new name Matrix21 with scope workbook.
Go to Sheet multInp, unprotect sheet. Add additional matrix, e.g. copy/paste from matrix 20 (2 matrices per rows, same structure as for matrix 1-10).
Mark content cells of new matrix and define new name “m_p21
Set it {=Matrix21} ( {} = array function, see below).
Mark the consolidated matrix (B9:K18), and modify the formula
{=(M9:V18*B22:K31* …*B74:K83)^(1/N4)} to include the added participant’s matrix.
3. Go to sheet Summary, unprotect sheet.
Mark matrix starting at line 38, and add new matrix m_p11 in the formula: {=IF(p_sel>0;CHOOSE(p_sel; m_p1; m_p2; … ; m_p20; m_p21);MatrixC)}.
Select field C7 (number of participants). Menu “Data – Data Validation”:
change range from 1 to 20 to 1 to 21.
4. Continue in the same way for additional participants.

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.)

## BPMSG Diversity Calculator – Excel

The diversity calculator is an excel template that allows you to calculate alpha-, beta- and gamma diversity for a set samples (input data), and to analyze similarities between the samples based on partitioning diversity in alpha and beta diversity.

The template works under Windows OS and Excel 2010 (xlsx extension). No macros or links to external workbooks are necessary. The workbook consists of an input worksheet for a set of data samples, a calculation worksheet, where all necessary calculations are done, and a result worksheet “beta” displaying the results.

## Applications

The template may be used to partiton data distributions into alpha and beta diversity, it can be applied in many areas, for example

• Bio diversity – local (alpha) and regional (beta) diversity
• AHP group consensus – identify sub-goups of decision makers with similar priorities
• Marketing – cluster analysis of similarities in markets
• Business diversification over time periods
• and many more.

Let me know your application! If you just need to calculate a set of diversity indices, you can use my online diversity calculator here.

## Calculations and results

Following data will be calculated and displayed:

• Shannon Entropy H (natural logarithm) alpha-, beta- and gamma, and corresponding Hill numbers (true diversity of order one) for all samples
• Homogeneity measure
1. Mac Arthur homogeneity indicator M
2. Relative homogeneity S
3. AHP group consensus S* (for AHP priority distributions)

• Table 1: Shannon alpha-entropy, Equitability, Simpson Dominance, Gini-Simpson index and Hill numbers for each data sample

• Table 2: Top 24 pairs of most similar samples
• Page 2: Matrix of pairs of data samples
• Diagram 1: Gini-Simpson index and Shannon Equitability
• Diagram 2: Average proportional distribution for all classes/categories
• Diagram 3: Proportional distribution sorted from largest to smallest proportion (relative abundance)

Limitations:

• Maximum number of classes/categories: 20
• Maximum number of samples: 24

Description of the template:  BPMSG-Diversity-Calc-v14-09-08.pdf

Other posts explaining the concept of diversity

 PLEASE READ before DOWNLOAD The template is free. So I would really appreciate, if you could – at least – feedback or write me about your application of AHP, and the use of the template. Thank you!

Download BPMSG Diversity Calculator Version 14.02.13 (zip)

As this version is the first release, please feedback any bugs or problems you might encounter.

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• Alpha Diversity Calculator
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## Diversity Calculation in Excel – Diversity Indices and True Diversity

In my video “Diversity Index as Business KPI – The Concept of Diversity” I explain the mathematical concept of diversity introducing the Simpson Index λ and its complement (1-λ) as a measure of product diversification in markets.

Beside the Simpson Index there are many other indices used to describe diversity. I have developed a simple Diversity Excel template to calculate a couple of diversity indices for up to 20 categories. The following diversity indices are calculated:

• Richness
• Shannon entropy
• Shannon equitability
• Simpson dominance
• Gini-Simpson Index
• Berger-Parker Index
• Hill numbers (“true diversity”) and Renyi entropy of order one to four

For a quick calculation of diversity indices you might also use my online calculator

For calculation of Shannon entropy and its partitioning into independent alpha and beta components  see here.

Any feedback is welcome!

#### Incoming search terms:

• diversity index calculator
• simpson diversity index calculator
• simpsons diversity index calculator
• simpson index calculator
• shannon wiener index calculator
• simpson diversity index online calculator

## Welcome to BPMSG – Dec 2012

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:

• Asset management prioritisation
• BPMSG AHP template as a teaching tool
• Weights of textual elements that affect difficulty of a given text
• Environmental quality
• Threads to biodiversity
• Green supply chain

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.