Welcome to BPMSG – Feb 2017

Concepts, Methods and Tools to manage Business Performance

Dear friends, dear visitors,

Using Google search for my own website, I could see a message like Your website is not mobile friendy. It was really time to update my website theme in order to make it better readable for visitors using their smart phone or tablet.

Now you see the new design using the standard wordpress theme from 2015. I simplified the menu structure to the categories:

  • AHP Articles – Material and Information about the Analytic Hierarchy Process
  • Other Articles – Material and Information about Business Performance
  • Tools – Links to my online tools, like the AHP online system and excel templates
  • Other – Posts related to other topics
  • About – Information about the author
  • Feedback – A place where you can leave your feedback as comments
  • Contact – A web form to contact me personally via e-mail

I hope with these changes navigation on the site is much easier, and you can find required information in shorter time.

Again, a big Thank You to all donors! Please note that the website is a non-commercial website for educational purposes. Your donation is used to cover running costs like web hosting, antispam services etc. PLEASE, help to support this website with a small donation. I spend a lot of time, sharing my knowledge for free. Thank you in advance!

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.

Klaus D. Goepel,

Singapore, Februar 2017

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 work, or make a small donation to support my effort to maintain this website.

About the author

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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

Here the link: BPMSG AHP Online System

How to use the tool

Short description  (pdf) for download.

The online template is easy to use, three steps are necessary:

  1. Define the objective and relevant criteria of your decision problem and structure them in a hierarchy.
  2. Compare criteria in categories and sub-categories with respect to the objective to find their weights based on pairwise comparisons.,
  3. Name a set of alternatives and compare, how good they match your decision criteria. Again pairwise comparisons based on the AHP are used.

1. Define Hierarchy

Hierarchies are defined in a text field using the following simple syntax:

Each branch in the hierarchy is defined by its node (the category) and the node’s leafs (the sub-categories). The node is followed by a colon, leafs are separated by comma, and a branch is closed by a semicolon:

category: sub-category 1, sub-category 2, sub-category 3;

If a sub-category branches out in further sub-categories, you add a line, repeating the sub-category’s name (case sensitive!) as a new node, i.e. followed by a colon:

sub-category 1: sub-sub-1, sub-sub-2;

2. Compare Criteria

To find the weight (importance) of criteria, click AHP to start pairwise comparisons. Compare each pair of criteria with respect to the project and category: which criterion in each pair is more important, and how much more on a 1 – 9 scale? Once you have finished click Calculate Result. A table with priorities for each criterion is shown.

It could happen that your pairwise comparison is not consistent, then the most inconsistent judgments are highlighted, and the most consistent judgment is marked light green. In order to improve consistency, check whether you are able to adjust your original mark by plus or minus two on the scale. Click Calculate to re-calculate. Once finished, and you are satisfied with you answers, press Submit Priorities to submit. Completed branches in the hierarchy tree are marked green.

When all comparisons in the hierarchy are done, you might continue to evaluate alternatives. Press Evaluate Alternatives. Note: You only get the selection, if all necessary pairwise comparisons are completed, or the hierarchy text input already contains pre-defined priorities. A table with criteria and alternatives will be displayed.

3. Evaluation of Alternatives

Before you start the evaluation, you might input the number and names of your decision alternatives. Enter the number (1 – 5) and press Go. Then input the names of alternatives and press ok. The procedure of pairwise comparisons is exactly the same as for the criteria. Each completed comparison is highlighted in green. When all evaluations are done, the result is shown.

4. Download

You might download the data in csv format (comma separated values) for further processing in a spread sheet program. The table starts with a title line; then each row shows one criterion with the columns: (hierarchy level, local priority), global priority, alternatives (local and global priority).

All (decision) matrices are shown below, with category name as heading and criteria for the matrix rows. Alternatives show the heading “Alternatives for” and the respective criterion.

More Examples

Program Limitations and Input Restrictions

  • Display length of category names: 25 characters max.
  • Hierarchy levels 6 max.
  • Nodes: 15 max.
  • Each node (category) has to have at least 2 branches (sub-categories)
  • Endnodes: 100 max.
  • Names of categories/sub-categories have to be unique.
  • Numbers as category names are not allowed (though names may contain numbers).
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Welcome to BPMSG – Oct 2013

Dear Friends, dear Visitors,

Nearly half a year has passed since my last update in May on this page, and the year 2013 is soon coming to an end. In June, I had the opportunity to present my practical experience with the Analytic Hierarchy Process (AHP) on the International Symposium ISAHP 2013 in Kuala Lumpur, Malaysia. You can download my paper here. It was interesting to meet the experts from around the world, dealing with decision making methods, and listening to some of their presentations. A short video shows my impressions of the meeting and the nice touristic spots in K.L.

I was invited to the panel discussion, and could discuss my newly introduced AHP consensus indicator for group decisions. It is based on the concept of diversity. Like AHP, diversity is a very interesting topic, as it can be applied in so many different areas. Originating from information theory (Shannon 1948), it became a well-established concept in ecology and economy. I used the principles to develop a key performance indicator (KPI), describing the diversification of businesses and the quality of growth. Feel free to watch my videos or read my posts on this blog.

What is coming next?

There will be one more video on my YouTube channel, showing the application of Shannon diversity to measure the quality of growth. Looking at diversity and growth over time we can display a growth trajectory of a company, giving a clear picture about the direction, where the company is heading.

The larger project will be the implementation of my AHP template as an AHP online tool. The idea is that you can input your criteria and do the pair-wise comparison online, to get as a result the calculated priorities. So at the moment I am busy to practice some web scripting and become more familiar with php. A first small exercise was my online diversity calculator.

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


Klaus D. Goepel,

Singapore, Oct 2013

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

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AHP Introduction

This is my 2-page simple write-up about AHP for people, who have not heared about the method. You might download the paper as pdf document.

Principia Mathematica Decernendi

or “Mathematical Principles of Decision Making” is the title of a book by Prof. Thomas L. Saaty, in which he describes his method for the mathematical treatment of decision problems, which he developed in the 70s. Called AHP, it is now used around the world in many different fields. AHP stands for analytic hierarchy process, and belongs to the multi-criteria decision making methods (MCDM) group.

In AHP, values like price, weight, or area, or even subjective opinions such as feelings, preferences, or satisfaction, can be translated into measurable numeric relations.

Mathematically, the method is based on the solution of an “eigenvalue problem” – but this is mentioned here only tangentially and is not meant to dissuade anyone.

Analytic hierarchy process

The basic steps in the solution of a decision problem using AHP are quite simple:

  1. Define the goal of the decision – what do I want to decide, for what purpose, and what are my alternatives?
  2. Structure the decision problem in a hierarchy – what are the categories and criteria that figure into my decision?
  3. Pair comparison of criteria in each category – e.g. blue or green? Which do I prefer, and by how much do I prefer one or the other color?
  4. Calculate the priorities and a consistency index – were my comparisons logical and consistent?
  5. Evaluate alternatives according to the priorities identified – what alternative optimum solution is there to the decision problem?

Sometimes alternatives are already implicitly defined by the problem and it is sufficient merely to define the priorities.

The core of AHP is the comparison of pairs instead of sorting (ranking), voting (e.g. assigning points) or the free assignment of priorities. Validation of the method in practical testing shows surprisingly good agreement with actual measured values.

One of the most interesting fields and a very current application of AHP is the identification of suspects by witnesses in criminal cases, where the candidates for identification are not shown all together or sequentially, but in pairs. AHP is then used to evaluate the results. Initial studies show that this increases the reliability of identification from 55 % to 83 % and reduces the false identification rate from 20 % to 17 %, and that the consistency index is a good measure of the reliability of statements by witnesses.


To demonstrate how the method works, let us take a simple example. I want to buy an MP3 player. I have the choice of colors (pink, blue, green, black, red), storage (8, 16, 32, 64 Gbyte), and availability (immediate, 1 week, 1 month). The available models are:

  • Model A – pink, 32 Gbyte, immediate availability, USD 120
  • Model B – blue , 16 Gbyte, immediate availability, USD 120
  • Model C – black , 32 Gbyte, 1 week wait, USD 150
  • Model D – red, 64 Gbyte, 1 month wait, USD 150

We can structure the problem hierarchically as shown in Fig. 1.  In the solution process itself each element is compared by pairs in each category and sub-category, and the criteria are weighted.

Fig. 1 AHP hierarchy for solving a decision problem

Complex decision problems and networks

For complex decision problems a two-layer model can be introduced, in which hierarchies are examined separately by the criteria Benefits (B), Opportunities (O), Costs (C) and Risks (R). This is known as the BOCR model. The problem is then evaluated using the simple formula (B*O)/(C*R) (multiplicative) or (B+O)-(C-R) (additive).

The analytical network process (ANP) is a further development of AHP. In it, the decision problem is modeled not as a hierarchy, but as a network. However, its practical application and mathematical treatment are much more involved.


AHP has been used successfully in many institutions and companies. Although the method is so universal, it is still simple enough to execute in Excel. One of AHP’s great advantages is the ability to use it for group decisions, in which all participants evaluate pairs and the group result is determined as the mathematically optimum consensus. In practice the solutions arrived at by the method are well accepted, since the results are objective and free of political influence.

Examples of projects in a business context are the weighting of key performance indicators (KPI) or the identification of key strategies for sustained growth.

Klaus D. Goepel – Singapore Aug 2013. 

Calculate priorities using my AHP online calculator or handle a complete AHP project using my AHP online system.

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ISAHP 2013 – International Symposium on the Analytic Hierarchy Process

ISAHP-2013The 12th International Symposium on the Analytic Hierarchy Process – Multi-criteria Decision Making – took place under the theme “Better world through better decision making” from June 23rd to 26th in Kuala Lumpur, Malaysia.

Organized by the International Islamic University Malaysia (IIUM), scientists and experts from all continents presented and discussed the latest theoretical developments in AHP and its application in the areas of environment, transportation, CSR, healthcare, SCM, banking and finance, manufacturing, education, IT/IS and group decision making. After the official opening and a welcome speech by Prof. Thomas L. Saaty  – connected via video from US – approx. 100 papers  were presented in several parallel sessions. The successful meeting ended with a key note speech by Prof. William C. Wedley, “AHP/ANP – Before, Present and Beyond”, and  two panel discussions, one about group decision making and the other about publishing AHP/ANP papers.

A half-day tour to interesting places in K.L and the following Gala Dinner with the award giving ceremony gave delegates opportunity for some relaxation and networking.

Many thanks to the organizers, have a look at some impression from the meeting in the video.

Your feedback is  always welcome!
You might find my paper, presented on the ISAHP 2013, for download here.

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BPMSG on Youtube – Channel Introduction Video

Enjoy Watching!

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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

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Diversity as Business KPI – Alpha and Beta Diversity – Video

a-b-diversityThe video explains partitioning of Shannon diversity into two independent components: alpha (within group) and beta (in between groups) diversity. It helps to understand beta diversity as a measure of variation between different samples of data distributions. Some practical applications in the field of business analysis are shown.

Enjoy watching!

More posts about diversity:

Any feedback is welcome!

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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.

About the author

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Diversity Index as Busines Performance Indicator – The Concept of Diversity

A business relying on a single type of product or services can be highly risky. Any change in the market place – a change of customer behavior, a new competitor – might have a high impact on the business results. Diversification is an opportunity to spread and reduce the potential risks.

The mathematical concept of diversity has many applications, ranging from ecology over demography to information science. In the context of business performance diversity indices can be used as key performance indicators (KPIs) to analyze markets, define targets for diversification, and track the success of derived business actions.

Download Presentation Slides (pdf)

See also

Video: Diversity as Business KPI – Alpha and Beta Diversity

Diversity Calculation in Excel – Diversity Indices and True Diversity

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