AHP-OS Implementation – working paper

For anyone, who is interested in the implementation of my free AHP-OS online software, and needs a reference:

Please cite:

Goepel, K. D. (2017). Implementation of an Online Software Tool for the Analytic Hierarchy Process – Challenges and Practical Experiences.  Working paper prepared for publication, Singapore July 2017, available from http://bpmsg.com/ahp-software/

I hope to finalize the paper soon so that I can submit it for publication.

Download the working paper from here.

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AHP-OS Data Download and Import in Excel

Most data generated with AHP-OS can be downloaded as csv files for import into a spreadsheet program and further analysis:

  • From the Hierarchy Input Menu – decision hierarchy and local & global priorities
  • From the Group Result Menu – Priorities by node and consolidated decision matrix
  • From the Project Data Menu – Decision matrices from each participant

For each download you can select “.” or “,” as decimal separator. The downloaded csv (text) file is coded in UTF-8 and supports multi-language characters like Chinese, Korean, Japanese and of course a variety of Western languages.

How to import into excel?

Open Excel, click on “File” -> “New” to have a blank worksheet. Click on “Data“. On the left top you will find the “Get External Data” box.

Click on From Text to select the downloaded cvs file for import. The Text Import Wizzard will open.

Now it is important to select 65001 : Unicode (UTF-8) under File origin.

Then, depending on your decimal separator, select Comma or Semicolon as Delimiters:

When the import is done, your text characters should be displayed correctly.  Save the file “Save as” as Excel workbook (*.xlsx).

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AHP Online Software CSV Data Export

AHP-OS allows for downloading your project data as a comma separated value text file. The following menus include a csv download key:

  • Hierarchy Input Menu – download the AHP hierarchy
  • Group Result Menu – download resulting priorities and consolidated (aggregated) decision matrix
  • Project Data Menu – download decision matrices for all individual participants

Depending on your regional settings of your PC, for each download you can select the decimal point or decimal comma as decimal separator.

Text encoding of the CVS file is UTF-8. If you are using country specific characters and Windows Excel, you can convert from UTF-8 to ANSI. Open the CSV file with notepad, and save as a new file with Encoding set to ANSI.


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AHP Excel Template Version 2016-05-04

Just a small correction in the summary sheet: Now the correct name of the selected scale is displayed.

You can download the latest version of the AHP Excel Template from here.

Please consider a small donation, if you find the template useful for your work.

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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.

You might download the latest version from my AHP template download page.

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AHP Online Calculator – Update 2013-12-20

In this latest version of the AHP online calculator I made some changes:

  • The three judgments with highest inconsistency will be highlighted with the last column showing the recommended judgment for lowest inconsistency
  • Selection of fundamental AHP or balanced Scale
  • Number of Criteria changed from 12 to 15 max.1)
  • Length of criteria names changed from 15 to max. 20 characters
  • Download of result (decision matrix, eigen vector, CR) as csv (comma separated values) instead of txt file

The .csv  file uses “,” as field separator and “.” as decimal symbol (unchanged). Depending on your operating system it will directly open in Excel.

1) Important Note: Though the maximum number of criteria is 15, you should always try to structure your decision problem in a way that the number of criteria is in the range Seven Plus or Minus Two.

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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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A new Consensus Indicator in Group Decision Making with the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is one of the multi-criteria decision making methods helping decision makers in rational decision making using a mathematical method. AHP as a practical tool can be especially helpful, when making group decisions.

Download (pdf):

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 2013

Group Decision Making

Group decisions are often made because decision problems can become very complex by nature; they could require special expertise and complementing skills, as they cannot be provided by a single person. Another reason could be the wish to spread responsibility or to get a higher commitment from a team for necessary actions as a consequence of the decision to be made.

Group-DecisionThere are different possible approaches to come to a decision. In the ideal case we get a consensus – an agreement through discussion and debate – but often a decision is a compromise. Group members readjust their opinions and give up some demands. Another way is a majority vote or a single leader’s final decision, based on his position and power.

In any case a possible disadvantage is that during group discussions a strong individual takes the lead, suppressing or ignoring others’ opinions and ideas (dominance), or people don’t want to speak up and conform to whatever is said (conformance).

Table 1: Reasons for group decision making and group decision approach

Reasons for group decisions Group Decision Approach
Special expertise
Subject matter experts
Complementing skills
Different viewpoints/departments
Spread of responsibility
Board, committee members
Higher commitment
Team decision
Agreement through discussion and debate
Readjustment, giving up some – demands
Majority vote
Opinion of majority
Single leader’s final decision

 The Analytic Hierarchy Process (AHP) in Group Decision Making

When using AHP with its questionnaire, these problems can be avoided. Each member of the group has to make judgment by doing a pairwise comparison of criteria in the categories and subcategories of the hierarchical structured decision problem. Advantages are:

  • It is a structured approach to find weights for criteria and sub-criteria in a hierarchically structured decision problem.
  • All participants’ inputs count; no opinion or judgment is ignored and all group members have to fill-out the questionnaire.
  • Participants’ evaluation can be weighted by predefined (and agreed) criteria, like expertise, responsibility, or others, to reflect the actual involvement of decision makers.
  • The consolidated group result is calculated using a mathematical method; it is objective, transparent and reflects the inputs of all decision makers.

From practical experience, especially the last point results in a usually high acceptance of the group result. Aggregation of individual judgments (AIJ) in AHP can be done using the geometric mean: each matrix element of the consolidated decision matrix is the geometric mean of the corresponding elements of the decision makers’ individual decision matrices. The outcome – consolidated weights or priorities for criteria in a category – can be used as group result for the calculation of global priorities in the decision problem.

AHP Consensus Indicator

Although mathematically it is always possible to calculate a group result, the question remains, whether a calculated group result makes sense in all cases. For example, if you have two totally opposite judgments for two criteria, an aggregation will result in equal weights (50/50) for both criteria. In fact, there is no consensus, and equal weights may result in a deadlock situation to solve a decision problem.

Therefore, it will be necessary to analyze individual judgments, and find a measure of consensus for the aggregated group result. We use Shannon entropy and its partitioning in two independent components  (alpha and beta diversity) to derive a new AHP consensus indicator. Originating from information theory, the concept of Shannon entropy is well established in biology for the measurement of biodiversity. Instead of relative abundance of species in different habitats, we analyse the priority distribution of criteria among different decision makers.

Further Reading, References and Examples of Practical Applications

The AHP consensus indicator is calculated in my free AHP Excel template. Group analysis by partitioning of  Shannon entropy in alpha and beta entropy can be done by transferring the calculated priorities (AHP priority vector) from each decision maker to the BPMSG Diversity calculator.

Feedback and Comments are welcome!

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Video Editing Workflow – Canon XA-10


Camera settings depend on the type of recorded video. The Canon XA-10 has only two full HD (1920×1080) recording modes: FXP and MXP. Based on these, most of my videos are recorded in FXP mode as it is a good trade-off between quality and file size.

Recording Modes of Canon XA-10

Edit and Archive

For video editing I use Adobe Premier Elements 10. Editing is done without changing codec (H264), resolution, interlacing, etc. As I have the PAL version of the XA-10, the Adobe project settings are AVCHD Full HD 1080i 25 under PAL. Once the video is edited, I  render the clip with the highest quality settings (2 Pass VBR, Render at max. depth, Macro block Adaptive Frame-Field Coding), and a maximum bitrate corresponding to the source (FXP: 17 Mbps) for archiving. In Adobe Premier Elements 10 and for XA-10 FXP mode the settings are:

Archive settings in Adobe Premier Elements 10 for XA-10 FXP mode

Target Media

Depending on the target media the clip to be published is adjusted in codec, resolution etc. I have predefined settings for:

  • Standard clips to be watched on a PC:
    MP4 – PAL DV Widescreen SD – HiQ (576p, VBR 3/6 MBps)
  • Tablet/phones:
    MP4 – PAL DV Widescreen SD – LoQ (576p, VBR 1.3/2.6 Mbps)
  • Youtube as basic HD clip:
    MP4 – HD 720p 25 (720p, VBR 2.5/5 Mbps)

Calculation of Video Bitrates in Excel

I use a simple excel template to calculate the bitrate for the target medium. As input you simply select:

  • Codec (H264, MPEG-2)
  • Standard (PAL, NTSC, FILM)
  • Definition (VCD, SD, HD 720, HD, full HD)
  • Channel (PC/Web, Disk/TV)
  • Action/Motion (low, normal, medium, high)

and as a result you get the recommended bitrate for rendering your video clip.

Comments and feedback are welcome!

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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.

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