Tag: Analytic Hierarchy Process

Welcome to BPMSG – March 2019

Dear Friends, dear Visitors,

here is the link to the ISAHP 2018 papers and authors. From there you might download my presentation Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). It is a short conference paper about my free AHP online software, the complete article – showing was published as

Goepel, K.D. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Journal of the Analytic Hierarchy Process, Vol. 10 Issue 3 2018, pp 469-487

https://doi.org/10.13033/ijahp.v10i3.590

My second contribution was a presentation about  Judgment Scales of the Analytical Hierarchy Process –The Balanced Scale. As above, it is a short part of a pubication about AHP scales:

Goepel, K.D. (2018). Comparison of Judgment Scales of the Analytical Hierarchy Process — A New Approach. International Journal of Information Technology & Decision Making, published Dec 11, 2018

https://doi.org/10.1142/S0219622019500044

Over the last couple of months my AHP excel template was updated to show errors for the resulting weights based on the work of Tomashevskii (2014, 2015). You find more details in my post from September 2018. I still have to implement the same calculation into AHP-OS.

Many thanks to all donors, supporting this website. Unfortunately, over the last months I didn’t receive many donations. The annual invoice from my hosting provider is expected to come soon, therefore, please continue to support my effort with a small donation, especially when you use my free template or online software.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated. And keep in mind: Better to be approximately right than precisely wrong.

Klaus

Klaus D. Goepel, Singapore, March 2019

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.

4.8 (95.53%) 94 votes

 

Author: Klaus D. Goepel, BPMSG, Contact

AHP Excel Template Update Version 2018-09-15

A new version of of the AHP Excel template with some major updates is now available for download. Based on the work of Tomashevskii (2014, 2015), errors for the resulting priorities/weights are shown.

Calculated weights with error indication

In addition the overall dissonance (ordinal inconsistency) according to Sajid Siraj (2011) is indicated. The zip file for download also contains the updated manual, showing the calculations and references.

Continue reading AHP Excel Template Update Version 2018-09-15

AHP Excel Template Update Version 2018-08-22

In this latest version of the template, the balanced scale was replaced by the generalized balanced scale (balanced-n), and the adaptive scale was added. The maximum number of iterations for the power method was increased from 12 to 20.

If you need inputs for more than 20 participants, please contact the author. A version for up to 225 participants is available.

Go to download page.

For more information about AHP scales, please read my paper Comparison of Judgment Scales.

Welcome to BPMSG – July 2018

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

the international symposium on the Analytic Hierarchy Process ISAHP 2018 in Hongkong is just finished, and I gave two presentations in the track Multi-criteria Decision Analysis – Methodology and Theory. One about the AHP balanced scale, and the other about the implementation of my AHP online software AHP-OS.

I’m thankful to the program committee to have received the most innovative idea reward for the paper about AHP-OS.

Some interesting papers were presented, for example Cardinal and Ordinal Inconsistency in pairwise Comparison Matrices by Konrad Kulakowski, or Coherency: an Innovation to Test Data Quality and Reduced Comparisons in the ANP by Orrin Cooper, just to mention two.

I will update you with the link, once the conference proceedings are published.
The conference gave participants also an opportunity for many discussions and the exchange of ideas.

Please continue to support my effort, either with a donation, or a rating to my web posts, which will help me as a feedback to my work.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated. And don’t forget: Better to be approximately right than precisely wrong.

Klaus

Klaus D. Goepel,

Singapore, July 2018

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.

AHP Judgment Scales

A revised version of my paper can now be downloaded:

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)

Welcome to BPMSG – Jan 2018

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

I wish all of you a Happy and Prosperous New Year 2018!

From July 13th to 15th the International Symposium on the Analytic Hierarchy Process (ISAHP) for Decision Making takes place in Hong Kong. Poster submission is possible from Nov 1st, 2017 to Mar 15th, 2018 and individual paper submission from Nov 1st, 2017 to Mar 6th. Early registration deadline May 15th, 2018. More Information about the ISAHP 2018 can be found on their website.

After my last participation in 2013, I plan to attend the conference in July. If you want to meet me personally, feel free to contact me. I submitted an individual paper about the implementation of my AHP-OS software; it is a short version of my detailed working paper. In additon I will probably submit a short version of my paper Comparison of Judgment Scales of the Analytical Hierarchy Process – A New Approach. This paper was submitted to the International Journal of Information Technology and Decision Making in June 2017, and is under review since then. All attempts to contact the editors and to find out, why the review process takes so long, were unsuccessful.

My AHP-OS software has now reached nearly 6000 registrations since its implementation in 2014. It should be quite stable and without major bugs. Unfortunately, there is still a minor sporadic problem with the storage of pairwise comparisons. It appears in 1 out of 1000 projects that a set pairwise comparisons just disappears. I am still trying to find the reason, kindly contact me, when this happens to you, and let me know the circumstances (It seems to have something to do with the browser and stored session data).

Please continue to support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.

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

Klaus

Klaus D. Goepel,

Singapore, Jan 2018

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.

 

Welcome to BPMSG – September 2017

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

Over the last three months I did a lot of under-the-hood changes and clean-up on the website to improve safety and user experience. As you may have noticed, the protocol is now https: the web traffic is encrypted using an SSL client certificate. After some tweaking the page performance could be improved significantly, loading time is nearly reduced by half. All pages, including my AHP-OS online software and the diversity calculator, were made mobile friendly, though I don’t recommend to use AHP-OS on a small mobile phone screen.

In addition some new features were added to the AHP-OS online software:

I also wrote a paper about the AHP software implementation, where you can find a description of the structure and all mathematical formulas and references. Please make a reference to this paper, when you use the software in your work to be published.

Kindly support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.

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

Klaus

Klaus D. Goepel,

Singapore, September 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.

 

Last update: Sep 14, 2017 Author: Klaus D. Goepel, BPMSG, Contact

AHP-OS Update Version 2017-08-31

The latest update of AHP-OS comprises of some minor changes to make the program flow easier to understand for participants w/o background in AHP.

  • The group session input screen does no longer show the headline to login or register, as for participants there is no need to be registered.
  • The text introduction was shortened to two and a half line of text.
  • Menu buttons intended to be clicked are highlighted.

Continue reading AHP-OS Update Version 2017-08-31

Sensitivity Analysis in AHP

Sensitivity analysis is a fundamental concept in the effective use and implementation of quantitative decision models, whose purpose is to assess the stability of an optimal solution under changes in the parameters. (Dantzig)

Weighted sum model (Alternative Evaluation)

In AHP the preference Pi of alternative Ai is calculated using the following formula (weighted sum model):
(1)with  Wj the weight of criterion Cj, and aij the performance measure of alternative Ai with respect to criterion Cj. Performance values  are normalized.
(2)

Example


Table 1

Sensitivity analysis will answer two questions:

  • Which is the most critical criterion, and
  • Which is the most critical performance measure,

changing the ranking between two alternatives?

Continue reading Sensitivity Analysis in AHP

Why the AHP Balanced Scale is not balanced

As part of my current work about AHP scales, here an important finding for the balanced scale:

Salo and Hamalainen [1] pointed out that the integers from 1 to 9 yield local weights, which are not equally dispersed. Based on this observation, they proposed a balanced scale, where local weights are evenly dispersed over the weight range [0.1, 0.9]. They state that for a given set of priority vectors the corresponding ratios can be computed from the inverse relationship

r = w / (1 – w)      (1a)

The priorities 0.1, 0.15, 0.2, … 0.8, 0.9 lead, for example, to the scale 1, 1.22, 1.5, 1.86, 2.33, 3.00, 4.00, 5.67 and 9.00. This scale can be computed by

wbal = 0.45 + 0.05 x     (1b)

with x = 1 … 9 and

 (1c)

c ( resp. 1/c) are the entry values in the decision matrix, and x the pairwise comparison judgment on the scale 1 to 9.

In fact, eq. 1a or its inverse are the special case for one selected pairwise comparison of two criteria. If we take into account the complete n x n decision matrix for n criteria, the resulting weights for one criterion, judged as x-times more important than all others, can be calculated as:

(2)

Eq. 2 simplifies to eq. 1a for n=2.

With eq. 2 we can formulate the general case for the balanced scale, resulting in evenly dispersed weights for n criteria and a judgment x with x from 1 to M:

(3)

with

(3a)

(3b)

(3c)

We get the general balanced scale (balanced-n) as

(4)

Continue reading Why the AHP Balanced Scale is not balanced

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