Welcome to BPMSG – October 2015

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

it’s soon coming to five years that my webpage has been online, and things getting slowly a bit messy … There was a need to clean-up the pages, posts and directories, so that the necessary maintainance will take less time, and future updates are possible. As you should know, this project is done in my free time as a hobby, I still have a full-time job for another couple of years.

Unfortunatly, during the whole process, some links were broken and it will take time to repair. Sorry, when you experience missing images or a broken link. Just let me know using my contact page. I am still working on it and plan to simplify the navigation in order  to make it easier for you to find relevant information.

AHP as one category, where you find information about the analytic hierarchy process, will stay in focus. From the start this was the nost frequently visited part of the site, and my AHP excel template slowly reaches 15 thousand (!) downloads. Under  the category Articles you find posts about other topics, mainly the concept of diversity, as I was using it for  different applications. All more personal related  topics under the category Other will move to my new personal blog – Klaus & Lita – running on my own server with topics like multicopter, programming and – maybe – cooking in future.

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

Klaus D. Goepel,

Singapore, October 2015

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.


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AHP online software – how it was implemented

When I was asked just now in an e-mail, how my AHP online software operates,   I realized that I have never published a description about it. Therefore, here a short summary:

The AHP-OS software implementation is based on my AHP excel template. I have published one paper about it in 2013. All mathematical formulas used, are shown in this conference paper or in the excel template manual on the last 2 pages. The online version is realized in PHP, using OOP (object oriented programming), running on a Linux server.

The core module is the ahp class. It contains the routines to fill the decision matrix from the pairwise comparisons, to find the dominant eigenvalue using the power method, and to calculate the consistency ratio.

A second important class is the hierarchy class. It translates the text file – defining the hierarchy – into a hierarchical data array. When I implemented the software, I wanted to get a flexible tool, which can be used for all kind of hierarchical problems. This was actually more difficult than the implementation of all mathematical calculations, especially under the aspect of safety and malicious online attacks. The feature also differentiates the online version from the excel implementation. The excel template cannot handle hierarchies at all.

The third important class implements the database and its management. I use SQL with either sqlite or mysql drivers. There are 4 tables:

  • one for user management (registration, password, etc.),
  • one for projects (hierarchy data, description, session code etc.),
  • one for pairwise comparisons (participants, judgments etc.) and
  • one for handling alternatives.

The rest of classes contain supporting functions, like html in/output, excel download and consolidation for group results. I use a basically two open source packages, phpMailer and phpGraphlib, the rest is all realized by myself from scratch.

Please consider a donation, it will help me to maintain the website and program:

Your Donation (1 Singapore Dollar is approx. 0.7 USD):



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