Advanced Process Combinatorics

Combinatorics refers to a branch of mathematics that is useful to the analysis and management of processes. VirtECS^® is built on a substantial foundation of mathematics, science, and engineering. For example, the initial underlying breakthroughs are described in an invited article in Science Magazine in the early 1990s. This early work showed the importance of algorithm engineering for applications where there are a number of choices that imply a very large number of possibilities, which is true for almost all practical processes. However, a great many innovations were necessary to extend this basic work to the real world. VirtECS^® incorporates these innovations. The features that these innovations address include:

• Making decisions along a time line and accounting for the very different results that unfold with different choices.
• Describing processes at an appropriate level of detail.
• Achieving lightning fast answers so that attention can be focused on creativity in realizing value.
• Providing intuitive and transparent control over sophisticated functionality.

NP-Completeness presents a fundamental challenge for most combinatorial problems, including virtually all practical applications on which VirtECS^® is used. Of course, APC customers do not worry about the details of combinatorics or these fundamental challenges, because VirtECS^® incorporates years of research and development. In the words of one APC customer "VirtECS^® just works".

For a historical perspective on combinatorics and business, please see:

Bishop, J. E. (1991) "Mathematicians Find New Key to Old Puzzle", The Wall Street Journal, Section B, February 15, pp 5.

This national newspaper article was published in response to the Science article mentioned above.