In part 1 we explained why small and medium businesses or SMEs needed risk analytics. In part 2 we described a few common risk related issues that affect SMEs. In this concluding part, we will describe a very basic scenario that relates to the twin problems of capacity utilization and demand uncertainty.

Frank Buytendiyk in his wide ranging article here makes an argument for

This flash video explains in a minute how entropy can work for measuring risk and uncertainty for business analytics problems. You can continue reading below or simply watch the video.

Imagine a box that can contain one of three colored balls inside - red, yellow and blue. Without opening the box, if you were to guess what colored ball is inside, you are basically dealing with uncertainty. Now what is the highest number of "yes"/"no" questions that can be asked to reduce this uncertainty?

Is it red? No.

Is it yellow? No.

Then it must be blue. That is two questions. If there was a fourth color, green, then the highest number of (yes/no) questions is three. If you extend this reasoning, it can be mathematically shown that the maximum number of binary questions needed to reduce uncertainty is essentially log (T) where the log is taken to base 2 and T is the number of possible outcomes. (ex: If you have only 1 outcome, then log (1) = 0 which means there is no uncertainty)! If there are T events with equal probability of occurrence then T = 1/P.

Claude Shannon used this idea to define entropy as log (1/P) or -log P where P is the probability of an event occurring. If the probability for all events is not identical, we need a weighted expression and thus entropy, H

`H = -Summation (pi log pi)`

The venerable World Economic Forum recently published their 5th annual "Global Risks" report. While clearly this is a very timely analysis, we see a few problems with their report.