My colleague and friend Andrew Abela recently published a book on the Extreme Presentation method.
I have attended his seminars, and definitely recommend his method. For anyone interested in improving their presentation skills, and generating action out of their presentations, it is must-read.
One of the activities conducted during the System Dynamics class in Colombia was the Beer Game – El Juego de la Cerveza
It allows students to experience first-hand how structure of business organizations impact their behavior, to some extent irrespectively of how skilled their managers may be. In the game, a 3 tier distribution system delivers beer from a factory to consumers. Only the retailer knows the consumer demand. As information and goods propagates through the chain with delays, oscillation occurs.
Students play competitively, as a pool of money collected from them at the start of the game will be awarded to the winners. A very entertaining and active dynamic develops during the 4 hour exercise.
The Systems Dynamics Society offers kits for playing the beer game, that I recommend. They include everything you need to run the game, as well as videos of Professor Sterman running a session.
I have attended many of his sessions, both as student and observer – my employer sponsors the Beer Game during incoming MBA orientation at MIT. Professor Craig Kirkwood at Arizona State University also has very good materials and hints.
I decided to run with a low-budget version that uses beans, pieces of paper and boards printed on common plotter paper. Everything is in Spanish language. I believe publishing the materials here may be useful to colleagues in Latin America and other Spanish-speaking countries.
Here is the board for the game, and here are the slides
For editable versions of these files, please contact me directly.
This is a short note to talk about Harmonic Averages. Most people are familiar with Weighted Averages, as they are a valuable tool for aggregation. For instance, with the data below, the average profitability (~1735) can be easily calculated using weighted averages.
Avg_Profit = (1000*1200 + 200*300 + 500*2500 + 10*600 + 100*300) / (1000 + 200 + 500 + 10 + 100)
or
Avg_Profit = SUMPRODUCT(UnitsSold,ProfitPerUnit)/SUM(UnitsSold)
I’m using Excel notation, and assuming it is clear from the context that UnitsSold is a range that covers the second column, for all models, etc.
A less known way of averaging are Harmonic Averages. It is relevant when the data to aggregate is actually a ratio whose denominator is proportional to the weighting factor. A typical case is miles per gallon (MPG) for a bunch of vehicles. Gas consumption is directly proportional to the number of units.
Let’s add some MPG data to the table above.
Using Weighted Averages for an inverse ratio like MPG is plain wrong (24.3 MPG is NOT the average fuel economy)
The right thing is to use Harmonic Average:
Harm_Avg_MPG = (1000 + 200 + 500 + 10 + 100) / (1000/22.5 + 200/15.0 + 500/32.0 + 10/12.0 + 100/24.0)
As Excel doesn’t have a similar function to SUMPRODUCT for adding 1000/22.5, 200/15.0, etc. I will not use Excel notation, but plain math notation:
UPDATED formula
If you have to deal with Harmonic Averages, you may find interesting this note on how to do PivotTable Multidimensional Analysis with Harmonic Averages. There’s a similar one for Weighted Averages as well.
Let me know what you think.