In a previous post, we evaluated an office's coffee supply, and discovered policies which would allow the office to keep a sufficient supply of coffee, given the assumption of even consumption throughout the week. What happens to the system if coffee consumption varies through the week? As our office seems to be running every day (to simplify math) lets assume that the coffee consumed varies sinusoidally over the week, from a low of 10 cups per day on the weekend to a high of 30 cups per day on Wednesday:

As we have the model, its pretty easy to plug in our consumption data and see what happens:

The first thing I notice is that the threshold value increases from its original (clearly very low) value to a stable state in 3 major intervals, and that those intervals are not aligned with the weeks. That's surprising, but it seems to be due to the somewhat erratic behavior of the coffee supply. These could be start-up dynamics, so lets set the threshold equal to its final value, start the supply above that threshold and run over 300 days, to try and get as close to a long term trend as possible:

To see this data in tabular format, visit this spreadsheet.

We still see the somewhat erratic behavior of the coffee supply, but now we can see that in the long term, the behavior forms a repeating pattern ever 35 days. The threshold condition, demand, and purchasing volume being what they are, the time between coffee supply runs follows a pattern of 5,6,4,5,6,4,5 days, coming to an even average of 5 days between runs.

Now we're starting to get a sense for why the behavior should repeat with period 35 days. We have two periodic behaviors with different frequencies, and are experiencing beats! That's pretty neat! The beat period (35 days) is what we get when we multiply the two driving periods together (7 day consumption period, 5 day replenishment period).

To play with this model, visit: http://insightmaker.com/insight/2427#