Little’s Law everywhere – even in the “body of Christ”

January 15, 2009

Little’s Law dictates the relationship between three performance metrics in a process, Inventory, Flow Rate and Flow Time:

Inventory = Flow Rate x Flow Time

If you know two of them, then you can calculate the third. It is hard to not be a Little’s Law junkie – seeing the application of Little’s Law everywhere.  Here is an application that you might not expect – the production of communion wafers. The New York Times published an article about a company in Rhode Island that makes a lot of communion wafers – about 1 billion per year. It comes with a short audio slide show which is reasonably interesting.

So what is the Little’s Law question from the article? Wafers are produced at the rate of 100 per second. They spend 15 minutes in a cooling tube. How many wafers does the cooling tube hold on average? Use Little’s Law! Inventory = 100 x 15 x 60 = 90,000, or enough for 360 Sundays at a medium sized church that serves 250 per service. (360 Sundays is almost 7 years.)

If Little’s Law isn’t your thing, then you can calculate out their process utilization. At 100 wafers per second, that is 100 x 60 x 60 x 24 x 365 = 3.2 billion wafers per year.  They only sell about 1 billion per year, so their process utilization is about 1 b / 3.2 b  = 31%