Variability Affects Throughput

The Game: Goldratt presents a game in Chapter 14, the “die and matchsticks” game. The heart of the game is this: suppose you have 5 people taking matchsticks from a bowl to its left (if there are any) and putting them on a bowl to its right. The first person takes from an infinite bowl, so the first person always has matchsticks to move to its right. Also, the persons have a random efficiency, so they can transfer a random number of tokens from 1 to 6 (a dice roll) during each round, Its important to realize that people can only pick up matchsticks if they are there: if a person wants to pick up 6 matchsticks but there are only 2 in its “source” bowl, it will only pick up the two available. This example game removes many distractions from an often complex manufacturing problem. There are no shifts, downtime, processing time, move time, time for cadence, The problem accentuates how variability affects the system throughput.

Is your intuition right?

A chain of workers try to move matchsticks to the right, and because of the “random pick between “1 and 6”, we can safely say that on average the first worker will move, on average, 3.5 matchsticks at each turn. We might be tempted to think that the whole chain will have the same overall efficiency and will hence move 3.5 tokens at each turn on average. Clearly, this is not the case, because the difference between the assumption and a statistically calculated version is 28%.

Why is the “chained throughput” (total throughput) so much lower that anticipated?

Lower throughput resulting from variability of the stations is the key learning objective of this exercise and is applicable to all service and manufacturing systems. When a station is expected to move a specified quantity forward, but insufficient quantity is available, production is lost forever. The principle is not just true for quantities. The same principle applies to times. For this reason, systems under perform from a plan developed using averages.

What additional lessons come from this example?

Additional samples provide greater accuracy but at a cost of reduced value

Increasing the samples improves the accuracy of the calculation. but consider the accuracy of the input before deciding how many samples might be needed. If your input is accurate to plus or minus five percent, then don’t try to gain more accuracy by running excessive samples. On the other hand, if the inputs are accurate to a hundredth of a percent, then increased sample is important.

Manually calculating the throughput is challenging

Most calculations assume an average rate of production, because handling variability is complex. However, using average calculations would be off by about 30%! How would you accurately calculate the throughput of this system manually? Most people lack the skill to accurately calculate the throughput of this simple system. If you did calculate it manually, how would you check your work? If you could make the calculation and verify that the work was accurate, what would you do when management decided to change the way the system worked or wanted to try several options? What if, instead of 5 identical stations, each station was different or consisted of more stations? How would you convince your audience that your projections’ were accurate?