# An analogy: Marching soldiers, revisited

In Eliyahu Goldratt's book ``The Goal'', the importance of a bottleneck in a factory is described through an analogy to a troop of boy scouts out for a march. One of the scouts, who is carrying an extra-heavy backpack, walks more slowly than the rest, so a gap keeps opening between him and the scouts in front. This is then connected to how inventory masses up in front of a slow machine in the factory.

But this is less than half the story. In a column of marching soldiers, the problem is not a slow marcher falling behind. Each soldier carries the same weight, so the line is balanced, and there is no pronounced bottleneck. The problem is variability amplification: If the first soldier for some reason speeds up a little bit, the second soldier will see a gap open in front of him, and take this as a signal to speed up, as well. But he will have to speed up more than the first soldier did, in order to catch up with him. When he has caught up, he then needs to slow down again to avoid bumping into the one in front.

Now the third soldier sees a gap opening up even faster than the second one did, so he has to speed up by even more, and has to slow down more abruptly when he has closed the gap. This way, the small change in speed amplifies down the line like a whiplash, and the poor guy at the end of the line will alternate between running flat out and marching in place.

This is what occurs in a kanban line. The last machine in the line tries to track the demand process, but adds some noise to it due to process variability. The second last machine tries to track the input process of the last machine, but adds some more noise. This amplifies the noise upstream, so the first machine in the line will alternate between working at capacity and waiting for something to be taken out of its output buffer. To get rid of the problem, one has to eliminate all process variability, such as machine failures and operation time variability. This can be time-consuming and expensive.

How do soldiers counteract this age-old problem? Very simple. If the soldiers are recruits, they get the attention of a very loud drill sergeant that yells out the cadence. More seasoned soldiers will be singing a marching song as they go along, and any infantry outfit has a large supply of these songs. Both of these techniques have the effect of distributing the proper cadence to every soldier in the line, simultaneously.

This is what the CONWIP control does. It passes the demand information, without any noise, to the first machine in the line. All downstream machines know that any part arriving in their input buffer can be worked on, so they hear the signal, too.

But marching soldiers do not close their eyes and march blindly. Even if they receive the proper cadence, they will still be watching the distance to the marcher in front. If the gap widens, they will take longer strides, and if it narrows, they will shorten their steps. This way, the marchers act on two types of information at once: The global information flow that determines the overall speed, and the local information that is used for minor adjustments.

This is also the way our hybrid policy works: The CONWIP control gives a global information flow (like the drill sergeant), and the kanban control gives a local flow of information (like watching the distance to the guy in front). In our hybrid policy, the global information flow from the demand process is supplemented by the local information from the buffer levels. This attains the advantages of CONWIP control, while using the strengths of kanban control to cancel its disadvantages.

References

This page is written by Asbjoern M. Bonvik. Last modified on March 29, 1996. It is based on research by Asbjoern M. Bonvik, Christopher Couch and Stanley B. Gershwin. It is related to the research efforts of the Leaders for Manufacturing Program at MIT, especially its Research Group 5. Please send comments to gershwin@mit.edu.