Tuesday, April 27, 2004
Variance and Drum-Buffer-Rope
Over the last few evenings, I’ve been acutely reminded of how variability affects a Drum-Buffer-Rope flow solution for TOC. It’s been pretty nice weather here in Seattle recently and the evenings have often been blue skied and sunny. Every evening after dinner and before I write this weblog, I take my dog for a walk. In summer my daughter comes too. She is now 22 months and very insistent that riding in the stroller is only for babies and she prefers to walk. So she comes along, walking on her own. She also likes to hold the dog’s leash (ah hem lead, if your reading this in English). Now Nicola is 25 lbs and the dog is 45 lbs. He is very strong and pulls a lot. He was, after all, half-bred to herd sheep down a mountain with the other design to pull carts around China - definitely not the ideal combination to mix with a fragile toddler. Meanwhile, my daughter is still a novice at walking and wobbles a lot. So dad has to be very careful and keep the dog on a tight leash - see graphic…
As shown, dad is acting as the Drum because my daughter, the constraint, is too young and weak in comparison to pull from the system input, the dog. The Rope is the leash. The Buffer is the slack in the leash between dad and daughter. Often times, the buffer is twice the length of the rope between the input and the drum. However, it takes very little variance in the constraint - the rate at which a not-quite-two-yet can walk - or variance (in the strength of pull) at the input to cause the whole system to become unstable and have to stop and reset. This makes overall productivity - the rate at which ground is consumed in the direction of the park - very low.
In this example, the rope is only a total of 6 feet long and between input and drum it is only 2 feet. However, the desired production rate is perhaps 2 feet per second, or even more. The system is inherently unstable because there is insufficient rope and insufficient buffer in comparison to the desired production rate. In order to stabilize the system, either the production rate has to be lowered to a snails pace - and I have tried this and it works or the variability in the constraint needs to be greatly reduced - try telling that to a not-quite-two-yet toddler! An alternative solution would be a much longer rope (leash) to provide for a much greater buffer.
So there it is! With the Drum-Buffer-Rope solution, production rate can only increase in a stable fashion, if you either (a) increase the size of the buffer or (B) decrease the variability in the constraint whilst avoiding moving the constraint somewhere else in the system.