Thursday, July 11, 2013

More Musings on Little's Law

My previous posting about why not  to use Cycle Time in Kanban resulted in some interesting discussions, and I'm grateful to +Steve Tendon for pointing me in the direction of this paper [1] by John D.C. Little and Stephen C. Graves which gives some very helpful historical background into the derivation of Little's Law, its applicability and some of the terminology used.

From Little and Graves (2008)
Little's own formulation of the "law" was as follows:

L=λW

where

L = average number of items in the queuing system,
(equivalent to WIP in Kanban terminology)

W = average waiting time in the system for an item,
(equivalent to System Lead Time)

λ = average number of items arriving per unit time
(equivalent to Delivery Rate, assuming "stationarity")

With Kanban preferred terms we can see this maps to:

WIP =  Delivery Rate * Lead Time
or
Delivery Rate = WIP / Lead Time

Little used "waiting time" for the time taken by one unit to traverse the system (W) because his original context was queuing systems. For other applications he suggested Flow Time, which I think is a very useful alternative.

He also notes though that other authors use other terms for W, including cycle time, throughput time, and sojourn time, depending on the context. Yes - cycle time I'm afraid is in that list which is why confusion still abounds. This conflicts with the more generally accepted definition of cycle time in manufacturing, which corresponds to the target rate of working expressed as Takt Time, and is the reciprocal of Delivery Rate. In other words this confusion of terminology is at least as old as the reference Little and Graves cite: Factory Physics by Hopp and Spearman (1st edition:1996).

Useful background, but the message to me is still: "Don't use Cycle Time in Kanban!".


References:

[1] Little, J. D. C and S. C. Graves (2008). Little's Law, pp 81-100, in D. Chhajed and TJ. Lowe (eds.) Building Intuition: Insights From Basic Operations Management Models and Principles. doi: 10.1007/978-0-387 -73699-0, (c) Springer Science + Business Media, LLC http://web.mit.edu/sgraves/www/papers/Little%27s%20Law-Published.pdf

[2] Hopp, W. J. and M. L. Spearman (2000). Factory Physics: Foundations of Manufacturing Management, 2nd (ed.), Irwin McGraw Hill, New York, NY.
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