# Little’s Law

The inventory in a process is related to the throughput rate and throughput time by the following equation:

W.I.P. Inventory = Throughput Rate x Flow Time

This relation is known as Little’s Law, named after John D.C. Little who proved it mathematically in 1961. Since the throughput rate is equal to 1 / cycle time, Little’s Law can be written as:

Flow Time = W.I.P. Inventory x Cycle Time

What Little actually said was, “The average number of customers in a system (over some interval) is equal to their average arrival rate, multiplied by their average time in the system.”  A corollary has been added: “The average time in the system is equal to the average time in queue plus the average time it takes to receive service.” The application to office work is also counter intuitive for many business leaders. Stuffing more projects, goals, assignments on a critical resource is almost always guaranteed to slow things down, yet we do it all the time. Recent observations of a purchasing group made this clear; releasing yearly contracts, all in a huge batch, made a normal one week purchase order turn around become more than a month. If there are no controls over the number of projects-in-process, then there can be no control over the lead time.

References:

http://en.wikipedia.org/wiki/Little’s_law

John D. C. Little