Little's Law (Work in Process)

John Little proved in 1961 what the shop floor already suspected: the work sitting inside a system equals the rate it flows through times how long each job stays. $\mathit{WIP} = \mathit{TH} \ imes \mathit{CT}$. Twenty units an hour with a five-hour flow time means 100 jobs somewhere on the floor at any instant, and there is no arrangement of machines or people that changes that.

What makes it remarkable is how few assumptions it needs. It holds for any stable system regardless of the arrival pattern, the service-time distribution, the queue discipline or the number of servers. Random arrivals, batch arrivals, priority jumping, machines breaking down: none of it matters. Very little else in operations research is that unconditional, and that is why the law shows up in call centres, emergency departments, software backlogs and supermarket checkouts as readily as in factories.

Use it in the direction that settles arguments. Count the jobs on the floor, measure completions per hour, and the law hands you the lead time you are actually quoting, whatever the schedule claims. Three hundred jobs at 25 an hour is a twelve-hour lead time, and promising eight is a promise the arithmetic has already broken. The corollary is the one managers resist: releasing more work into a system that is not faster does not increase output, it only increases WIP, and therefore lengthens every quoted lead time in proportion.