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Little’s Law: WIP, throughput, and cycle time
Little’s Law is the closest thing operations has to a conservation law. The average amount of work in a system equals the rate work arrives multiplied by the average time each piece spends inside. It holds for any stable system, with no assumption about how anything is distributed — which is exactly why it is so useful and so easy to misuse.
L = λ W — or, on a factory floor: WIP = throughput × cycle time
What it tells you that you did not already know
Rearranged, the law says cycle time = WIP ÷ throughput. On a line already running at its bottleneck rate, throughput cannot rise — so every extra unit of work-in-process converts directly into lead time. That is the quantitative case for pull systems: the WIP you release beyond what the constraint can absorb does not become output, it becomes waiting.
Measured on Flowline’s canonical line, going from 6 to 24 Kanban cards per edge raises jobs in the system by 53% and measured flow time by 44%, while throughput moves 7%. Extra WIP buys time in system, not output.
The trap: measuring the law with the law
Most dashboards compute cycle time as WIP divided by throughput. Check Little’s Law against that number and you have proved nothing — you restated a definition. For most of this project’s life the law was on the explicitly-not-claimed list for exactly that reason.
What makes it evidence is a second, independent measurement. Flowline now stamps each unit when a chain-head station releases it, has it inherit the latest stamp among its inputs at every station after that, and measures it when it ships. That number contains no WIP term anywhere, so comparing it against a time-averaged job count and a counted throughput is arithmetic that can actually come out wrong.
| Line | Ratio |
|---|---|
| ~4% cumulative scrap | 0.975 |
| ~34% cumulative scrap | 0.776 |
The second row is not an error. The law relates WIP to all departures; flow tracking measures only units that ship. A scrapped unit is work-in-process while it lives and then leaves unmeasured, so the ratio is pulled down by roughly the scrap fraction — certified on the low-scrap line, with the bias asserted separately rather than absorbed into a wider tolerance.
Try it on a real line
Each of these is a fixed-seed puzzle factory in Flowline’s Challenge Mode. Every one is verified before it ships: the intended fix must win, doing nothing must fail, and a plausible wrong fix must also fail — so the puzzle isolates the idea it claims to teach. They run in your browser.
- The Warehouse Tax — Bank $25,000 of profit A working line still leaving money on the table: inventory hoarded behind a bottleneck earns nothing and costs rent every second.
- Cut the Lot — Ship 13 machines/min with parts flowing through in under 27s Throughput and flow time have separate bars, and separate fixes. Clearing one leaves the other exactly where it was.
- Too Few Cards — Ship $6,000 of toys The other direction: a perfectly capable line that ships nothing at all, because release discipline was set too tight.