What is Little's law in manufacturing?

WIP = Throughput x Average Lead Time, for a stable process measured over the same boundary and time unit. A cell finishing 50 units a day with a 4-day lead time carries about 200 units of work in process.

How do I calculate lead time from WIP?

Divide the WIP by the throughput: lead time = WIP / throughput. With 240 units on the floor and 50 completed a day, new work will take about 4.8 days to come out, 0.8 days longer than the 4-day target.

What is the formula for the total cost of work in process?

In cost accounting, ending WIP = beginning WIP + total manufacturing costs (materials, labor and overhead) - cost of goods manufactured. Little's law answers the unit question; multiply its WIP units by the average cost per unit in process to estimate the money tied up.

Does Little's law work for a single order?

No. It is a statement about long-run averages in a stable system. One order's time depends on its priority and route; the law tells you what the average order will see given the WIP you are carrying.

Why does reducing WIP shorten lead time?

Because throughput is set by the bottleneck, not by how much work is released. Holding throughput at 50 units a day, cutting WIP from 240 to 200 units cuts the lead time from 4.8 to 4 days without losing any output.

Production and Throughput

Little's Law WIP Formula

Little's law links the three numbers every flow line lives by: work in process, throughput and lead time. Use it to predict how much WIP a line should carry, or how long work will take to get through it at the WIP you count on the floor.

Formula

WIP = Throughput x Average Lead Time

Variables

WIP: Average units started but not yet finished inside the process boundary
Throughput: Average completion rate, in units per day (or per hour)
Average Lead Time: Average time a unit spends inside the same boundary, in the same time unit

Understanding the Little's Law WIP Formula

Little's law says that, on average and over a stable period, the work inside a process equals the rate work leaves it multiplied by the time each unit spends inside. In the example, 50 units a day for 4 days means 200 units are in the system at any moment. It holds for any stable process regardless of the distribution of times, which is why lean teams use it to sanity-check WIP limits and quoted lead times.

Rearranged, it gives the other two: lead time = WIP / throughput and throughput = WIP / lead time. The most useful form on the floor is the first. Count the WIP, divide by the daily output, and you have the lead time a new order will see; 240 units at 50 a day is 4.8 days, whatever the schedule says.

The law describes averages over a period in which the process is roughly stable; it will not predict a single order's time or a day of a ramp-up. The lever it exposes is WIP: with throughput fixed by the bottleneck, every unit of WIP you add only adds lead time, which is why capping WIP shortens lead time without slowing output.

Worked Example

A cell completes 50 units a day and work takes 4 days on average from release to finish. The floor count today is 240 units.

Predicted WIP = 50 units/day x 4 days = 200 units
Flow time at the counted WIP = 240 / 50 = 4.8 days
The extra 40 units add 0.8 days to every order's lead time

Result: 200 units of WIP predicted; the 240 counted means 4.8 days of lead time

Common Mistake

Mixing boundaries or time units. Throughput, WIP and lead time must describe the same stretch of the process and the same calendar: a lead time in calendar days with throughput per working day overstates WIP by about 40%.

Frequently Asked Questions

What is Little's law in manufacturing?: WIP = Throughput x Average Lead Time, for a stable process measured over the same boundary and time unit. A cell finishing 50 units a day with a 4-day lead time carries about 200 units of work in process.
How do I calculate lead time from WIP?: Divide the WIP by the throughput: lead time = WIP / throughput. With 240 units on the floor and 50 completed a day, new work will take about 4.8 days to come out, 0.8 days longer than the 4-day target.
What is the formula for the total cost of work in process?: In cost accounting, ending WIP = beginning WIP + total manufacturing costs (materials, labor and overhead) - cost of goods manufactured. Little's law answers the unit question; multiply its WIP units by the average cost per unit in process to estimate the money tied up.
Does Little's law work for a single order?: No. It is a statement about long-run averages in a stable system. One order's time depends on its priority and route; the law tells you what the average order will see given the WIP you are carrying.
Why does reducing WIP shorten lead time?: Because throughput is set by the bottleneck, not by how much work is released. Holding throughput at 50 units a day, cutting WIP from 240 to 200 units cuts the lead time from 4.8 to 4 days without losing any output.