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Little’s law and WIP calculator
Work in process, throughput and lead time from Little’s law L = λ · W: give any two and get the third, in pieces, per hour, shift or day and in working time.
Input
Give two of work in process, throughput and lead time; the third is calculated and its field is switched off. Times are working time: a working day is the shift length × the shifts per day.
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Results
4 working daysLead time
480 pcsWork in process
7.5 pcs/hThroughput per hour
64 hLead time in hours
Lead time = WIP / throughput = 480 pcs / 7.5 pcs/h = 64 h
| Quantity | Value |
|---|---|
| Work in process | 480 pcs |
| Throughput per hour | 7.5 pcs |
| Throughput per shift | 60 pcs |
| Throughput per working day | 120 pcs |
| Lead time in minutes | 3840 min |
| Lead time in hours | 64 h |
| Lead time in shifts | 8 |
| Lead time in working days | 4 |
| Working hours per day | 16 h |
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How Little’s law is calculated
Little’s law links three averages of a stable flow: how many pieces are inside, how fast they leave and how long each one stays. It needs no assumption about the order of work or the variation of the times, only that the averages cover the same period and the same part of the process, and that what goes in also comes out.
Formulas
- Little’s law: L = λ · W, where L is the average work in process (pieces), λ the average throughput (pieces per unit of time) and W the average lead time (time per piece).
- Lead time W = L / λ, throughput λ = L / W, WIP L = λ · W.
- Units: every time is turned into hours of working time first: a minute is 1/60 h, a shift its length in hours, a working day the shift length × the shifts per day. The answer is then shown in every unit.
- The work in process that comes out is an average over time, so it need not be a whole number.
Worked example (the tool’s example)
- 480 pieces are between the first and the last operation of a line, which finishes 60 pieces per shift; two 8-hour shifts make a working day of 16 h.
- Throughput = 60 / 8 = 7.5 pieces per hour, 120 per working day.
- Lead time = WIP / throughput = 480 / 7.5 = 64 h of working time = 8 shifts = 4 working days.
- With the WIP limited to 120 pieces at the same throughput, the lead time would be 120 / 7.5 = 16 h, one working day.
Common mistakes
- Counting WIP and throughput at different boundaries (WIP of the whole plant, output of one line).
- Taking the throughput of the fastest machine instead of the rate at which pieces actually leave.
- Mixing working and calendar time: a throughput per working day with a lead time in calendar days.
- Using one snapshot of WIP on an unusual day; the law is about averages over a period.
- Applying it to a system that is filling up or emptying (a ramp-up, a build-ahead): the averages are then not in balance.
Input and files
- Numbers may use a decimal comma or point. The settings file keeps every field as typed; the results CSV lists every unit.
Questions
- What does Little’s law say?
- Over a long enough period, the average number of pieces in a system (work in process, L) equals the average rate at which pieces leave it (throughput, λ) times the average time one piece spends inside (lead time, W): L = λ · W. It holds for any stable system whatever the order of work or the variation, as long as the three are averages over the same period and nothing is lost or created inside.
- How do I use it to cut lead time?
- At a given throughput, lead time is proportional to work in process: halving the WIP between two points halves the time a piece spends there. That is why limits on WIP (kanban, FIFO lanes with a maximum) shorten lead time without making anyone work faster.
- Which throughput should I use?
- The rate at which pieces leave the part of the process you are looking at, averaged over the same period as the WIP count: the output of the line or the bottleneck, not the speed of the fastest machine. Count WIP at the same boundaries as the throughput, from the first operation you include to the last.
- Why working days and not calendar days?
- Throughput per day means per day that the line works, so the lead time that comes out is in working time too. To estimate calendar time, add the non-working days yourself; mixing a throughput per working day with a lead time in calendar days gives a wrong WIP.
Related tools
- Kanban sizing: the number of cards that caps the WIP of each part.
- Takt time calculator: the pace of demand the throughput must reach.
- SMED change-over analysis: shorter change-overs allow smaller batches and less WIP.
- OEE calculator: the losses that lower the throughput.