WIP Limit Decision

How this works

Little's Law fixes the relationship between work-in-process, throughput, and lead time for any process running in steady state: average work-in-process equals average throughput times average lead time. Reversed, it gives the work-in-process cap that holds lead time at or under a target, throughput times target lead time. That cap has to be a whole job, and it has to be rounded down, not up. Admitting one more job than the floored cap allows pushes the expected lead time past the target, which defeats the reason for setting a cap in the first place.

When a current work-in-process level is entered, the engine also reports the lead time that level implies and how far it sits from the calculated cap, so a manager can see immediately whether the line is running over the cap (and by how much lead time is stretching) or has room to take on more work.

Key terms

• Little's Law: the identity WIP = throughput times lead time (or lead time = WIP divided by throughput), true for any stable process regardless of its internal variability.
• WIP (work-in-process): the number of jobs or units that have started but not yet finished at a given moment.
• Lead time: the average time a single job spends in process, from release (start) to completion.
• Throughput: the average rate at which the process completes finished jobs or units, in units per day here.

Assumptions

• Throughput is steady-state, the process's average completion rate, not a single day's output
• One process or line with one lead time measured start to finish
• The work-in-process cap must be a whole job and is rounded down, never up

Limitations

• Does not model variability or queueing distributions beyond the mean relationship
• Does not sequence or prioritize individual jobs once WIP is capped, that is the next step, comparing dispatch rules
• Not a multi-stage routing model, treats the process as a single stage

Sources

Little's Law and work-release control (CONWIP) follow Hopp and Spearman, Factory Physics, and the APICS CPIM Body of Knowledge's capacity and priority planning material.

Worked example

A line completes 10 jobs per day and the target lead time is 4.35 days. Throughput times target lead time is 43.5, so the work-in-process cap is 43 jobs, not 44. At 43 jobs in process, expected lead time is 43 divided by 10, or 4.3 days, at or under the 4.35-day target. Rounding up to 44 instead would raise expected lead time to 4.4 days, past target, which is exactly the outcome the cap exists to prevent. If the line is currently running 55 jobs in process, that is 12 jobs over the 43-job cap, on pace for 5.5 days lead time, nearly a full day past target.

Common use cases

• Setting a CONWIP-style work-release cap for a production line or job shop
• Checking whether a current work-in-process level is consistent with a promised lead time
• Sizing a kanban or card count for a pull-based work cell
• Diagnosing why lead times have drifted when throughput has not changed