Conceptually, Little's Law can be understood by considering a water tank into which water is added at the exact same rate that water is removed so that the water can be maintained at a constant level. A more full tank will have more water molecules – more WIP Inventory – than a less full tank, and if both tanks have the same flow rate the molecules in the more full tank will, on average, stay in the tank for a longer period of time than those in the tank with the lower level. As Little's Law states, at constant throughput, Lead Time correlates directly to WIP Inventory level.
Mathematically, Little's Law is most easily understood when considering a conveyor belt. For the purposes of clarity we will look at the best case – when variability is ignored.
Consider a belt surface sixteen feet long moving at two feet per hour. Four operations, in four workstations, are performed along that belt, each taking exactly two hours, for a total processing time of eight hours. A red box placed on the belt will move through each operation in a total of eight hours; its lead time is 8 hours. In the course of eight hours the belt will have delivered one piece to the end (throughput = 1/8 per hour). As the piece is completed another is added to the conveyor, so WIP Inventory remains at one.
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If a second box is added to the line it will wait until the first workstation is open. Each additional box added to the line will move into the first workstation as that workstation becomes available until all four workstations are full. At this time the line is said to be "wetted" and the process will be at steady state; one box will enter the line as one box exits it. It still takes eight hours for a box to move through the four operations, but a completed box is output every two hours. Because no more than 1/2 box per hour can be produced this is the line capacity. Because the line is balanced – the cycle time of all workstations is the same – any of the four machines can be considered the bottleneck, with a capacity of 1/2 box per hour. Ignoring variation, lead time will never be shorter than this; lead time is equal to total processing time.
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If a fifth box is added to the line it must wait for workstation one to open, even after the steady state condition is reached. Because we measure lead time from the time a box is released to the line, the time it waits for workstation one to open (two hours) is added to its lead time. Throughput remains at 1/2 box per hour but lead time suddenly takes a step change.
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Now, if eight boxes are placed on the table labeled "Safety Stock" and replenished at the still unchanged throughput rate of one unit every two hours as they are fed into the process, the first box must wait 2 hours to get into the process, adding 2 hours to its lead time. The second box fed into the process suffers four hours in queue. The eighth box fed into the process has a lead time of twenty-four hours; sixteen hours in queue and eight hours being processed. This can be calculated using Little's Law, since Lead Time equals WIP divided by Throughput, or Lead Time = (12 units) / (.5 units/hour) = 24 hours.
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Accumulating finished goods into a batch before transporting them (often to a downstream assembly area) similarly extends Lead Time, but in steady state conditions the effect is less than that for WIP held ahead of the process. If eight boxes are accumulated before transport the first piece has no lead time penalty and the eighth piece has a sixteen hour penalty as above. The average impact is an eight hour penalty for each box in the accumulated batch.
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It is important to note that the best efficiency in this particular example is when WIP=4; when all workstations are full, yet with no additional WIP in the process. If there were variability the optimum WIP will be more than four boxes. The optimum amount of WIP for the current system is termed Standard WIP. It's level will be reduced as the variability is reduced and the system is improved. Little's Law (cycle time equals WIP divided by throughput) holds true even when variability is present.
Uses: While the best use of Little's Law may be to reduce process Lead Time by reducing WIP inventory, it can also be used to: calculate the number of jobs in queue (backlog) based on throughput and cycle time; calculate cycle time given WIP and throughput values when cycle time can not be directly observed; calculate inventory turns, which is the inverse of lead time, or; calculate the workstation utilization if the number of jobs in queue is less than one.
In most batch operations the inventory is not kept moving as it is on a conveyor belt system or at its ends. Some operations, such as heat treatment, may need to be done in batches, depending on the current equipment. What cannot be worked at each operation is set aside, to wait for other items in the batch to be done. The attached file shows how to calculate lead time delays based on several batched operations.