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The Relationship Between Cycle Time and WIP

The relationship between cycle time and WIP was first documented in 1961 by J. D. C. Little. Little’s Law states that at a given WIP level, the ratio of WIP to cycle time equals throughput, as shown in the formulas below:

In other words, for a factory with constant throughput, WIP and cycle time are proportional. If throughput is held constant, it is impossible to reduce average WIP without reducing average cycle time, and vice versa. It is important to understand that this is a known mathematical relationship. Over the long term, it will hold true for an entire factory, or for a single workstation (as long as the units used for each term are consistent with one another). 

Little’s Law can be illustrated with a simple example: assume a factory with a capacity of 500 wafers per week and no variability. Although this is a highly unrealistic assumption, we will relax it later in the tutorial. Under these assumptions, if we start 500 wafers or less in each week, the cycle time for each will be one week (because we have enough capacity to process them all during the week). 

However, suppose that we start out with a backlog of 500 wafers in the fab. Each week we get 500 more in, so that the total WIP is 1000. We can only process 500 of the wafers in a given week. On average, each wafer will spend two weeks in the factory (one week waiting for the backlog of other wafers to be processed, the next week being processed). Similarly, if we have 1500 wafers in the factory at a time, the average cycle time will be three weeks, etc. This is shown in the graph below.

As another way of looking at this, the following graph shows average throughput vs. average WIP. Up to the capacity of the factory, the throughput (the amount we get out per week) will equal the amount that we start per week. However, when the WIP in the factory reaches the capacity of 500 wafers per week, throughput can no longer increase. No matter how much WIP we cram into this factory, we will never get more than 500 wafers per week out (without increasing the fab capacity in some way). And, as shown in the first chart, the more WIP we cram in, the longer the average cycle time will be.

In this example, the best thing to do is clear - start exactly 500 wafers each week. This will maximize throughput, while cycle time remains at the minimum of one week. However, the situation is only this black and white for systems with no variability. For fabs that operate in the real world, we have to consider the relationship between cycle time and variability.