# Lead Time and Replenishment Interval (RI) Limit Minimum Confidence

To make sense of this statement, let’s recall the earlier, intuitive situation in which a very large replenishment interval, or RI (and correspondingly large MOQ) results in virtually 100% confidence, requiring practically no expediting to achieve or even exceed the fill-rate target. In this situation, it is nearly impossible to have less than 100% confidence, unless we can significantly reduce the RI and, correspondingly, the MOQ.

Consider the real inventory item JKL. Item JKL has 7-day RI and a 14-day lead time. We explore whether or not this combination permits a 50% confidence of achieving the fill-rate target with minimal expediting. The following chart shows three curves. Each curve represents possible combinations of lead time and RI for which it is possible to achieve the given target confidence. In other words, for these combinations of lead time and RI, the MOQ and RI permit these confidence values.

On the combination chart above, JKL’s actual RI/ lead-time combination is shown as a green filled circle. Note that, at each of the 80% and 90% confidence levels, the actual RI/lead-time combination of 7 RI days and 14 lead-time days allows safety-stock values to be computed that permit the specified confidence value to be achieved.

However, for JKL, at 70% confidence, the possible RI and lead-time combinations average around 4 RI days and range from 1 to 3 lead-time days. (A maximum actual combination is a 5-day RI and 3-day lead time.) At the actual RI days of 7 and lead-time days of 14, a 70% confidence simply cannot be achieved for this item. We conclude that, for JKL with its current RI and lead time, safety stock cannot be set so as to obtain confidence values as low as 70%.

For item JKL, consider achieving a 98% fill rate with a 90% confidence. The chart below shows the relationship between those combinations of RI days and lead-time days that support these requirements. The chart shows, for example, that if JKL has a lead time of 10 days and a desired 90% confidence of achieving a 98% service level target, its RI can be no more than about 20 days.

We have shown that confidence is directly influenced by RI (equivalently, MOQ) and lead time. Confidence also directly and dramatically drives safety-stock level. Using the earlier example of average daily demand (ADD) ranging from 96 to 104 for an entire year, the safety stock required for 99.5% confidence, which would give a high likelihood of achieving the fill-rate target for the 104-ADD year, may be 2-3 times more than that required for the 50% confidence, which would give a reasonable likelihood of achieving the fill-rate for the 100-ADD year. In this example, if lead time and RI were sufficiently small to enable 50% confidence, and if expediting were inexpensive, an economic analysis of total costs may result in a desired confidence closer to 50% than to 100%.