Understanding Random Demand Variation: Frequent Replenishments

Inventory analysts, planners, and supply chain professionals must address many issues. Some of the more pressing ones depend on correctly addressing random demand variation. We are going to examine a variety of difficult to manage, random demand variation scenarios over the next few blog posts.

Do you have inventory items that behave like those pictured below?

This is an A-item component that is not a finished, saleable product. Its demand chart shows consumption into a manufacturing process, not end-customer demand. It is definitely high-volume and non-intermittent. Can we determine the safety-stock level that optimally balances inventory performance and service-level achievement?

Is there any non-random behavior that we might forecast and exclude from safety stock?

  • The 700,000 spike at the end of September 2011 is statistically (and graphically) unusual. It is actually an inventory adjustment, as are several other smaller “spikes” at the ends of months. Normally, we would not consider inventory adjustments for safety stock. However, in this case, due to the nature of the item and its consuming process, the daily “actual” consumption is estimated, and only a monthly physical count makes the on-hand quantity correct. Since this item is replenished on a computer-generated, not visual, signal, these monthly adjustments can and do trigger replenishments.
  • The chart suggests a pattern that sometimes follows a cycle of 3-4 weeks. The manufacturer concluded that this is a result of internal planning and scheduling, does not reflect end-customer demand and is not predictable.

First, we’ll try using a common safety-stock calculation:

Z*SQRT((avg lead time * std dev of demand^2)+(avg demand^2 * std dev of lead time^2))

For this item:

  • Avg demand = 98,685
  • Std dev of demand = 47,657
  • Avg lead time = 18.4 days
  • Std dev of lead time = 5.7 days
  • Target service level = 99% = 2.33 Z

Calculated (from the formula) safety stock = 1,392,317


  • This item’s EOQ and MOQ are 70,000, and its order multiple is also 70,000.
  • It is managed using reorder point (ROP).
  • ROP = 3,208,121 = 98,685 demand * 18.4 lead time + 1,392,317 calculated safety stock.
  • Theoretical average quantity on hand = 1,427,317 = 1,392,317 safety stock + (50% * 70,000 EOQ).

Is the formula’s calculated safety stock optimal? No. It’s much too high. The formula’s calculated safety-stock level and the on-hand portion of EOQ and order multiple are providing virtually a 100% service level, not the 99% target.

To achieve its 99% service-level target reliably with minimal inventory and expediting, safety stock should be 826,325, and ROP should be 1,990,005. This item’s EOQ is less than a day’s worth, in comparison to an 18-day average lead time. This means that replenishments are being received every day or two, and this steady stream of replenishments is providing considerable de facto safety stock. As compared to the formula’s results, reducing safety stock to 826,325 reduces the theoretical average quantity on hand by 40%, from 1,427,000 to 861,000.

How did we arrive at the effects of frequent replenishments on safety stock? Not by using a formula, but by using a correct, objective analysis that correctly accommodates the reorder quantity and reorder interval.

Do you ever experience this kind of random demand pattern? How have you managed the fundamentals of service level and financials?
If you need help managing inventory variation like this, comment here or visit our web site – we would be happy to help you get the correct levels of safety stock to meet your service level and financial goals.