Understanding Random Demand Variation: Items with Steady Demand

Inventory anal
ysts, 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?

Notice the comparatively steady volume, few demand spikes, insignificant trend and seasonality.  An item like this should be an ideal candidate for a “simple” or Excel-friendly safety-stock calculation. If you have items like this, and yet you’re unsatisfied with their service-level and/or inventory performance, might safety stock be a culprit?

As a first review, let’s make sure we have eliminated all variation that we are forecasting, or could forecast. In this example, we know what causes the largest spikes. But we still can’t predict the timing of these spikes, so they are part of overall random variation. Statistical tests for significant trend and seasonality all come up negative. So the historical data offers no intrinsic predictors for forecasting. That leaves safety stock, or inventory buffer, as our best option for consistently achieving our target fill rate. So how do we find the optimal balance of service level and inventory performance?

First, let’s try this common, popular safety-stock formula:

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

For this item:
• Avg demand = 95.88
• Std dev of demand = 87.32
• Coefficient of variation = 0.91
• Avg lead time = 8 days
• Std dev of lead time = 0.92 day
• Target service level = 98% = 2.05 Z

Calculated (from the formula) safety stock = 539


  • • This item’s EOQ is 1898.
  • • It is managed using reorder point (ROP).

o ROP = 1306 = 95.88 demand * 8 lead time + 539 calculated safety stock.
o Theoretical average quantity on hand = 1488 = 539 safety stock + (50% * 1898 EOQ).

Is the calculated safety stock optimal? No. It’s much too high. The formula’s calculated safety-stock level and the on-hand portion of EOQ are providing virtually a 100% service level, not the 98% target.

To achieve its 98% service-level target reliably with minimal inventory and expediting, no safety stock is required, and ROP should be 647. This item’s EOQ is about a month’s worth, in comparison to an 8-day lead-time. EOQ is providing so much de facto safety stock that EOQ could be reduced by 780 units without negatively affecting the target service level. As compared to the formula’s results, reducing ROP to 647 reduces the theoretical average quantity on hand by 36%, from 1488 to 949. If the EOQ can also be reduced by 780 units, the inventory performance will improve even more.

How did we arrive at no safety stock, ROP of 647 and a recommended EOQ reduction of 780? Not by using a formula, but by using a correct, objective analysis that correctly accommodates the reorder quantity (EOQ, in this case).

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, contact us via email, or give us a call – we would be happy to help you get the correct levels of safety stock to meet your service level and financial goals.