# Understanding Random Demand Variation: Intermittent, Spiky

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 the one pictured below?

•  Are you having trouble finding the optimal balance of service level and inventory performance?
•  Can you forecast better, and how much safety stock do you need?

Daily demand is either zero or over 500!

Is this random? The answer depends on

1. identifying non-random behavior and
2. Forecasting the timing and magnitude of non-random demand.

Are there predictable special causes? This pattern doesn’t “feel” random. In this case, we know the cause, but the timing still isn’t predictable.

Is there seasonality? Nothing obvious, and nothing statistically significant.

A statistical non-random-behavior analysis identified these unusual issues:

1. A spike of 1,650 on a single day, shown in blue
2. A run of zero-demand days from 1/4/2010 to about 5/30/2010.

We know what caused these, but – can we predict their timing and magnitude? If not, they affect safety stock, even though they aren’t technically “random.”

We can minimize safety stock if:
• We have enough demand visibility (backlog) to make or procure this item to order, or

• We can use extrinsic indicators – the historical data offers nothing meaningful – to forecast the timing and magnitude of seasonality, trend and spikes, or
• We can expedite frequently.

These are obvious solutions. If we could use them, we wouldn’t be discussing safety stock.

When these aren’t viable options, safety stock is an expedient choice. A Google search turns up this 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 = 26.62
Std dev of demand = 139.39
Avg lead time = 5 days
Std dev of lead time = 0.67 day
Target service level = 98% = 2.05 Z

Calculated safety stock = 641

NOTE:
EOQ = 553.
Managed using reorder point (ROP).
ROP = 774 = 26.62 avg demand * 5 day lead time + 641 calculated safety stock.
Theoretical average quantity on hand = 918 = 641 safety stock + (50% * 553 EOQ).

Is the calculated safety stock optimal? No. It’s much too high. The 641 safety-stock level alone supports all but a few daily demands, even before considering EOQ that’s on-hand.

To achieve its 98% service-level target reliably with minimal inventory and expediting, safety stock needs to be just 194, with an ROP of 327. As compared to the formula’s results, this reduces the theoretical average quantity on hand by more than one-third, from 918 to 604. With the greater-than-lead-time gaps of time in between this item’s highly-intermittent daily demands, both the reorder point (327) and the EOQ (553) are likely to be on-hand, making 880 available for the next demand day.

How did we arrive at optimal safety stock of 194? Not by an “eyeball” test of the time-series demand chart, but by using a correct, objective analysis that:

• Recognizes the non-normal, intermittent demand pattern, and
• 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, 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.