# A correlation between Inventories & Forecasting?

Some say yes………. and some say no!

There are many things questionable about Statistics and Modeling and of course, the famous or infamous, Normal Distribution.  Those who question the value of forecasting invariably point out that it is gravely inaccurate (and unfortunate) to assume that your demand is normally distributed.

Is Normal the tendency to be perfectly normal?  Or should we accept approximate normals and just only look for those that are perfectly Non-Normal?  Either your glass is half-empty or half-full!

So that we can come to meaningful conclusions, I am going to assume life is generally normal.

## The classic formula for Safety Stock states thus:

Safety Stock = Service Level Constant * SQRT (Lead Time) * Root Mean Squared Error of (Demand vs. Actual),

assuming you are using a Demand Forecast to produce and stock inventories.  There is a lot of debate as to what to use as the Demand Forecast Error.  Debates range from dismissing the Fitted Forecast Error (in-sample forecast error) to the question of whether we can even establish an Expected Forecast Error.

In any case, using the standard deviation of actual historical demand will over-state the Safety Stock in a majority of cases.

In the current state, you may be carrying inventory to compensate for poor demand visibility besides what you need for demand over lead time.  There is a portion of inventory you are carrying for safety stock.

Any improvements in Forecast quality can be related to improvement in Safety stock levels, if we hold other things constant.

For simplicity's sake, let us assume that your committed service level is 98% and your lead time is 2 months.  Then the above formula reduces to the following:

Safety Stock = 2.05  {Service} * Sqrt (2) {Lead time} * Expected Demand Forecast Error

Safety stock = 2.05 * 1.414 * EDFE (expected demand forecast error)

Safety stock = 2.90 * EDFE

In simplistic terms, the above means for every unit reduction in Error (Note Units not %), Safety stock will decrease by 2.9 units other things remain constant.

If we can assume what our current level of forecast error is and what our expected forecast error or target improvement is, we can establish a precise benefit in the form of safety stock reduction.  This assumes there is no forecast bias.  If there is a forecast bias (generally there is in organizations new to Demand Planning & S&OP), then there is another sizable reduction possible through the amount of inventory carried over lead time by reducing the bias.

Getting back to the no-bias assumption, what does it mean for a percentage point improvement in WMAPE?  What is the percent improvement in safety stock for every point reduction in WMAPE?

This entirely depends on your current level of forecast quality is.  If your current WMAPE is 50%, then every % point improvement in MAPE will result in a 2% reduction in Safety Stock.  Please see the chart that shows the reduction in safety stock for every point reduction in MAPE at different Starting points.

If your current WMAPE is 60%, then every % point improvement will result in a 2.5% improvement in safety Stock.

At higher levels of Forecast quality, it is difficult to make further climbs in forecast accuracy.  So any marginal improvement in Forecast quality with a higher starting point will result in more than proportionate benefits in inventory reduction.

There are other routes to go as well:

1.  Lead time Reduction – Reducing the lead time will result in Safety Stock as well but not as much compared to the reduction in Forecast Error.

2.  Variability in Lead time – If our supply is quite variable this has a much larger impact on Safety Stock.  This is not in the classic formula but the extended formula uses variability in lead time.

In practice, I have seen this being misused and abused with very poor proxies for variability in lead time.  In an uncertain world of demand, it is important to have better control over our own supply and schedule adherence.