More accurate demand forecasts generate savings as far inventory is concerned. This article quantifies savings for

For inventories with higher turnover, we suggest to use our alternative savings formula where the extra accuracy is invested in lowering stockout rates while keeping the inventory levels unchanged.

- $V$ the total inventory value.
- $H$ the yearly carrying cost (percentage), which represents the sum of all the frictions associated to the inventory.
- $\sigma$ the forecast error of the system in place expressed in
**unit MAE**(mean absolute error). The definition of this measure is given below. - $\sigma_n$ the forecast error of the new system being benchmarked (hopefully lower than $\sigma$).

The yearly benefit $B$ of revising the forecasts is given by: $$B=V H \left(\sigma - \sigma_n \right)$$

Although the MAPE (Mean Absolute Percentage Error) measured over the lead time would fit this definition, we strongly

In order to compute the

- $y_i$ the actual demand for the item $i$, for the lead time duration.
- $\hat{y}_i$ the demand forecast for the item $i$, for the lead time duration.

For the consistency of the measurement, we assume that the same starting date $t$ is used for all items. Then, for a set of items $i$, the unit MAE could be written as: $$\sigma = \frac{\sum_i |y_i - \hat{y}_i|}{\sum_i y_i}$$ This value is

- $V = 100,000,000$ € (100 millions Euros)
- $H = 0.2$ (20% yearly friction cost on inventory)
- $\sigma=0.2$ (old system has 20% error)
- $\sigma_n=0.16$ (new system has 16% error)

Based on the formula above, we obtain a gain at $B=800,000$€ per year.

- increasing the error of all underforecasts of $\sigma - \sigma_n$ percents.
- lowering the average error of overforecasts (however the quantification is unclear).

Dismissing the improvement brought by the bias on overforecasts, we see that, in the worst case, the accuracy of the new - and now biased - forecasting system is degraded of $\sigma - \sigma_n$ percents, which turns into an overall accuracy that remains lower or equal to $\sigma$.

Then, we note that the total amount of inventory $V$ is

By lowering the forecasts of $\sigma - \sigma_n$ percents, we are thus applying a similar reduction on the amount of inventory $V$. Then, since accuracy of the biased system remains lower to $\sigma$, the stockouts frequency should also stay lower than the one of the old system.

Finally, we have shown that based on a more accurate forecast, it is possible to build a lower inventory level of $\sigma - \sigma_n$ percents that does generate more stockouts - because forecasts remain better or equal (accuracy wise) to the ones of the old system.

Thus, the inventory reduction is $V \left(\sigma - \sigma_n \right)$. Considering the total yearly friction costs $H$, this reduction generates savings equal to $B=V H \left(\sigma - \sigma_n \right)$.

It's easy to turn cash into inventory, the challenge is to turn inventory back into cash.

Taking into account only the strict financial cost is vastly underestimating the real cost of inventory:
- The storage itself typically add an overhead of 2% to 5% on a yearly basis.
- Obsolescence costs account for 10% to 20% on a yearly basis for nearly all kind of manufactured products.

Thus a 20% yearly overhead is typically a rather sensible friction percentage for most finished products inventory.