More accurate demand forecasts are obviously good as far as inventory optimization is concerned. However, the

The viewpoint adopted in this article is a best fit for *high turnover* inventories, with turnovers above 15. For high turnover values, the dominant effect is not so much stockouts, but rather the sheer amount of inventory, and its reduction through better forecasts. If such is not your case, you can check out our alternative formula for low turnover.

- $D$ the turnover (total annual sales).
- $m$ the gross margin.
- $\alpha$ the
*cost of stockout to gross margin*ratio. - $p$ the service level achieved with the current error level (and current stock level).
- $\sigma$ the forecast error of the system in place, expressed in MAPE (mean absolute percentage error).
- $\sigma_n$ the forecast error of the new system being benchmarked (hopefully lower than $\sigma$).

The yearly benefit $B$ of revising the forecasts is given by: $$B = D (1 - p) m \alpha \frac{\sigma - \sigma_n}{\sigma}$$

It is possible to replace the MAPE error measurements by MAE (mean absolute error) measures within the formula. This replacement is actually strongly advised if slow movers exist in your inventory.

- $D=1,000,000,000€$ (1 billion Euros)
- $m=0.2$ (i.e.gross margin of 20%)
- $p=0.97$ (i.e. service level of 97%)
- $\alpha=3$ (stockouts cost 3x the gross margin loss)
- $\sigma=0.2$ (MAPE of 20%)
- $\sigma_n=0.18$ (MAPE of 18% - relatively 10% lower than the previous error)

Based on the formula above, we obtain a gain at $B=1,800,000€$ per year. If we assume that the overall profitability of the retailer is 5%, then we see that a 10% improvement in forecasting accuracy already contribute to 4% of the overall profitability.

Let's assume, for now, that, for a given stock level,

The total volume of sales lost through stockouts is simple to estimate: it's $D(1-p)$, at least for any reasonably high value of $p$. In practice, this estimation is very good if $p$ is greater than 90%.

Hence, the total volume of margin lost through stock-outs is $D(1-p)m$.

Then, in order to model the

Based the assumption (demonstrated below) that stockouts are proportional to the error, we need to apply the factor $(\sigma - \sigma_n) / \sigma$ as the

Hence, in the end, we obtain: $$B = D (1 - p) m \alpha \frac{\sigma - \sigma_n}{\sigma}$$

In order to do that, let's start with service levels at 50% ($p=0.5$). In this context, the safety stock formula indicates that

With zero safety stocks, it becomes easier to evaluate the loss caused by forecast errors. When the demand is greater than the forecast (which happens here 50% of the time by definition of $p=0.5$), then the average percentage of sales lost is $\sigma$. Again, this is only the consequence of $\sigma$ being the

Thus, we see that with $p=0.5$, stockouts are indeed proportional to the error. The reduction of the stockouts when replacing the old forecast with the new one will be $\sigma_n / \sigma$.

Now, what about $p \not= 0.5$? By choosing a service level distinct from 50%, we are transforming the

However, since we can assume here that the two mean forecasts (the old one, and the new one) will be extrapolated as quantile (to compute the reorder point), though the same formula, the

However, the cost for a stockout is typically greater than that the gross margin. Indeed, a stockout causes:

- a loss of client loyaulty.
- a loss of supplier trust.
- more erratic stock movements, stressing supply chain capacities (storage, transport, ...).
- overhead efforts for downstream teams who try to mitigate stockouts one way or another.
- ...

Among several large food retail networks, we have observed that, as a

Looking at the safety stock formula, one might be tempted to think that the impact of a reduced forecasting error will be limited to lowering the safety stock; all other variables remaining unchanged (stockouts in particular).

Classical safety stock analysis splits inventory in two components:

- the primary stock, equal to the lead demand, that is to say the average
**forecast demand**multiplied by the lead time. - the safety stock, equal to the
**demand error**multiplied by a safety coefficient that depends mostly of $p$, the service level.

Let's go back to the situation where the service level equals 50%. In this situation, safety stocks are at zero (as seen before). If the forecast error was only impacting the

Despite being incorrect, the

In practice, we observe that the uncertainty related to the lead time is typically small compared to the uncertainty related to the demand. Hence, neglecting the impact of varying lead time is reasonable as long as forecasts remain somewhat inaccurate (say for MAPEs higher than 10%).