How much do you get for 1% extra accuracy?

One of the problems that comes with being specialists of a subject is that you tend to take for granted what is obscure for anyone but your peers. At Lokad, despite our best efforts, we are no exception, especially when it comes to forecasting...

Recently, we realized that we had never provided any in-depth quantitative assessment of the financial gains generated by an increase of the forecasting accuracy, which is about the raison d'être for the company. Furthermore, after investigating the web, we realized that other forecasting vendors (competitors) were rather fuzzy too about the financial rewards that could be achieved through better forecasts.

However, it's not that complicated. With the following variables:

• $D$ 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 going for the new forecasting system is given by:

$$B = D (1 - p) m \alpha \frac{\sigma - \sigma_n}{\sigma}$$

For the proof of this result, check the full length article.