Difference between forecasting accuracy and forecasting error?

Question

I am working on a demand forecasting project and I am puzzled by the client's standards of forecast evaluation. The MAPE (Mean Absolute Percentage Error) with the sample data Forecast = 300 and Demand = 100 is $$ \text{MAPE} =\frac{|300-100|}{100} =2 $$

However the client focuses on forecasting accuracy. It is defined as $$ \text{Accuracy}=\max(0,1-\text{MAPE}) $$

This means that a MAPE of 1, 3 or 3000 gives the same forecasting accuracy of 0. To me this does not make sense, because it is equivalent to restricting MAPE to $\text{MAPE}_r = \max(1,\text{MAPE})$.

However, it seems to be in line with the measurement of forecasts in the demand planning ecosystem http://demandplanning.net/MAPE.htm. Can someone please explain to me why this could be useful?

EDIT: I understand that someone can define anything. My only question is whether the definition makes sense for the demand planning / management purpose.

Referring to the text in the link, restricting any error metric does not make sense to me especially(!) in demand planning. If the true demand is 1 unit but I forecasted 300, then 300 times more raw materials or human resources were planned for this product in this period. This overestimation must cause substantially higher cost than a forecast of 2 units, although both forecasts would result in a forecasting accuracy of 0. This is implied by MAPE but not by accuracy.

So why should forecasting accuracy defined as above be relevant at all? Why do I need it when MAPE is there already? What value does it add? To me it seems to introduce bias - if anything at all.

Answer 1

I love your quote:

He was told to evaluate the whole supply chain demand with this metric but cannot explain why.

You are completely correct that truncating "accuracy" makes no sense. It throws information away for no good reason. Much better to either accept negative "accuracy", or deal with the MAPE directly, and accept that MAPEs greater than 100% occur.

The only rationale for truncation is that there is no good interpretation of negative "accuracy". But that is a result of trying to work with "accuracy" and defining it as 1-error - where the error can be unbounded.

The following threads may be helpful:

• What are the shortcomings of the Mean Absolute Percentage Error (MAPE)?
• Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)?

Answer 2

Actually, this is described in the link you provided:

Error above 100% implies a zero forecast accuracy or a very inaccurate forecast. [...]

What is the impact of Large Forecast Errors?

Is Negative accuracy meaningful? Regardless of huge errors, and errors much higher than 100% of the Actuals or Forecast, we interpret accuracy a number between 0% and 100%. Either a forecast is perfect or relative accurate or inaccurate or just plain incorrect. So we constrain Accuracy to be between 0 and 100%.

Negative accuracy does not make any sense. This measure simply assumes that if something has bigger errors then the predicted value itself, then no matter how much bigger they are, they are equally bad. If you'd take a loan and then to repay it you'd have to make monthly payments that are greater then your salary, then it really does not matter how much greater they are, since you can't afford to pay them.

Answer 3

As a result, in the business model, the accuracy of the forecast is what leads to profit, otherwise it is considered a loss, So the range of accuracy is debatable in terms of demand planning to achieve planned profitability.