#### Response to MAPE and MPE Calculations - Mark Chockalingam

Thanks to Yingli for the question. Here are the equations that you originally sent through email. ? ==>  This calculates the average of the Percentages. ==>  This gives you the correct MAPE  weighted by volume. Averaging percentages can give you strange numbers.   This is not advised.  So equation 1 for MAPE is not the recommended solution, although many academics use this as a model diagnostic. Equation 2 gives you the correct MAPE as used by the Supply Chain practitioners.  This weights the MAPE by volume.   small numbers don't heavily influence this calculation.  So that was the easy part. MAPE can be defined as the volume weighted absolute error relative to the total actual demand.  In other words, this is the percent Mean absolute deviation or PMAD.  This can also be intuitively explained as the average absolute deviation relative to the average unit demand.  Please see a downloadable presentation at DemandPlanning.Net. Equation 3 and 4 describe a family of measures that are used to calculate forecast bias.  Forecast bias is just a component of total forecast error or MAPE.  The other component of MAPE is SKU Mix Error.  If you over-forecast all SKUs in your product portfolio, then your forecast bias will equal the MAPE. So let us examine 3 now.  I have defined this in my lectures and workshops as the classic measure of cross-sectional forecast bias. Equation 4 also measures forecast bias, but some what weakly.  We call equation 4 simply as MPE since it averages the percent errors and small volume SKUS may heavily influence the calculation. In essence, if you are measuring forecast performance across a portfolio of products, you would equation 2 for MAPE and equation 3 for Forecast Bias over the other two calculations. On the other hand, if you are measuring forecast error over time for the same sku, the other two equations 1 and 4 are also acceptable but 2 and 3 are much stronger calculations.