MAD Vs MAPE

[Former Member]

Can anyone please tell me What are the fundamental differences between applications of MAD versus MAPE, I am not asking the difference in these two in terms of thier formula, but what are the business or a statistical reasons behind using one over other ? I have a feeling that one of factors that could affect this decision depends on the level we are forecasting? Like MAPE being a better choice for Product groups /family or any aggregate level forecsating and MAD being suitable for product level forecasting ?

Please let me know if my knowledge of this is not correct or if there is more to just this.

[Former Member]

Hello,

I guess you are refering to Mean Absolute Deviation, not Median Absolute Deviation. However, it is true that when demand is sporadic or you have a small sample, fluctuations will have more impact on means than on medians and there are alternatives to standard MADs and MAPEs that use medians.

To contribute to the differences between MAD an MAPE: you can easily compare the MAPE's of different products (because they are dimensionless quantities) and not their MAD's because they have dimensions: if Prod1 has average sales of 100 and Prod2 has average sales of 500, if both have MAPE=5%, Prod2 will have a MAD value 5 times bigger than Prod1...

[Former Member]

Hi Tej,

Sorry that was a mistake about median absolute deviation, thanks Pablo for pointing it out.

But as median absolute deviation <= mean absolute deviation for any Gaussian distribution, the explanation will hold good.

regards,

biplab

[Former Member]

biplab, Thanks for the info. Dont feel sorry, in fact , it was good to know about Median Absolute Deviation.

Pablo, Thanks for your explanation with example.

Tej

[Former Member]

Hi Tej,

MAD is used for low volume / sporadic demand pattern, whereas MAPE is for high voulme / fairly consistent and regular demand pattern. Also, if you are doing lifecycle planning, you can model a shift from MAD to MAPE in growth phase and back to MAD in declining phase.

regards,

biplab

[Former Member]

Hello biplab,

Thanks for your response. This helped clarify some of my confusion. Additionally,though I am aware of the formula used in each case, If you know where I can find a more mathematical reason/justification or a statisitcal reason of the effects of using MAPE for high volume items and more stable demand and MAD for low volume/sporadic items, that would be great.

Your input on Lifecycle planning was informative, so the assumption here was that during growth the demand is more volume and steady growth and during declining phase, due to less volume, we could shift to MAD right?

Thanks

Tej

[Former Member]

Hi Tej,

You can check out the mathematical reasoning for using MAD and MAPE. Hope the below wikipedia links help.

http://en.wikipedia.org/wiki/Median_absolute_deviation

http://en.wikipedia.org/wiki/MAPE

regards,

biplab