Question

A company had developed a forecast using the Delphi method for January through June.  

Month	Demand	Forecast
January	225	240
February	240	230
March	230	235
April	225	230
May	229	225
June	260	230

Using the data provided what is the Mean Absolute Deviation for the forecast method?

3.17

-3.17

11.5

69

Using the data provided, what is the Mean Squared Error?

215.17

20.5%

9.4%

12%

Using the data provided what is the MAPD?

5.7%

2.1%

4.9%

3.6%

Answer 1

Solution:

Given:

A company had developed a forecast using the Delphi method for January through June.  

Month	Demand	Forecast
January	225	240
February	240	230
March	230	235
April	225	230
May	229	225
June	260	230

Part a) We have to find the Mean Absolute Deviation for the forecast method

Thus we need to make following table:

Dt	Ft	| Dt - Ft |
225	240	15
240	230	10
230	235	5
225	230	5
229	225	4
260	230	30
		$\sum \left | D_{t}-F_{t} \right | = 69$

Thus

$MAD = \frac{\sum \left | D_{t}-F_{t} \right |}{n}$

$MAD = \frac{69}{6}$

Part b) Find the Mean Squared Error

$MSE = \frac{\sum \left ( D_{t}-F_{t} \right )^{2}}{n}$

Thus we need to maje following table:

Dt	Ft	Dt - Ft	(Dt - Ft )^2
225	240	-15	225
240	230	10	100
230	235	-5	25
225	230	-5	25
229	225	4	16
260	230	30	900
			$\sum \left ( D_{t}-F_{t} \right )^{2}= 1291$

$MSE = \frac{\sum \left ( D_{t}-F_{t} \right )^{2}}{n}$

$MSE = \frac{1291 }{6}$

Part c) Find the MAPD

$MAPD = \frac{\sum \left | D_{t}-F_{t} \right |}{\sum D_{t}}$

Thus

Dt	Ft	| Dt - Ft |
225	240	15
240	230	10
230	235	5
225	230	5
229	225	4
260	230	30
$\sum D_{t}=1409$		$\sum | D_{t} - F_{t}|=69$

Thus

$MAPD = \frac{\sum \left | D_{t}-F_{t} \right |}{\sum D_{t}}$

$MAPD = \frac{69}{1409}$