Question

Problem 3-22

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows:

Month	Sales	Forecast 1	Forecast 2
1	830	800	780
2	835	825	830
3	790	800	820
4	800	815	830
5	785	820	815
6	825	805	786
7	775	770	805
8	860	830	820
9	810	805	785
10	810	845	840

     

a. Compute the MSE and MAD for each forecast. (Round your answers to 2 decimal places.)

	MSE	MAD
Forecast 1
Forecast 2

   

b. Compute MAPE for each forecast. (Round your intermediate calculations to 5 decimal places and final answers to 4 decimal places.)

MAPE F1	%
MAPE F2	%

Answer 1

Step 1

Calculate Error or deviation of forecast from Actual

Error = Forecast - Actual

e,g for Forecasrt method 1

Error for Month 1 = 800-830 = -30

Step2 :

Calculate Square of Error and Absolute value of Error

Step3

MAD = sum of Absolute Error / Number of Month = Average of Absolute Error

MSE = Sum of Error Square / Number of month = Average of error square

Forecast 1

Month	Sales	Forecast 1	Error	Absolute Error	Square Error
1	830	800	-30	30	900
2	835	825	-10	10	100
3	790	800	10	10	100
4	800	815	15	15	225
5	785	820	35	35	1225
6	825	805	-20	20	400
7	775	770	-5	5	25
8	860	830	-30	30	900
9	810	805	-5	5	25
10	810	845	35	35	1225
Average				19.5	512.5

MAD = 19.5

MSE = 512.5

Forecast Method 2

Month	Sales	Forecast 2	Error	Absolute Error	Square Error
1	830	780	-50	50	2500
2	835	830	-5	5	25
3	790	820	30	30	900
4	800	830	30	30	900
5	785	815	30	30	900
6	825	786	-39	39	1521
7	775	805	30	30	900
8	860	820	-40	40	1600
9	810	785	-25	25	625
10	810	840	30	30	900
Average				30.9	1077.1

MAD = 30.9

MSE = 1077.1

	MSE	MAD
Forecast1	512.5	19.5
Forecast2	1077.1	30.9

b.

Calculate Absolute Error Percentage = Absolute Error / Actual Demand

E.g for Forecast method 1

for month 1

Absolute Error Percentage = 30/ 830 = 0.036145 = 3.6145 %

Calculate for all months

Mean Absolute Percentage Error, MAPE = Sum of absolute percentage error/ Number of months -= Average of absolute Percentage Error

Forecast 1

Month	Sales	Forecast 1	Error	Absolute Error	Absolute Percentage
1	830	800	-30	30	3.6145%
2	835	825	-10	10	1.1976%
3	790	800	10	10	1.2658%
4	800	815	15	15	1.8750%
5	785	820	35	35	4.4586%
6	825	805	-20	20	2.4242%
7	775	770	-5	5	0.6452%
8	860	830	-30	30	3.4884%
9	810	805	-5	5	0.6173%
10	810	845	35	35	4.3210%
Average					2.3908%

MAPE = 2.391%

Forecast 2

Month	Sales	Forecast 2	Error	Absolute Error	Absolute Percentage
1	830	780	-50	50	6.0241%
2	835	830	-5	5	0.5988%
3	790	820	30	30	3.7975%
4	800	830	30	30	3.7500%
5	785	815	30	30	3.8217%
6	825	786	-39	39	4.7273%
7	775	805	30	30	3.8710%
8	860	820	-40	40	4.6512%
9	810	785	-25	25	3.0864%
10	810	840	30	30	3.7037%
Average					3.8032%

MAPE = 3.8032 %

	MAPE
Forecast1	2.3908%
Forecast2	3.8032%