Problem 3-22 Two independent methods of forecasting based on judgment and experi

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:

     

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

   

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

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

Explanation / Answer

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

MAD = 19.5

MSE = 512.5

Forecast Method 2

MAD = 30.9

MSE = 1077.1

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

MAPE = 2.391%

Forecast 2

MAPE = 3.8032 %

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

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