Weekly sales of the Weber Dicamatic food processor for the past
ten weeks have been:
Week |
Sales |
Week |
Sales |
1 |
980 |
6 |
990 |
2 |
1040 |
7 |
1030 |
3 |
1120 |
8 |
1260 |
4 |
1050 |
9 |
1240 |
5 |
960 |
10 |
1100 |
Determine, on the basis of minimizing the mean square error,
whether a three-period or four-period simple moving average model
gives a better forecast for this problem.
Answer:
Given that,
Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been:
Week |
Sales |
Week |
Sales |
1 |
980 |
6 |
990 |
2 |
1040 |
7 |
1030 |
3 |
1120 |
8 |
1260 |
4 |
1050 |
9 |
1240 |
5 |
960 |
10 |
1100 |
Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average model gives a better forecast for this problem.
Mean Square Error (MSE)=![]() |
|||||
Error | Error2 | ||||
Month | Demand | 3 Month MA | Absolute error | Square error | |
A | B | C=A-B | D=C2 | ||
1 | 980 | ||||
2 | 1040 | ||||
3 | 1120 | ||||
4 | 1050 | 1046.6667 | 3.3333 | 11.1111 | |
5 | 960 | 1070.0000 | -110.0000 | 12100.0000 | |
6 | 990 | 1043.33333 | -53.3333 | 2844.4444 | |
7 | 1030 | 1000.0000 | 30.0000 | 900.0000 | |
8 | 1260 | 993.3333 | 266.6667 | 21511.1111 | |
9 | 1240 | 1093.3333 | 146.6667 | 21511.1111 | |
10 | 1100 | 1176.6667 | -76.6667 | 5877.7778 | |
-160.0000 | 14955.5556 |
Eg Forecast Calculation | |||||
Month 4 | =(month 1+month 2 +month 3)/3 | ||||
=(980+1040+1120)/3 | |||||
=3140/3=1046.6667 | |||||
MSE=14955.5556/(7-1) | |||||
=2492.593 | |||||
Error | Error2 | ||||
Month | Demand | 4 Month MA | Absolute error | square error | |
A | B | C=A-B | D=C2 | ||
1 | 980 | ||||
2 | 1040 | ||||
3 | 1120 | ||||
4 | 1050 | ||||
5 | 960 | 1047.5000 | -87.5000 | 7656.2500 | |
6 | 990 | 1042.5000 | -52.5000 | 2756.2500 | |
7 | 1030 | 1030.0000 | 0.0000 | 0.0000 | |
8 | 1260 | 1007.5000 | 252.5000 | 63756.2500 | |
9 | 1240 | 1060.0000 | 180.0000 | 32400.0000 | |
10 | 1100 | 1130.0000 | -30.0000 | 900.0000 | |
-140.0000 | 10412.5000 | ||||
Eg Forecast Calculation | |||||
Month 5 | =(month 1+month 2+month 3+ month 4)/4 | ||||
=(980=1040+1120+1050)/4 | |||||
=4190/4=1047.50 | |||||
MSE=10412.50/(6-1) | |||||
=2082.50 | |||||
Four month moving average gives better forecast, | |||||
Forecast for period 11 | |||||
Using 3 month moving average | |||||
=(month 8+ month 9+ month 10)/3 | |||||
=(1260+1240+1100)/3 | |||||
=3600/3 | |||||
=1200 | |||||
Using 4 month moving average | |||||
=(month 7+month 8+month 9+month 10)/4 | |||||
=(1030+1260+1240+1100)/4 | |||||
=4630/4 | |||||
=1157.50 |
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