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A local restaurant has recorded the demand for bottled water in each of the last 15 months of business
A local restaurant has recorded the demand for bottled water in each of the last 15 months of business. Use the recorded demand data below to develop three-period and four-period moving-average forecasts for bottles of water.
| Period | Demand | Period | Demand | Period | Demand |
| 1 | 925 | 6 | 890 | 11 | 870 |
| 2 | 910 | 7 | 960 | 12 | 860 |
| 3 | 905 | 8 | 895 | 13 | 900 |
| 4 | 850 | 9 | 910 | 14 | 920 |
| 5 | 860 | 10 | 905 | 15 | 950 |
(Weights are t = 0.3, t-1 = 0.2, t-2 = 0.3 and t-3 = 0.2)
What is the MAPE for the three-period weighted moving average forecast as of period 15?
Expert Solution
| Period | Demand | Forecast-three period moving average | Absolute percentage error | Forecast-four period moving average |
|---|---|---|---|---|
| 1 | 925 | |||
| 2 | 910 | |||
| 3 | 905 | |||
| 4 | 850 | 917 | 7.88 | |
| 5 | 860 | 902 | 4.88 | 901 |
| 6 | 890 | 878.5 | 1.29 | 881 |
| 7 | 960 | 858 | 10.63 | 877.5 |
| 8 | 895 | 882 | 1.45 | 886 |
| 9 | 910 | 918.5 | 0.93 | 903 |
| 10 | 905 | 929 | 2.65 | 909.5 |
| 11 | 870 | 902 | 3.68 | 921 |
| 12 | 860 | 904 | 5.12 | 896 |
| 13 | 900 | 886.5 | 1.50 | 887 |
| 14 | 920 | 869 | 5.54 | 883.5 |
| 15 | 950 | 882 | 7.16 | 887 |
| 52.72 |
Three period moving average:
Ft =(0.5 × Dt − 1) + (0.4 × Dt − 2) + (0.1 × Dt − 3)Ft =(0.5 × Dt − 1) + (0.4 × Dt − 2) + (0.1 × Dt − 3)
Mean absolute percentage error = Sum of absolute percentage errors12Mean absolute percentage error = 52.7212Mean absolute percentage error = 4.393%Mean absolute percentage error = Sum of absolute percentage errors12Mean absolute percentage error = 52.7212Mean absolute percentage error = 4.393%
Four period moving average:
Ft = (0.3 × Dt − 1) + (0.2 × Dt − 2) + (0.3 × Dt − 3) + (0.2 × Dt − 4)
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