## Expert Answer

Please see relevant data on three period moving average , 4 period moving average and MAPE for 3 period moving average as presented in below table :

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 |

SUM = | 52.72 |

Please make note of following :

a) Three period moving average :

i) Ft = 0.5x Dt-1 + 0.4 x Dt-2 + 0.1 x Dt-3

Where ,

Ft = Forecast for period t

Dt-1 = Actual demand during period t-1

Dt-2 = Actual demand during period t-2

Dt-3 = Actual demand during period t-3

ii) Absolute percentage error for period t

= Absolute Difference ( Ft – Dt)/ Dt x 100

Sum of Absolute percentage errors ( from period 4 through period 15) = 52.72

Thus ,

MAPE ( Mean Absolute Percentage error )

= Sum of absolute percentage errors / 12 ( i.e number of data)

= 52.72 / 12

= 4.393 %

MAPE FOR THREE PERIOD WEIGHTED MOVING AVERAGE = 4.393 % |

B ) Four period moving average :

Ft = 0.3x Dt-1 + 0.2 x Dt-2 + 0.3 x Dt-3 + 0.2 x Dt-4

Where ,

Ft = Forecast for period t

Dt-1 = Actual demand during period t-1

Dt-2 = Actual demand during period t-2

Dt-3 = actual demand during period t-3

Dt-4 = Actual demand during period t-4