Solved: Week 1 2 3 4 5 6 Sales ($) 16 18 14 10 20 22

1) Using a moving average method with AP=2 is called two period moving average.A two period moving average method averages the actual values of the previous two periods to generate the forecast for the next period.This can be calculated using the formula: Sum of the actual values for previous two periods / 2

Using the above formula the forecast for week 4 through 6 is calculated below:

• Forecast for week 4 = (18 + 14) / 2 = 32/2 = 16
• Forecast for week 5 = (14 + 10) / 2 = 24/2 = 12
• Forecast for week 6 = (10 + 20) / 2 = 30/2 =15

2)Forecast for a period using three period weighted moving average is caculated as : the sum of the products of the actual values and their respective weight for the previous three periods

Using the above formula the forecast for week 4 through 6, using weights of 0.5 (most recent); 0.4 and 0.1 (oldest) is calculated below:

• Forecast for week 4 = (16×0.1) + (18×0.4) + (14×0.5) = 1.6 + 7.2 + 7 = 15.8
• Forecast for week 5 = (18×0.1) + (14×0.4) + (10×0.5) = 1.8 + 5.6 + 5 = 12.4
• Forecast for week 6 = (14×0.1) + (10×0.4) + (20×0.5) = 1.4 + 4 + 10 = 15.4

3) To calculate Mean absolute deviation we have to calculate the deviation and absolute deviations for all,the periods

Deviation = Actual value – forecast value

Absolute deviation = Absolute value of deviation

MAD = Sum of the absolute deviation for all the periods / number of periods

Using the above formula the deviation, absolute deviation and MAD for each of the method is calculated below;

Calculation of MAD for moving average method

• For week 4, Deviation = 10-16 = -6

Absolute deviation = 6

• For week 5, Deviation = 20 – 12 = 8

Absolute deviation = 8

• For week 6, Deviation = 22 – 15 = 7

Absolute deviation = 7

MAD = (6 + 8 +7) / 3 = 21/3 = 7

Calculation of MAD for weighted average method

• For week 4, Deviation = 10-15.8 = -5.8

Absolute deviation = 5.8

• For week 5, Deviation = 20 – 12.4 = 7.6

Absolute deviation = 7.6

• For week 6, Deviation = 22 – 15.4 = 6.6

Absolute deviation = 6.6

MAD = (5.8 + 7.6 +6.6) / 3 = 20/3 = 6.67

Using the MAD for comparison ,the better forecasting method is the weighted average method as it has a lower MAD than the moving average method