Answer: See explanation
Explanation:
a. The moving average is calculated as:
= sum demand for 2 yr/2
The moving average for next year will be:
= (3800+3700)/2
= 7500/2
= 3,750 Miles
(b) The mean absolute deviation(MAD)
= Sum(|Dt-Ft|)/n
Therefore, the moving average for Y3 will be:
= (3000+4000)/2
= 7000/2
= 3500
Moving Avge for Y4 F(4) will be:
= (4000+3400)/2
= 3700
Moving Avge for Y5 will be:
= (3400+3800)/2
= 7200/2
= 3600
Therefore, MAD will be:
= Sum (|3500-3400|+|3700-3800|+|3600-3700|)/3
(100+100+100)/3
= 300/3
= 100
(c) Weighted moving average = sum (weight in period n) × (demand in period n)/Sum weights
So Weighted moving average for Y6 will be:
= ((3800 × 0.4)+(3700 × 0.6))/(0.4+0.6)
=1520 + 2220
= 3,740
MEAN ABSOLUTE DEVIATION:
= Sum(|Dt-Ft|)/n
Weighted moving average for Y3:
= (3000 × 0.4c+ 4000 × 0.6)/(0.4+0.6)
= 3600
Weighted moving average for Y4:
= (4000 × 0.4 + 3400 × 0.6)/(0.4+0.6)
= 3640
Weighted moving average for Y5:
= (3400 × 0.4+3800 × 0.6)/(0.4+0.6)
= 3640
Therefore, MAD
= Sum(|3600-3400|+|3640-3800|+|3640-3700|)/3
MAD = (200+160+60)/3 = 140
(d)Expomentioal Smoothing F(t) will now be:
SO F(1) = 3000 + 0.5 × (3000-3000)
= 3000
F(2) = 3000 + 0.5 × (4000-3000)
= 3500
F(3) = 3500 + 0.5 × (3400-3500)
= 3450
F(4) = 3450 + 0.5 × (3800-3450)
= 3625
F(5) = 3625 + 0.5 × (3700-3625)
= 3663
Therefore, forecast will now be 3663 miles
