Question

In: Statistics and Probability

Use an exponential smoothing method with a starting forecast of 21 for month 1 and a...

Use an exponential smoothing method with a starting forecast of 21 for month 1 and a smoothing constant α = 0.5 to calculate month-in-advance forecasts for months 4–12 and forecast for the ﬁrst month of next year. Calculate the MAD.

Expert Solution

ANSWER::

a).

FORECAST = FORECAST + (ALPHA * (ACTUAL DEMAND - FORECAST))

FORECAST 2 = 21 + (0.5 * (23 - 21) = 22

FORECAST 3 = 22 + (0.5 * (26 - 22) = 24

FORECAST 4 = 24 + (0.5 * (24 - 24) = 24

FORECAST 5 = 24 + (0.5 * (28 - 24) = 26

FORECAST 6 = 26 + (0.5 * (24 - 26) = 25

FORECAST 7 = 25 + (0.5 * (30 - 25) = 27.5

FORECAST 8 = 27.5 + (0.5 * (24 - 27.5) = 25.75

FORECAST 9 = 25.75 + (0.5 * (20 - 25.75) = 22.88

FORECAST 10 = 22.88 + (0.5 * (31 - 22.88) = 26.94

FORECAST 11 = 26.94 + (0.5 * (22 - 26.94) = 24.47

FORECAST 12 = 24.47 + (0.5 * (27 - 24.47) = 25.74

FORECAST 13 = 25.74 + (0.5 * (31 - 25.74) = 28.37

FORECAST ERROR

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	ABS DEVIATION
1	23	21	2	2
2	26	22	4	4
3	24	24	0	0
4	28	24	4	4
5	24	26	-2	2
6	30	25	5	5
7	24	27.5	-3.5	3.5
8	20	25.75	-5.75	5.75
9	31	22.88	8.12	8.12
10	22	26.94	-4.94	4.94
11	27	24.47	2.53	2.53
12	31	25.74	5.26	5.26
SIGMA			14.72	47.1

MAD = SIGMA(ABSOLUTE DEVIATION) / N, WHERE N = 12

MAD = 47.1 / 12

MAD = 3.93

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orchestra answered 1 year ago

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