Question

The following table contains the demand from the last 10 months:

MONTH	ACTUAL DEMAND
1	33
2	29
3	32
4	33
5	35
6	32
7	35
8	42
9	44
10	45

a. Calculate the single exponential smoothing forecast for these data using an α of 0.10 and an initial forecast (F₁) of 33. (Round your answers to 2 decimal places.)

b. Calculate the exponential smoothing with trend forecast for these data using an α of 0.10, a δ of 0.20, an initial trend forecast (T₁) of 1.00, and an initial exponentially smoothed forecast (F₁) of 32. (Round your answers to 2 decimal places.)

c-1. Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round your answers to 2 decimal places.)

c-2. Which is best?

• Exponential smoothing with trend forecast

• Single exponential smoothing forecast

Answer 1

(a)

Forecast
33
33
32.6
32.54
32.59
32.83
32.74
32.97
33.87
34.89

(b)

Smoothed Forecast, Ft
33
33.9
33.41
33.27
33.24
33.42
33.28
33.45
34.30
35.27

(c-1)

3.98

MAD

3.95

MAD

(c-2) Exponential smoothing with trend forecast

Alpha	0.1
Data			Forecasts and Error Analysis
Period	Demand		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	33		33	0	0	0	00.00%
Period 2	29		33	-4	4	16	13.79%
Period 3	32		32.6	-0.6	0.6	0.36	01.88%
Period 4	33		32.54	0.46	0.46	0.2116	01.39%
Period 5	35		32.59	2.414	2.414	5.827396	06.90%
Period 6	32		32.83	-0.8274	0.8274	0.684591	02.59%
Period 7	35		32.74	2.25534	2.25534	5.086559	06.44%
Period 8	42		32.97	9.029806	9.029806	81.5374	21.50%
Period 9	44		33.87	10.12683	10.12683	102.5526	23.02%
Period 10	45		34.89	10.11414	10.11414	102.2959	0.2247587
			Total	28.97271	39.82751	314.556	99.98%
			Average	2.897271	3.98	31.4556	10.00%
				Bias	MAD	MSE	MAPE
					SE	6.270526
Next period	35.8972714

Alpha	0.1
Beta	0.2
Data			Forecasts and Error Analysis
Period	Demand		Smoothed Forecast, Ft	Smoothed Trend, Tt	Forecast Including Trend, FITt	Error	Absolute	Squared	Abs Pct Err
Period 1	33		33	1	34	0	0	0	00.00%
Period 2	29		33.9	0.98	34.88	-4.9	4.9	24.01	16.90%
Period 3	32		33.41			-1.41	1.41	1.9881	04.41%
Period 4	33		33.27			-0.269	0.269	0.072361	00.82%
Period 5	35		33.24			1.7579	1.7579	3.090212	05.02%
Period 6	32		33.42			-1.41789	1.41789	2.010412	04.43%
Period 7	35		33.28			1.723899	1.723899	2.971828	04.93%
Period 8	42		33.45			8.551509	8.551509	73.12831	20.36%
Period 9	44		34.30			9.696358	9.696358	94.01936	22.04%
Period 10	45		35.27			9.726722	9.726722	94.60913	0.216149
			Total			23.4595	39.45328	295.8997	100.51%
			Average			2.34595	3.95	29.58997	10.05%
						Bias	MAD	MSE	MAPE
							SE	6.081732