Question

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

MONTH	ACTUAL DEMAND
1	34
2	37
3	38
4	37
5	40
6	37
7	42
8	44
9	41
10	42

a. Calculate the single exponential smoothing forecast for these data using an ? of 0.20 and an initial forecast (F₁) of 34. (Round your intermediate calculations and answers to 2 decimal places.)

Month	Exponential Smoothing
1
2
3
4
5
6
7
8
9
10

b. Calculate the exponential smoothing with trend forecast for these data using an ? of 0.20, a ? of 0.30, an initial trend forecast (T₁) of 1.00, and an initial exponentially smoothed forecast (F₁) of 33. (Round your intermediate calculations and answers to 2 decimal places.)

Month	FITt
1
2
3
4
5
6
7
8
9
10

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

	MAD
Single exponential smoothing forecast?
Exponential smoothing with trend forecast?

c-2. Which is best?

	Single exponential smoothing forecast
	Exponential smoothing with trend forecast

Answer 1

a.

Exponential smoothing (with a smoothing constant, ? = 0.2)
Month (t)	Demand (actual, A)	Forecast: Ft= F(t-1)+ ? {A(t-1) - F(t-1)}
1	34	34.00
2	37	34.00
3	38	34.60
4	37	35.28
5	40	35.62
6	37	36.50
7	42	36.60
8	44	37.68
9	41	38.94
10	42	39.35

b.

?	0.2
?	0.3
Initial trend adjustment T(1)	1
Initial exponentially smoothed Forecast F (1)	33
Month (t)	Demand (actual, A)	Forecast Ft = FIT(t-1)+ ? [A(t-1) - FIT(t-1)]	Trend T(t)= T(t-1)+? [Ft - FIT (t-1)]	Forecast including trend FIT(t)= Ft +Tt
1	34	33.00	1	34.00
2	37	34.00	1.00	35.00
3	38	35.40	1.12	36.52
4	37	36.82	1.21	38.02
5	40	37.82	1.15	38.97
6	37	39.17	1.21	40.38
7	42	39.71	1.01	40.71
8	44	40.97	1.08	42.05
9	41	42.44	1.20	43.64
10	42	43.11	1.04	44.16

c-1. the mean absolute deviation (MAD) for the last nine months of forecasts

Single exponential smoothing forecast

Demand	Forecast	Deviation (demand -forecast)	Absolute deviation (data without negative sign)
34
37	34.00	3.00	3.00
38	34.60	3.40	3.40
37	35.28	1.72	1.72
40	35.62	4.38	4.38
37	36.50	0.50	0.50
42	36.60	5.40	5.40
44	37.68	6.32	6.32
41	38.94	2.06	2.06
42	39.35	2.65	2.65
			3.27
			Mean Absolute Deviation (MAD)

Exponential smoothing with trend forecast

Demand	Forecast	Deviation (demand -forecast)	Absolute deviation (data without negative sign)
34
37	35.00	2.00	2.00
38	36.52	1.48	1.48
37	38.02	-1.02	1.02
40	38.97	1.03	1.03
37	40.38	-3.38	3.38
42	40.71	1.29	1.29
44	42.05	1.95	1.95
41	43.64	-2.64	2.64
42	44.16	-2.16	2.16
			1.88
			Mean Absolute Deviation (MAD)

	MAD
Single exponential smoothing forecast?	3.27
Exponential smoothing with trend forecast?	1.88

C-2.  Exponential smoothing with trend forecast is best estimate as the mean absolute deviation (MAD) is lower for this.