Question

Problem 3-7

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

MONTH	ACTUAL DEMAND
1	33
2	36
3	37
4	38
5	42
6	38
7	41
8	43
9	40
10	41

a. Calculate the single exponential smoothing forecast for these data using an α of 0.20 and an initial forecast (F₁) of 33. (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 α of 0.20, a δ of 0.20, an initial trend forecast (T₁) of 1.00, and an initial exponentially smoothed forecast (F₁) of 32. (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?

	Exponential smoothing with trend forecast
	Single exponential smoothing forecast

References

Worksheet

Answer 1

Solution a): Calculate the single exponential smoothing forecast

The formula for Exponential Smoothing is=Ft=Ft−1+α(At−1−Ft−1)
As per the problem a):α=0.20and F1=33 Ft=33+0.20*(33-33)=33

Month	Actual Demand		Exponentially Smoothed Forecast and alpha=0.20
1	33		33
2	36		33
3	37		33.6
4	38		34.28
5	42		35.02
6	38		36.42
7	41		36.74
8	43		37.59
9	40		38.67
10	41		38.94

b) The formula for exponential smoothing using trend forecasting is= AF= At+Ft; Ft=Ft−1+α(At−1−Ft−1) and Tt=Tt-1+β(Ft−Ft−1). AFt = Adjusted Forecast for period t, Ft = Forecast for period t, Ft−1 = Forecast for period (t-1), At−1 = Actual for period (t-1), Tt = Trend for period T, Tt−1 = Trend for period (t-1), α = Apha = Exponential smoothing forecast=0.20 β = Beta = Exponential smoothing trend = 0.20 .

α=0.20 and β=0.20

Ft=F2=33+0.2*(33-33)=33 and Tt=T2=1+0.2*(33-33)= 1; FIT2=33+1.0=34

Month	Actual Demand	Exponentially Smoothed Forecast and alpha=0.20	MAD	Forcast (Ft)	Trend (Tt)	FITt	MAD
1	33	33		32	1	33
2	36	33	3	33	1	34	2.00
3	37	33.6	3.4	34.40	1.08	35.48	1.52
4	38	34.28	3.72	35.78	1.14	36.92	1.08
5	42	35.02	6.98	37.14	1.18	38.32	3.68
6	38	36.42	1.58	39.06	1.33	40.39	2.39
7	41	36.74	4.26	39.91	1.24	41.15	0.15
8	43	37.59	5.41	41.12	1.23	42.35	0.65
9	40	38.67	1.33	42.48	1.26	43.73	3.73
10	41	38.94	2.06	42.99	1.11	44.09	3.09
			3.53				2.03

c1)The mean absolute deviation (MAD) for the last nine months of forecasts

a)Single exponential smoothing forecast=3.53

b) Exponential smoothing with trend forecast=2.03

c2)Based on a mean absolute deviation criterion, Exponential smoothing with trend forecast=2.03 is best with over the exponential smoothing with α=0.20.