Question

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

MONTH	ACTUAL DEMAND
1	36
2	38
3	40
4	41
5	43
6	42
7	43
8	45
9	46
10	48

a. Calculate the single exponential smoothing forecast for these data using an α of 0.30 and an initial forecast (F₁) of 36. (Round your intermediate calculations and answers to 2 decimal places.)

b. Calculate the exponential smoothing with trend forecast for these data using an α of 0.30, a δ of 0.40, an initial trend forecast (T₁) of 1.00, and an initial exponentially smoothed forecast (F₁) of 35. (Round your intermediate calculations and answers to 2 decimal places.)

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.)

c-2. Which is best?

• Exponential smoothing with trend forecast

• Single exponential smoothing forecast

Answer 1

Answer a is in BOLD

Period	Actual demand	Forecast exponential smoothing with constant 0.3
1	36	36.0
2	38	36.00
3	40	36.60
4	41	37.62
5	43	38.63
6	42	39.94
7	43	40.56
8	45	41.29
9	46	42.40
10	48	43.48

• the formula to be used in Exponential smoothing is

F_t+1= alpha*A_t + (1-alpha) F_t

A_t means Actual demand of t'th month, if you want to find out the Forecast through exponential smoothing= forecast of 3rd month = alpha*actual demand of 2nd month+(1-alpha) *forecast demand of 2nd month

remember forecast of 1st month is given as 36.

Answer b is in BOLD

Period	Actual demand	Exponential smoothing, Ft	Trend, Tt	forecast including trend, FITt
1	36	35.00	1.00	36.00
2	38	36.00	1.00	37.00
3	40	37.30	1.12	38.42
4	41	38.89	1.31	40.20
5	43	40.44	1.41	41.85
6	42	42.19	1.54	43.74
7	43	43.22	1.34	44.55
8	45	44.09	1.15	45.23
9	46	45.16	1.12	46.28
10	48	46.20	1.09	47.29

• the formula to be used in Trend smoothing is

F_t+1= FIT_t + alpha*(A_t+1 – FIT_t)

FIT_t is Forecast including trend, F_t+1 means Exponential forecast demand of t+1'th period, if you want to find out the Trend smoothing Forecast = forecast of 3rd period = Forecast including of 2^nd period + alpha*(Actual demand of 3^rd period – Forecast including trend of 2^nd period)

remember forecast of 1st month is Given

• the formula to be used in Trend smoothing is

T_t+1= T_t + beta*(F_t+1 – FIT_t)

F_t+1 means Exponential forecast demand of t+1'th period, if you want to find out the Trend smoothing Forecast = forecast of 3rd period = Trend smoothing Forecast of 2^nd period + beta*(Exponential forecast of 3^rd period – Forecast including trend of 2^nd period)

remember forecast of 1st month is Given

• the formula to be used in Forecast including Trend is

F_t= T_t + F_t

Answer c-1

Formula used:

Absolute deviation= |Forecast - Sales|

MAD= mean absolute deviation= sum of absolute deviation/no. of periods

Period	Actual demand	forecast including trend, FITt	FITt based Absolute deviation= |Forecast - Actual|
1	36	36.00
2	38	37.00	1.00
3	40	38.42	1.58
4	41	40.20	0.80
5	43	41.85	1.15
6	42	43.74	1.74
7	43	44.55	1.55
8	45	45.23	0.23
9	46	46.28	0.28
10	48	47.29	0.71
			1.01
			MAD

Answer c-1

Formula used:

Absolute deviation= |Forecast - Sales|

MAD= mean absolute deviation= sum of absolute deviation/no. of periods

Period	Actual demand	Ft, Forecast exponential smoothing with constant 0.3	Absolute deviation= |Forecast - Actual|
1	36	36.0
2	38	36.00	2.00
3	40	36.60	3.40
4	41	37.62	3.38
5	43	38.63	4.37
6	42	39.94	2.06
7	43	40.56	2.44
8	45	41.29	3.71
9	46	42.40	3.60
10	48	43.48	4.52
			3.27
			MAD

Answer c-2: Forecast including trend id better than single exponential forecast, because the MAD value for forecast including trend is least among the two.