Question

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

MONTH	ACTUAL DEMAND
1	31
2	34
3	35
4	39
5	40
6	45
7	45
8	47
9	43
10	44

a. Calculate the single exponential smoothing forecast for these data using an α of 0.30 and an initial forecast (F₁) of 31. (Round your 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 0.30, an initial trend forecast (T₁) of 1.00, and an initial exponentially smoothed forecast (F₁) of 30. (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.)

Answer 1

· the formula to be used in Simple Exponential smoothing is

Ft+1= alpha*At + (1-alpha) Ft

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

· remember forecast of 1st period is 31, alpha= 0.3

· Alpha= 0.3, Beta= 0.3

· the formula to be used in Exponential smoothing, Ft is

Ft+1= FITt + alpha*(At – FITt)

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

· the formula to be used in Trend smoothing, Tt is

Tt+1= Tt + beta*(Ft+1 – FITt)

Ft+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 2nd period + beta*(Exponential forecast of 3rd period – Forecast including trend of 2nd period)

remember Trend of 1st period is 1

· the formula to be used in Forecast including Trend, FIT is

FITt= Tt + Ft

a.

Month, t	Actual , At	Ft, Exponential Forecast	Absolute deviation= |Forecast - Actual|
1	31	31.0
2	34	31.0	3.0
3	35	31.9	3.1
4	39	32.8	6.2
5	40	34.7	5.3
6	45	36.3	8.7
7	45	38.9	6.1
8	47	40.7	6.3
9	43	42.6	0.4
10	44	42.7	1.3
			4.48
			MAD

b.

MONTH, t	ACTUAL, At	Exponential smoothing, Ft	Trend, Tt	forecast including trend, FITt	Absolute deviation= |Forecast - Actual|
1	31	30.00	1.00	31.00
2	34	31.00	1.00	32.00	2.00
3	35	32.60	1.18	33.78	1.22
4	39	34.15	1.29	35.44	3.56
5	40	36.51	1.61	38.12	1.88
6	45	38.68	1.78	40.46	4.54
7	45	41.82	2.19	44.01	0.99
8	47	44.31	2.28	46.59	0.41
9	43	46.71	2.31	49.02	6.02
10	44	47.22	1.77	48.99	4.99
					2.85
					MAD

c: Based on MAD, Exponential smoothing forecast with trend is better.