Question

Your manager is trying to determine what forecasting method to use. Based on the following historical data, calculate the following forecasts and specify what procedure you would utilize.

MONTH	ACTUAL DEMAND
1	53
2	56
3	58
4	65
5	74
6	75
7	76
8	77
9	77
10	79
11	81
12	82

c. Calculate the single exponential smoothing forecast for periods 2–12 using an initial forecast (F₁) of 61 and an α of 0.30.

d. Calculate the exponential smoothing with trend component forecast for periods 2–12 using an initial trend forecast (T₁) of 1.70, an initial exponential smoothing forecast (F₁) of 62, an α of 0.30, and a δ of 0.20

Answer 1

c. Single Exponential Smoothing

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

t = current time period

= Exponential smoothing Constant

At = Demand at period t

Ft  =Forecast for period t

Ft+1 = Forecast for period following t

F1 = 61

F2 = 0.3*A1 + 0.7*F1 = 0.3*53+ 0.7*61 = 58.6 = 59

In the same way calculate forecast value for other period also

MONTH	ACTUAL DEMAND	Single exponential Smoothing Forecast
1	53	61
2	56	59
3	58	58
4	65	58
5	74	60
6	75	64
7	76	67
8	77	70
9	77	72
10	79	74
11	81	75
12	82	77

D)

exponential smoothing with trend component forecast

St+1 = *At  +(1-)*(St + Tt )

Tt+1 = δ *(St+1 - St ) + (1-δ ) *Tt

Ft+1 = St+1 + Tt+1  

where,

Ft+1 = Trend-corrected forecast for period t+1

St = Initial Forecast for period t

Tt = Trend for period t

δ = Trend smoothing constant

S1  = 62

T1 = 1.7

F1 = S1 + T1 = 62 +1.7 = 63.7 = 64

S2 = 0.3 *A1 + (1-0.3)*(S1 + T1) = 0.3*53 + 0.7*63.7 = 60.49

T2 = 0.2*( S2 - S1 ) +0.8*T1 = 0.2*(60.49-62) +0.8*1.7 = 1.06

F2 = S2 + T2  = 60.49 + 1.06 = 62

In the same way calculate S , T & F

MONTH	ACTUAL DEMAND	S	T	F
1	53	62	1.70	64
2	56	60	1.06	62
3	58	60	0.73	61
4	65	60	0.57	60
5	74	62	0.84	63
6	75	66	1.53	68
7	76	70	1.97	72
8	77	73	2.23	75
9	77	76	2.33	78
10	79	78	2.26	80
11	81	80	2.20	82
12	82	82	2.15	84