Question

A large Portland manufacturer wants to forecast demand for a piece of pollution-control equipment. A review of past sales (At), as shown below, indicates that an increasing trend is present. Smoothing constants are assigned the values of a = 0.20 and ß = 0.4. The firm assumes the initial forecast for month 1 (F1) was 9.00 units and the trend over that period T1 was 2.00 units. Using trend-adjusted exponential smoothing, Forecasts (Ft), Trend (Tt), and Forecasts Including Trend (FIT+) for months 1 through 4 have already been developed and are provided below. Continue with the process and determine Ft, Tt, and FIT/ for months 5 and 6 (round your responses to two decimal places): Month (t) Actual Demand (At) Forecast (Ft) Trend (T4) Forecast Including Trend (FIT) 1 2 10.0 17.0 24.0 18.0 9.00 10.80 13.58 17.47 2.00 1.92 2.26 2.91 11.00 12.72 15.84 20.38 3 5 22.0 6 23.0 7 8 31.0 27.0 38.0 9 10

Answer 1

α = 0.2

β = 0.4

Initial forecast for month 1 = 9 units

Trend over that period = 2 units

Adjusted Exponential Smoothing forecast or Forecast including trend is FIT_t = F_t + T_t = 9+2 = 11 for the month 1

F_(t+1) = α*A_t + (1-α)*F_t

where t+1 = next period

t = current period

Forecast for 2nd month = 0.2*10 + 0.8*9 = 9.2

The forecast (F_t) and T_t are already calculated. The above value is not what is present in the table.

In the given table, forecast (F_t) is 10.8

Now again calculating the forecast for 2nd period using the FIT_t

F_(t+1) = α*A_t + (1-α)*FIT_t = 0.2*10 + 0.8*11 = 10.8

The trend is calculated by:

T_(t+1) = β*(F_(t+1) - F_t) + (1-β) * T_t

Trend for the 2nd month = 0.4*(10.8-9) + 0.6*2 = 1.92

Similarly, the F_t and T_t value is calculated for 5th and 6th month as well

The calculated values are as mentioned below:

Month (t)	Actual Demand (At)	Forecast (Ft)	Trend (Tt)	Forecast Including Trend (FITt)
1	10	9.00	2.00	11.00
2	17	10.80	1.92	12.72
3	24	13.58	2.26	15.84
4	18	17.47	2.92	20.39
5	22	19.91	2.72	22.63
6	23	22.51	2.67	25.18
7	31	-	-	-
8	27	-	-	-
9	38	-	-	-
10	-	-	-	-