Question

A large Portland manufacturer wants to forecast demand for a piece of pollution-control equipment. A review of past sales

(Upper A Subscript tAt ), as shown below, indicates that an increasing trend is present. Smoothing constants are assigned the values of

alpha α= 0.2 and beta β=0.4 The firm assumes the initial forecast for month 1 (Upper F 1F1 )was13.00 units and the trend over that period Upper T 1T1 was

2.00 units.

Using trend-adjusted exponential smoothing, Forecasts (Upper F Subscript tFt ), Trend (Upper T Subscript tTt ), and Forecasts Including Trend (FIT Subscript tFITt ) for months 1 through 4 have already been developed and are provided below. Continue with the process and determine Upper F Subscript tFt , Upper T Subscript tTt , and FIT Subscript tFITt for months 5 and 6 (round your responses to two decimal places):

  

Month (t )	Actual Demand (Upper A Subscript tAt )	Forecast (Upper F Subscript tFt )	Trend (Upper T Subscript tTt )	Forecast Including Trend (FIT Subscript tFITt )
1	14.0	13.00	2.00	15.00
2	16.0	14.80	1.92	16.72
3	20.0	16.58	1.86	18.44
4	20.0	18.75	1.98	20.73
5	25.0	?	?	?
6	21.0	?	?	?
7	32.0	−	−	−
8	26.0	−	−	−
9	38.0	−	−	−
10	-	−	−	−

Answer 1

Forecast by trend adjusted exponential smoothing

formula of  

Forecast_t = Forecast Including Trend_t-1 + Alpha * (Actual _t-1 -  Forecast Including Trent_t-1 )

and

Trend_t = Trend _{t -1} + Beta * (Forecast _t - Forecast Including Trend_t-1 )

Using the above formula we draw a excel table

(t )	(Upper A Subscript tAt ) Actual	(Upper F Subscript tFt ) Forecast t	(Upper T Subscript tTt ) Trend t	(FIT Subscript tFITt ) Forecast Including Trentt-1
1	14	13.00	2.00	15.00
2	16	14.80	1.92	16.72
3	20	16.58	1.86	18.44
4	20	18.75	1.98	20.74
5	25	20.59	1.92	22.51

6

21

23.01

2.12

25.13

Example for Month 5

Forecast_t = Forecast Including Trend_t-1 + Alpha * (Actual _t-1 -  Forecast Including Trent_t-1 )

= 20.74 + 0.2 *(20 - 20.74)

= 20.59

Trend for Month 5

Trend_t = Trend _{t -1} + Beta * (Forecast _t - Forecast Including Trend_t-1 )

= 1.98 + 0.4 *( 20.59 - 20.73)

= 1.92

Similarly for month is calculated

Forecast = 22.51 + 0.2 * (25 - 22.51)

= 23.01

Trend = 1.92 + 0.4 ( 23.01- 22.51)

=2.12