Question

Marie Bain is the production manager at a company that manufactures hot water heaters. Marie needs a demand forecast for the next few years to help decide whether to add new production capacity. The company's sales history (in thousands of units) is shown in the table below. Construct a forecast for period 7 in two ways. First, use exponential smoothing where the initial forecast for period 1 was 11 units and the smoothing constant is α = 0.5. For the second forecast, use linear trend. Which forecasting method is likely to give a better forecast for period 7 and why? Show all work in Excel.

Period	Actual	Forecast
1	12	11.00
2	16
3	14
4	17
5	16
6	18

Answer 1

Method 1 - Exponential Smoothening

Exponential forecasting coefficient ? = 0.5,

Actual Demand is A_t

Forecast is F_t

F_t = F_t-1 + ? (A_t-1 - F_t-1)

Let us calculate the forecast and MAD (mean absolute deviation) -

Period	Actual (At)	Forecast(Ft)	Absolute Error
1	12.00	11	1.00
2	16.00	11.50	4.50
3	14.00	13.75	0.25
4	17.00	13.88	3.13
5	16	15.44	0.56
6	18.00	15.72	2.28
7		16.86
		MAD	1.95

Forecast for Period 7 = 16.86

Method 2 - Linear Trend

Let Period be denoted by x and demand by y

Let the Regression line be y = b_o + b₁x

where,

b_o = ( Σy Σx² - Σx Σxy ) / ( nΣx² - (Σx)² )

b₁ = ( nΣxy - ΣxΣy ) / ( nΣx² - (Σx)² )

	x	y	x2	xy
	1	12.00	1	12
	2	16.00	4	32
	3	14.00	9	42
	4	17.00	16	68
	5	16	25	80
	6	18.00	36	108
Σ	21	93	91	342

b_o = ( 93*91 - 21*342 ) / ( 6*91 - 21² ) = 12.2

b₁ = ( 6*342 - 21*93 ) / ( 6*91 - 21² ) = 0.943

=> y = 12.2 + 0.943x

Hence, the forecast using the above linear line is -

Period	Actual (At)	Forecast(Ft)	Absolute Error
1	12.00	13.14	1.14
2	16.00	14.09	1.91
3	14.00	15.03	1.03
4	17.00	15.97	1.03
5	16	16.92	0.91
6	18.00	17.86	0.14
7		18.80
		MAD	1.03

Forecast for Period 7 = 18.80

Since the MAD of Linear forecast is lower than that of exponential forecasting, the linear trend forecast is better