Question

Goodyear Tire and Rubber Company is the ninth largest tire manufacturer in the world. Here are the sales revenues for the past five years:

Year	Revenue (millions)
1	$4,877.9
2	5,065.4
3	5,525.6
4	5,729.8
5	5,499.7

a.When might a manager prefer linear trend/double exponential smoothing techniques to moving average/simple exponential smoothing techniques and why? (5 points)

b. Based on MAD for the last three years (years 3, 4, and 5), which method (linear-trend or double-exponential smoothing method with a = 0.4 and b = 0.2 (start with initial estimates S₁ = $4,867.90 and T₁ = $201.5 for year 1)) provides the better forecasts? Explain. Then, use your selected forecasting method, forecast the revenue for year 6 and year 7.

Answer 1

A and B combined

Linear trend:

	n=	5
	X	Y	X^2	XY	Forecast	AD
	Week	Revenue			(a+bX)
	1	4,877.90	1	4877.9	4958.08
	2	5,065.40	4	10130.8	5148.88
	3	5,525.60	9	16576.8	5339.68	185.92
	4	5,729.80	16	22919.2	5530.48	199.32
	5	5,499.70	25	27498.5	5721.28	221.58
Sum	15	26698.4	55	82003.2	MAD	202.2733
		a =	4767.28
		b =	190.80
		Y = a+ bX
	6				5912.08
	7				6102.88

Doublt exponential

	a =	0.4			b=	0.2
Period	Sales	St	S't	S (2*St-S't)	T	Forecast (S+T)
				Base	Trend		AD
1	4,877.90	4,867.90	4,867.90	4,867.90	201.50	5069.40
2	5,065.40	4871.90	4869.50	4874.30	202.78	5077.08
3	5,525.60	4949.30	4901.42	4997.18	227.36	5224.54	301.06
4	5,729.80	5179.82	5012.78	5346.86	297.29	5644.15	85.65
5	5,499.70	5399.81	5167.59	5632.03	354.33	5986.36	486.66
						MAD	291.12
6	5,499.70	5439.77	5276.46	5603.07	348.53	5951.61
7	5,499.70	5463.74	5351.37	5576.11	343.14	5919.25

So as per the MAD for 3-5 we see the MAD for linear trend is lower and hence it is better in forecasting year 6 and 7 (shown above)