Question

Looking for the steps for the double exponential smoothing part of b. Please DO NOT use excel. Thank you.

Q3. (Total 25 points) Goodyear Tire and Rubber Company is the ninth largest tire manufacturer in the world. Here are the sales revenues for the past five years: Revenue (millions) y $4,887.9 5,065.4 5,535.6 5,730.8 5,499.7 Year t 2 3 4 5 a. When might a manager prefer linear trend technique to simple moving average technique? Explain your answer. (5 points) b. Based on MAD for 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 Si $4,867.90 and Ti $201.5 for the year 1)) provides the better forecasts? Explain. Forecast the sales revenues for years 6 and 7 based on your preferred method (20 points)

Answer 1

Double exponentially smoothed forecast (or trend-adjusted exponentially smoothed) forecast is calculated by the following formulas:

S_t+1 = $\inline \alpha$*At + (1-$\inline \alpha$)*St, where

T_t+1 = $\inline \beta$*(S_t+1-S_t) + (1-$\inline \beta$)*T_t

TAF_t+1 = S_t+1+T_t+1

For year 2, S2 = .4*4887.9+(1-.4)*4867.9 = 4875.9

T2 = .2*(4875.9-4867.9)+(1-0.2)*201.5 = 162.8

TAF2 = 4875.9+162.8 = 5038.7

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For year 3, S3 = .4*5065.4+(1-.4)*4875.9 = 4951.7

T3 = .2*(4951.7-4875.9)+(1-0.2)*162.8 = 145.5

TAF3 = 4951.7+145.5 = 5097.1

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For year 4, S4 = .4*5535.6+(1-.4)*4951.7 = 5185.26

T4 = .2*(5185.26-4951.7)+(1-0.2)*145.5 = 163.03

TAF4 = 5185.26+163.03 = 5348.29

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For year 5, S5 = .4*5730.8+(1-.4)*5185.26 = 5403.48

T5 = .2*(5403.48-5185.26)+(1-0.2)*163.03 = 174.07

TAF5 = 5403.48+174.07 = 5577.55

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For year 6, S6 = .4*5499.7+(1-.4)*5403.48 = 5441.97

T6 = .2*(5441.97-5403.48)+(1-0.2)*174.07 = 146.95

TAF6 = 5441.97+146.95 = 5588.92

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[Forecast for year 7 cannot be calculated using double-exponential smoothing method]