The Andes Mining Company mines and ships copper ore. The company’s sales manager, Juanita Valdes, has been using the moving-average method based on the last three years of sales to forecast the demand for the next year. However, she has become dissatisfied with the inaccurate forecasts being provided by this method.
Here are the annual demands (in tons of copper ore) over the past 10 years: 382 405 398 421 426 415 443 451 446 464
(a) Explain why this pattern of demands inevitably led to significant inaccuracies in the moving-average forecasts.
(b) Determine the moving-average forecasts for the past 7 years. What is MAD? What is the forecast for next year?
(c) Determine what the forecasts would have been for the past 10 years if the exponential smoothing method had been used instead with an initial estimate of 380 and a smoothing constant of α = 0.5. What is MAD? What is the forecast for next year?
(d) Determine what the forecasts would have been for the past 10 years if exponential smoothing with trend had been used instead. Use initial estimates of 370 for the expected value and 10 for the trend, with smoothing constants α = 0.25 and β = 0.25.
(e) Based on the MAD values, which of these three methods do you recommend using hereafter