11 Forecasting



chapter 12:?ForecastingProblems1. The chairperson of the department of management at Tech wants to forecast the number of students who will enroll in operations management next semester in order to determine how many sections to schedule. The chair has accumulated the following enrollment data for the past eight semesters:a. Compute a three-semester moving average forecast for semesters 4 through 9.b. Compute the exponentially smoothed forecast (α=0.20) for the enrollment data.c. Compare the two forecasts using MAD and indicate the most accurate.2. The Bee Line Café is well known for its popular homemade ice cream, which it makes in a small plant in back of the cafe. People drive long distances to buy the ice cream. The two ladies who own the café want to develop a forecasting model so they can plan their ice cream production operation and determine the number of employees they need to sell ice cream in the café. They have accumulated the following sales records for their ice cream for the past 12 quarters:Develop an adjusted exponential smoothing model with α = 0.50 and β = 0.50 to forecast demand, and assess its accuracy using cumulative error (E) and average error (E ).Does there appear to be any bias in the forecast?3. For the demand data in Problem 2, develop a seasonally adjusted forecast for 2011. (Use a linear trend line model to develop a forecast estimate for 2005.) Which forecast model do you perceive to be the most accurate, the adjusted exponential smoothing model from Problem 2 or the seasonally adjusted forecast?4. Develop a statistical control chart for the forecast error in Problem 2 using 63_ control limits, and indicate if the forecast seems to be biased.5. ITown is a large computer discount store that sells computers and ancillary equipment and software in the town where State University is located. It has collected historical data on computer sales and printer sales for the past 10 years as follows:a. Develop a linear trend line forecast to forecast printer demand in year 11.b. Develop a linear regression model relating printer sales to computer sales to forecast printer demand in year 11 if 1500 computers are sold.c. Compare the forecasts developed in parts (a) and (b) and indicate which one appears to be the best.6. Develop an exponential smoothing model with α= 0.30 for the data in Problem 5 to forecast printer demand in year 11, and compare its accuracy to the linear regression forecast developed in Problem 5 (a).7. In Problem 5, ITown believes its printer sales are also related to the average price of its printers. It has collected historical data on average printer prices for the past 10 years as follows:a. Using Excel, develop the multiple regression equation for these data.b. What is the coefficient of determination for this regression equation?c. Determine a forecast for printer sales based on personal computer sales of 1500 units and an average printer price of $300.Answers:1.Exponential smoothing is most accurate.2.3.Seasonal factors: Quarter 1: Quarter 2: Quarter 3: Quarter 4: Forecast for 2005: Seasonally adjusted forecasts:Quarter 1: Quarter 2: Quarter 3: Quarter 4: The seasonal factor seems to provide a more accurate forecast.4.The data has a slight positive bias to it.5.a.b.c.MAD for the linear trend line forecast in a. equals 85.69 while MAD for the linear regression forecast in b. equals 45.20. In addition, the correlation coefficient for the linear trend is whereas the correlation coefficient for the linear regression is This evidence seems to indicate the forecast model in b is best.6.YearDemandForecast1381—2579381.003312440.404501401.885296431.626415390.937535398.858592439.219607485.0410473521.6311507.04The exponential smoothing forecast appears to be less accurate than the linear regression forecast developed in 12-35a.7.a.y = 144.67 + 0.371X1 – 0.307X2b.c.= 144.67 + 0.371(1500)-0.307(300) = 608.50 ................
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