Practice Problems Chapter 4, Forecasting

1、Practice Problems: Chapter 4, ForecastingProblem 1:Auto sales at Carmens Chevrolet are shown below. Develop a 3-week moving average.WeekAuto Sales18210394115106137-Problem 2:Carmens decides to forecast auto sales by weighting the three weeks as follows:Weights AppliedPeriod3Last week2Twoweeks ago1Th

2、ree weeks ago6TotalProblem 3:A firm uses simple exponential smoothing with to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8.Problem 4:Exponential smoothing is used to

3、 forecast automobile battery sales. Two value of are examined, and Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below:MonthActual Battery SalesForecastJanuary2022February21March15April14May13June16Pr

4、oblem 5:Use the sales data given below to determine: (a) the least squares trend line, and (b) the predicted value for 2008 sales.YearSales (Units)2001100200211020031222004130200513920061522007164To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate ye

5、ar 2001 as year 1, 2002 as year 2, etc.Problem 6:Given the forecast demand and actual demand for 10-foot fishing boats, compute the tracking signal and MAD.YearForecast DemandActual Demand1787127580383101484845886068573Problem: 7Over the past year Meredith and Smunt Manufacturing had annual sales of

6、 10,000 portable water pumps. The average quarterly sales for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index.Problem: 8Using the data in Problem 7, Meredith and Smunt Manufacturing expects sales of pumps to grow by 10% next year.

7、Compute next years sales and the sales for each quarter.ANSWERS:Problem 1:WeekAuto SalesThree-Week Moving Average1821039411(8 + 9 + 10) / 3 = 9510(10 + 9 + 11) / 3 = 10613(9 + 11 + 10) / 3 = 107-(11 + 10 + 13) / 3 = 11 1/3Problem 2:WeekAuto SalesThree-Week Moving Average1821039411(3*9) + (2*10) + (1

8、*8) / 6 = 9 1/6510(3*11) + (2*9) + (1*10) / 6 = 10 1/6613(3*10) + (2*11) + (1*9) / 6 = 10 1/67-(3*13) + (2*10) + (1*11) / 6 = 11 2/3Problem 3:Problem 4:MonthActual Battery SalesRounded Forecast with a =0.8Absolute Deviation with a =0.8Rounded Forecast with a =0.5Absolute Deviation with a =0.5January

9、20222222February21201210March15216216April14162184May13141163June16133151Sum = 15162.52.75SE3.74.1On the basis of this analysis, a smoothing constant of a = 0.8 is preferred to that of a =0.5 because it has a smaller MAD.Problem 5:YearTime Period (X)Sales (Units) (Y)X2XY20011100110020022110422020033

10、122936620044130165202005513925695200661523691220077164491148S X = 28S Y =917S X2=140S XY = 3961Therefore, the least squares trend equation is:To project demand in 2008, we denote the year 2008 as and:Sales in 2008 = 89.16 + 10.46 * 8 = 172.84 Problem 6:YearForecast DemandActual DemandErrorRSFE17871-

11、7-7275805-238310118164848401658860-28-1268573-12-24YearForecast DemandActual Demand|Forecast Error|Cumulative ErrorMADTracking Signal17871777.0-1.0275805126.0-0.3383101183010.0+1.6484840307.5+2.158860285811.6-1.068573127011.7-2.1Problem 7: Sales of 10,000 units annually divided equally over the 4 seasons is and the seasonal index fo