ࡱ> a Xjbjb11 [[<DDDD\U\U\U8U\UDj<@Y*["L[L[L[_\_\_\ujwjwjwjwjwjwj,:lRnj_\[\_\_\_\j\DDL[L[j\\\_\XD8L[L[uj\LhDDDD_\uj\\|\4Y ,QN\U\:\\ j0j\*o\*o\\D<?d?Practice Problems: Chapter 4, Forecasting Problem 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 ago1Three weeks ago6TotalProblem 3: A firm uses simple exponential smoothing with  EMBED Equation  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 forecast automobile battery sales. Two value of  EMBED Equation  are examined,  EMBED Equation  and  EMBED Equation  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 SalesForecastJanuary2022February21March15April14May13June16 Problem 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)2001100200211020031222004130200513920061522007164 To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate year 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 Demand1787127580383101484845886068573 Problem: 7 Over the past year Meredith and Smunt Manufacturing had annual sales of 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: 8 Using the data in Problem 7, Meredith and Smunt Manufacturing expects sales of pumps to grow by 10% next year. Compute next years sales and the sales for each quarter. ANSWERS: Problem 1:  EMBED Equation  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 1/3 Problem 2:  EMBED Equation  WeekAuto SalesThree-Week Moving Average1821039411[(3*9) + (2*10) + (1*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 2/3 Problem 3:  EMBED Equation  Problem 4: MonthActual Battery SalesRounded Forecast with a =0.8Absolute Deviation with a =0.8Rounded Forecast with a =0.5Absolute Deviation with a =0.5January20222222February21201210March15216216April14162184May13141163June16133151Sum = 1516  INCLUDEPICTURE "E:\\html\\pracprobs\\images\\Imagea4.gif" \* MERGEFORMATINET 2.52.75SE3.74.1 On 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)X2XY20011100110020022110422020033122936620044130165202005513925695200661523691220077164491148S X = 28S Y =917S X2=140S XY = 3961  EMBED Equation   EMBED Equation   EMBED Equation   EMBED Equation  Therefore, the least squares trend equation is:  EMBED Equation  To project demand in 2008, we denote the year 2008 as  EMBED Equation  and: Sales in 2008 = 89.16 + 10.46 * 8 = 172.84 Problem 6: YearForecast DemandActual DemandErrorRSFE17871-7-7275805-238310118164848401658860-28-1268573-12-24  EMBED Equation  YearForecast DemandActual Demand|Forecast Error|Cumulative ErrorMADTracking Signal17871777.0-1.0275805126.0-0.3383101183010.0+1.6484840307.5+2.158860285811.6-1.068573127011.7-2.1  EMBED Equation  Problem 7: Sales of 10,000 units annually divided equally over the 4 seasons is  EMBED Equation  and the seasonal index for each quarter is: spring  EMBED Equation  summer  EMBED Equation  fall  EMBED Equation  winter  EMBED Equation  Problem 8: Next years sales should be 11,000 pumps  EMBED Equation  Sales for each quarter should be 1/4 of the annual sales  EMBED Equation  the quarterly index.  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