chapter4b

# chapter4b - 4-1Operations Operations 4 Part 2Chapter 4 Part...

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Unformatted text preview: 4-1Operations Operations ManagementManagementForecastingForecastingChapter 4 - Part 2Chapter 4 - Part 24-2♦Trend is increasing or decreasing pattern.♦First, plot data to verify trend.♦If trend exists, then moving averages and exponential smoothing will always lag.Forecasting a TrendForecasting a Trend4-3Plot DataPlot DataPeriodActual453216841216204-4MA= 3 period Moving Average Moving Averages for a TrendMoving Averages for a TrendPeriodMA1821131341510.674.3351913.006.00MAError615.67?Sales4-5Trend GraphTrend GraphPeriodActualMA Forecast453216841216204-6MA= 3 period Moving Average ES = Exponential Smoothing with α=0.5 (F2=11)Exponential Smoothing for a Exponential Smoothing for a TrendTrend?PeriodMAES182113131141510.67124.333.051913.0013.56.005.5MAErrorESError615.671116.25?Sales4-7Trend GraphTrend GraphPeriodActualMA Forecast45321684121620ES Forecast4-8♦Moving Averages and (simple) Exponential Smoothing are always poor.♦For a linear trend can use:♦Exponential Smoothing with Trend Adjustment (skip: pp. 90-92).♦Linear Trend Projection (linear regression).♦For non-linear trend can use:♦Non-linear regression techniques.Forecasting a TrendForecasting a Trend4-9♦Used for forecasting linear trend line.♦PLOT TO VERIFY LINEAR RELATIONSHIP♦Assumes linear relationship between response variable, Y, and time, X.♦Y = a + bX♦a= y-axis intercept; b= slope♦Estimated by least squares method.♦Minimizes sum of squared errors.Linear Trend ProjectionLinear Trend Projection4-10Plot of X,Y DataPlot of X,Y DataTime (x)Values of Dependent Variable (Y)Actual observation4-11Least SquaresLeast SquaresDeviationDeviationDeviationDeviationDeviationDeviationDeviationTime (x)Values of Dependent Variable (Y)bxaY+=ˆActual observationPoint on regression line4-12Least SquaresLeast Squares♦Least squares line minimizes sum of squared deviations.♦This reduces large errors.♦Similar to MSE. ♦Deviations around least squares line are assumed to be random.4-13YabXii=+b> 0b< 0aaYXLinear Trend Projection ModelLinear Trend Projection Model4-14Least Squares EquationsLeast Squares EquationsEquation:iibxaYˆ+=Slope (p. 94):221=1=-∑-∑=xnxyxnyxbiniiiniY-Intercept:xbya-=4-15Linear Trend Projection ExampleLinear Trend Projection ExamplePeriod(x)18211313415519Sales(y)xy609582239xy=224x29162541x2=554.55156.25666.235552.13352242=-==×-××-=abx=3y=13.24-16TP = Trend Projection: Y = 5.4 + 2.6xLinear Trend Projection ExampleLinear Trend Projection ExamplePeriod(x)MAES12345811131519MAErr.610.6713.0015.67111213.51116.254.336.00Sales(y)3.05.5ESErr.TPErr.TP21.018.415.8-0.80.6Small errors!4-17Trend GraphTrend GraphMA ForecastES ForecastPeriodActual45321684121620TP Forecast4-18Models with SeasonalityModels with Seasonality♦Use if data exhibits seasonal patterns....
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chapter4b - 4-1Operations Operations 4 Part 2Chapter 4 Part...

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