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Rachmat A. Anggara PMBS, BOPR 5301, Session 4 O peration M anagement Forecasting

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Why we have to forecast?? ??

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Forecast Reduces Cost Under forecast the condition when capacity is below actual demand Over forecast the condition where capacity is above actual demand Increase Competitive advantage Economic Forecast Technological forecasts Demand forecasts

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FOR E CAST ING Process of predicting a future event Forecasting Time Horizons Short-range Forecast Medium-range Forecast Long-range Forecast

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Forecasting Approach

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Qualitative Methods Jury of executive opinion Sales force composite Quantitative Method Consumer Market Survey Delphi method 1.Naive approach 2.Moving averages 3.Exponential smoothing 4.Trend projection 5.Linear regression Time-Series Models Associative Model

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Qualitative Method Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet

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Quantitative Method Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet

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Quantitative Method 1. TIME SERIES Set of evenly spaced numerical data Obtained by observing response variable at regular time periods Forecast based only on past values Assumes that factors influencing past and present will continue influence in future

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Quantitative Method TIME SERIES COMPONENT Trend Seasonal Cyclical Random

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Component of Demand Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation

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Steps of Forecasting Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results

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1. Moving Average Moving average = ∑ demand in previous n periods n January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average (12 + 13 + 16)/3 = 13 2 / 3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1 / 3 101213 (10 + 12 + 13)/3 = 11 2 / 3

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2. Weighted Moving Average January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / 2 101213 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago

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Graph of Moving Averages 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average

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3. Exponential Smoothing F t = F t – 1 + (A t – 1 - F t – 1 ) whereF t =new forecast A t – 1 =previous Actual Demand A t – 1 =previous Actual Demand F t – 1 =previous forecast =smoothing (or weighting) constant (0 1) Example – Ford Mustangs : Predicted demand = 142 Actual demand = 153 Smoothing constant =.20 Next Period Forecast = …

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Measuring Forecast Error RoundedAbsolute(Error) 2 Absolute ActualForecastDeviationPercentage TonnagewithforError QuarterUnloaded =.10 =.10 118017555 2 =252.78% 21681768644.76% 31591751625610.06% 4175173241.14% 5190173172898.95% 62051753090014.63% 7180178241.11% 81821784162.20% 841,55845.63% MAD = ∑ |actual - forecast| n MSE = ∑ (forecast errors) 2 n MAPE = 100 ∑ |actual i - forecast i |/actual i nn i = 1

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Calculate MAPE, α = 0.50 RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded =.10 =.10 =.50 =.50 118017551755 2168176817810 31591751617314 417517321669 51901731717020 62051753018025 7180178219313 818217841864 84100

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4. Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FIT t ) = trend exponentiallyexponentially smoothed (F t ) +(T t )smoothed forecasttrend F t = (A t - 1 ) + (1 - )(F t - 1 + T t - 1 ) T t = (F t - F t - 1 ) + (1 - )T t - 1 Step 1: Compute F t Step 2: Compute T t Step 3: Calculate the forecast FIT t = F t + T t

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Gambar perbandingan (xls)Exponential ActualSmoothing TonnageF t T t with Trend QuarterUnloaded = 0.10 β =.20Adjustment 11801752177 21681772179.4 31591782180.1 41751781179.4 51901791180.3 62051812182.7 71801852186.9 81821862188.1

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Graphics

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Fitting a trend line to historical data points to project into the medium-to-long-range Linear trends can be found using the least squares technique y = a + bx ^ where y= computed value of the variable to be predicted (dependent variable) a= y-axis intercept b= slope of the regression line x= the independent variable ^ 5. Trend Projections

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Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^

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Least Squares Method Equations to calculate the regression variables b = xy - nxy x 2 - nx 2 y = a + bx ^ a = y - bx

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Least Squares Example b = = = 10.54 ∑xy - nxy ∑x 2 - nx 2 3,063 - (7)(4)(98.86) 140 - (7)(4 2 ) a = y - bx = 98.86 - 10.54(4) = 56.70 TimeElectrical Power YearPeriod (x)Demandx 2 xy 1999174174 20002794158 20013809240 200249016360 2003510525525 2004614236852 2005712249854 ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86

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Least Squares Example ||||||||| 199920002001200220032004200520062007 160 160 – 150 150 – 140 140 – 130 130 – 120 120 – 110 110 – 100 100 – 90 90 – 80 80 – 70 70 – 60 60 – 50 50 – Year Power demand Trend line, y = 56.70 + 10.54x ^

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Associative Forecasting Forecasting an outcome based on predictor variables. Methods: 1.Regression Analysis 2.Correlation Coefficients 3.Standard Error of the Estimate. 4.Multiple Regression Analysis.

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Regression Analysis SalesLocal Payroll ($000,000), y($000,000,000), x 2.01 3.03 2.54 2.02 2.01 3.57 y = a + bx ^ where y= computed value of the variable to be predicted (dependent variable) a= y-axis intercept b= slope of the regression line x= the independent variable though to predict the value of the dependent variable ^ Example:

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4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll y = 1.75 +.25x ^ Sales = 1.75 +.25(payroll) Sales = 1.75 +.25(6) Sales = $325,000 3.25 If payroll next year is estimated to be $600 million, then:

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Correlation Coefficient r = n xy - x y [n x 2 - ( x) 2 ][n y 2 - ( y) 2 ] How strong is the linear relationship between the variables? Correlation does not necessarily imply causality! Coefficient of correlation, r, measures degree of association Values range from -1 to +1

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Multiple Regression If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables y = a + b 1 x 1 + b 2 x 2 … ^ Computationally, this is quite complex and generally done on the computer

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FORECASTING Kusdhianto Setiawan Gadjah Mada University.

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