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© 2006 Prentice Hall, Inc.4 – 1 Short-range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job assignments, production levels Medium-range forecast 3 months to 3 years Sales and production planning, budgeting Long-range forecast 3 + years New product planning, facility location, research and development Forecasting Time Horizons

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© 2006 Prentice Hall, Inc.4 – 2 Trend Seasonal Cyclical Random Time Series Components

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© 2006 Prentice Hall, Inc.4 – 3 Components of Demand Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation Figure 4.1

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© 2006 Prentice Hall, Inc.4 – 4 Graph of Moving Average ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales 30 30 – 28 28 – 26 26 – 24 24 – 22 22 – 20 20 – 18 18 – 16 16 – 14 14 – 12 12 – 10 10 – Actual Sales Moving Average Forecast

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© 2006 Prentice Hall, Inc.4 – 5 Impact of Different 225 225 – 200 200 – 175 175 – 150 150 – |||||||||123456789123456789|||||||||123456789123456789 Quarter Demand =.1 Actual demand =.5

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© 2006 Prentice Hall, Inc.4 – 6 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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© 2006 Prentice Hall, Inc.4 – 7 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 ^ Least squares method minimizes the sum of the squared errors (deviations)

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© 2006 Prentice Hall, Inc.4 – 8 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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© 2006 Prentice Hall, Inc.4 – 9 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 The trend line is y = 56.70 + 10.54x ^

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© 2006 Prentice Hall, Inc.4 – 10 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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© 2006 Prentice Hall, Inc.4 – 11 Associative Forecasting Forecasting an outcome based on predictor variables 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 though to predict the value of the dependent variable ^

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© 2006 Prentice Hall, Inc.4 – 12 Associative Forecasting Example SalesLocal Payroll ($000,000), y($000,000,000), x 2.01 3.03 2.54 2.02 2.01 3.57 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll

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© 2006 Prentice Hall, Inc.4 – 13 Associative Forecasting Example Sales, y Payroll, xx 2 xy 2.0112.0 3.0399.0 2.541610.0 2.0244.0 2.0112.0 3.574924.5 ∑y = 15.0∑x = 18∑x 2 = 80∑xy = 51.5 x = ∑x/6 = 18/6 = 3 y = ∑y/6 = 15/6 = 2.5 b = = =.25 ∑xy - nxy ∑x 2 - nx 2 51.5 - (6)(3)(2.5) 80 - (6)(3 2 ) a = y - bx = 2.5 - (.25)(3) = 1.75

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© 2006 Prentice Hall, Inc.4 – 14 Associative Forecasting Example 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll y = 1.75 +.25x ^ Sales = 1.75 +.25(payroll) If payroll next year is estimated to be $600 million, then: Sales = 1.75 +.25(6) Sales = $325,000 3.25

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© 2006 Prentice Hall, Inc.4 – 15 Standard Error of the Estimate A forecast is just a point estimate of a future value This point is actually the mean of a probability distribution Figure 4.9 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll 3.25

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© 2006 Prentice Hall, Inc.4 – 16 Standard Error of the Estimate wherey=y-value of each data point y c =computed value of the dependent variable, from the regression equation n=number of data points S y,x = ∑(y - y c ) 2 n - 2

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© 2006 Prentice Hall, Inc.4 – 17 Standard Error of the Estimate Computationally, this equation is considerably easier to use We use the standard error to set up prediction intervals around the point estimate S y,x = ∑y 2 - a∑y - b∑xy n - 2

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© 2006 Prentice Hall, Inc.4 – 18 Standard Error of the Estimate 4.0 – 3.0 – 2.0 – 1.0 – |||||||01234567|||||||01234567 Sales Area payroll 3.25 S y,x = = ∑y 2 - a∑y - b∑xy n - 2 39.5 - 1.75(15) -.25(51.5) 6 - 2 S y,x =.306 The standard error of the estimate is $30,600 in sales

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© 2006 Prentice Hall, Inc.4 – 19 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 Correlation

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© 2006 Prentice Hall, Inc.4 – 20 Correlation Coefficient r = n xy - x y [n x 2 - ( x) 2 ][n y 2 - ( y) 2 ]

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© 2006 Prentice Hall, Inc.4 – 21 Correlation Coefficient r = n∑xy - ∑x∑y [n∑x 2 - (∑x) 2 ][n∑y 2 - (∑y) 2 ] y x (a)Perfect positive correlation: r = +1 y x (b)Positive correlation: 0 < r < 1 y x (c)No correlation: r = 0 y x (d)Perfect negative correlation: r = -1

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© 2006 Prentice Hall, Inc.4 – 22 Coefficient of Determination, r 2, measures the percent of change in y predicted by the change in x Values range from 0 to 1 Easy to interpret Correlation For the Nodel Construction example: r =.901 r 2 =.81

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© 2006 Prentice Hall, Inc.4 – 23 Multiple Regression Analysis 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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© 2006 Prentice Hall, Inc.4 – 24 Multiple Regression Analysis y = 1.80 +.30x 1 - 5.0x 2 ^ In the Nodel example, including interest rates in the model gives the new equation: An improved correlation coefficient of r =.96 means this model does a better job of predicting the change in construction sales Sales = 1.80 +.30(6) - 5.0(.12) = 3.00 Sales = $300,000

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© 2006 Prentice Hall, Inc.4 – 25 Measures how well the forecast is predicting actual values Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) Good tracking signal has low values If forecasts are continually high or low, the forecast has a bias error Monitoring and Controlling Forecasts Tracking Signal

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© 2006 Prentice Hall, Inc.4 – 26 Monitoring and Controlling Forecasts Tracking signal RSFEMAD= = ∑(actual demand in period i - forecast demand in period i) ∑|actual - forecast|/n)

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© 2006 Prentice Hall, Inc.4 – 27 Tracking Signal Tracking signal + 0 MADs – Upper control limit Lower control limit Time Signal exceeding limit Acceptable range

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© 2006 Prentice Hall, Inc.4 – 28 Tracking Signal Example Cumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD 190100-10-10101010.0 295100-5-155157.5 3115100+150153010.0 4100110-10-10104010.0 5125110+15+5155511.0 6140110+30+35308514.2

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© 2006 Prentice Hall, Inc.4 – 29Cumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD 190100-10-10101010.0 295100-5-155157.5 3115100+150153010.0 4100110-10-10104010.0 5125110+15+5155511.0 6140110+30+35308514.2 Tracking Signal Example Tracking Signal (RSFE/MAD) -10/10 = -1 -15/7.5 = -2 0/10 = 0 -10/10 = -1 +5/11 = +0.5 +35/14.2 = +2.5 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits

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