© 2006 Prentice Hall, Inc.4 – 1 Forcasting © 2006 Prentice Hall, Inc. Heizer/Render Principles of Operations Management, 6e Operations Management, 8e

© 2006 Prentice Hall, Inc.4 – 2 What is Forecasting?  Process of predicting a future event  Underlying basis of all business decisions  Production  Reengineering  Inventory  Personnel  Facilities  Risk Management ??

© 2006 Prentice Hall, Inc.4 – 3 Trend Seasonal Cyclical Random Time Series Components

© 2006 Prentice Hall, Inc.4 – 4  Persistent, overall upward or downward pattern  Changes due to population, technology, age, culture, etc.  Typically several years duration Trend Component

© 2006 Prentice Hall, Inc.4 – 5  Regular pattern of up and down fluctuations  Due to weather, customs, etc.  Occurs within a single year Seasonal Component Number of PeriodLengthSeasons WeekDay7 MonthWeek4-4.5 MonthDay28-31 YearQuarter4 YearMonth12 YearWeek52

© 2006 Prentice Hall, Inc.4 – 6  Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships Cyclical Component

© 2006 Prentice Hall, Inc.4 – 7  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and nonrepeating Random Component MTWTFMTWTFMTWTFMTWTF

© 2006 Prentice Hall, Inc.4 – 8 Naive Approach  Assumes demand in next period is the same as demand in most recent period  e.g., If May sales were 48, then June sales will be 48  Sometimes cost effective and efficient

© 2006 Prentice Hall, Inc.4 – 9  MA is a series of arithmetic means  Used if little or no trend  Used often for smoothing  Provides overall impression of data over time Moving Average Method Moving average = ∑ demand in previous n periods n

© 2006 Prentice Hall, Inc.4 – 10 January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / 3 Moving Average Example ( )/3 = 11 2 / 3

© 2006 Prentice Hall, Inc.4 – 11 Graph of Moving Average ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales – – – – – – – – – – – Actual Sales Moving Average Forecast

© 2006 Prentice Hall, Inc.4 – 12  Used when trend is present  Older data usually less important  Weights based on experience and intuition Weighted Moving Average Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

© 2006 Prentice Hall, Inc.4 – 13 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 Weighted Moving Average [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum of weights

© 2006 Prentice Hall, Inc.4 – 14 Moving Average And Weighted Moving Average – – – – – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average Figure 4.2

© 2006 Prentice Hall, Inc.4 – 15  Form of weighted moving average  Weights decline exponentially  Most recent data weighted most  Requires smoothing constant (  )  Ranges from 0 to 1  Subjectively chosen  Involves little record keeping of past data Exponential Smoothing

© 2006 Prentice Hall, Inc.4 – 16 Exponential Smoothing New forecast =last period’s forecast +  (last period’s actual demand – last period’s forecast) F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0    1)

© 2006 Prentice Hall, Inc.4 – 17 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20

© 2006 Prentice Hall, Inc.4 – 18 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142)

© 2006 Prentice Hall, Inc.4 – 19 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142) = = ≈ 144 cars

© 2006 Prentice Hall, Inc.4 – 20 Impact of Different  – – – – ||||||||| ||||||||| Quarter Demand  =.1 Actual demand  =.5

© 2006 Prentice Hall, Inc.4 – 21 Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error= Actual demand - Forecast value = A t - F t

© 2006 Prentice Hall, Inc.4 – 22 Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |actual - forecast| n Mean Squared Error (MSE) MSE = ∑ (forecast errors) 2 n

© 2006 Prentice Hall, Inc.4 – 23 Common Measures of Error Mean Absolute Percent Error (MAPE) MAPE = 100 ∑ |actual i - forecast i |/actual i n n i = 1

© 2006 Prentice Hall, Inc.4 – 24 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =

© 2006 Prentice Hall, Inc.4 – 25 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = ∑ |deviations| n = 84/8 = For  =.10 = 100/8 = For  =.50

© 2006 Prentice Hall, Inc.4 – 26 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = 1,558/8 = For  =.10 = 1,612/8 = For  =.50 MSE = ∑ (forecast errors) 2 n

© 2006 Prentice Hall, Inc.4 – 27 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE = 45.62/8 = 5.70% For  =.10 = 54.8/8 = 6.85% For  =.50 MAPE = 100 ∑ |deviation i |/actual i n i = 1

© 2006 Prentice Hall, Inc.4 – 28 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE MAPE5.70%6.85%

© 2006 Prentice Hall, Inc.4 – 29 Trend Projections 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 ^

© 2006 Prentice Hall, Inc.4 – 30 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 ^

© 2006 Prentice Hall, Inc.4 – 31 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)

© 2006 Prentice Hall, Inc.4 – 32 Least Squares Method Equations to calculate the regression variables b =  xy - nxy  x 2 - nx 2 y = a + bx ^ a = y - bx

© 2006 Prentice Hall, Inc.4 – 33 Least Squares Example b = = = ∑xy - nxy ∑x 2 - nx 2 3,063 - (7)(4)(98.86) (7)(4 2 ) a = y - bx = (4) = TimeElectrical Power YearPeriod (x)Demandx 2 xy ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86

© 2006 Prentice Hall, Inc.4 – 34 Least Squares Example b = = =  xy - nxy  x 2 - nx 2 3,063 - (7)(4)(98.86) (7)(4 2 ) a = y - bx = (4) = TimeElectrical Power YearPeriod (x)Demandx 2 xy  x = 28  y = 692  x 2 = 140  xy = 3,063 x = 4y = The trend line is y = x ^

© 2006 Prentice Hall, Inc.4 – 35 Least Squares Example ||||||||| – – – – – – – – – – – – Year Power demand Trend line, y = x ^

© 2006 Prentice Hall, Inc.4 – 36  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

© 2006 Prentice Hall, Inc.4 – 37 Correlation Coefficient r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ]

© 2006 Prentice Hall, Inc.4 – 38 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

© 2006 Prentice Hall, Inc.4 – 39  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