Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Forecasting Operations Management - 5 th Edition Chapter 11 Roberta Russell & Bernard W. Taylor, III

Copyright 2006 John Wiley & Sons, Inc.11-2 Lecture Outline   Strategic Role of Forecasting in Supply Chain Management and TQM   Components of Forecasting Demand   Time Series Methods   Forecast Accuracy   Regression Methods

Copyright 2006 John Wiley & Sons, Inc.11-3 Forecasting  Predicting the Future  Qualitative forecast methods subjective subjective  Quantitative forecast methods based on mathematical formulas based on mathematical formulas

Copyright 2006 John Wiley & Sons, Inc.11-4 Forecasting and Supply Chain Management  Accurate forecasting determines how much inventory a company must keep at various points along its supply chain  Continuous replenishment supplier and customer share continuously updated data supplier and customer share continuously updated data typically managed by the supplier typically managed by the supplier reduces inventory for the company reduces inventory for the company speeds customer delivery speeds customer delivery  Variations of continuous replenishment quick response quick response JIT (just-in-time) JIT (just-in-time) VMI (vendor-managed inventory) VMI (vendor-managed inventory) stockless inventory stockless inventory

Copyright 2006 John Wiley & Sons, Inc.11-5 Forecasting and TQM   Accurate forecasting customer demand is a key to providing good quality service   Continuous replenishment and JIT complement TQM eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a primary goal of TQM smoothes process flow with no defective items meets expectations about on-time delivery, which is perceived as good-quality service

Copyright 2006 John Wiley & Sons, Inc.11-6 Types of Forecasting Methods  Depend on time frame time frame demand behavior demand behavior causes of behavior causes of behavior

Copyright 2006 John Wiley & Sons, Inc.11-7 Time Frame  Indicates how far into the future is forecast Short- to mid-range forecast Short- to mid-range forecast typically encompasses the immediate future typically encompasses the immediate future daily up to two years daily up to two years Long-range forecast Long-range forecast usually encompasses a period of time longer than two years usually encompasses a period of time longer than two years

Copyright 2006 John Wiley & Sons, Inc.11-8 Demand Behavior  Trend a gradual, long-term up or down movement of demand a gradual, long-term up or down movement of demand  Random variations movements in demand that do not follow a pattern movements in demand that do not follow a pattern  Cycle an up-and-down repetitive movement in demand an up-and-down repetitive movement in demand  Seasonal pattern an up-and-down repetitive movement in demand occurring periodically an up-and-down repetitive movement in demand occurring periodically

Copyright 2006 John Wiley & Sons, Inc.11-9 Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Demand Demand Demand Random movement Forms of Forecast Movement

Copyright 2006 John Wiley & Sons, Inc Forecasting Methods  Qualitative use management judgment, expertise, and opinion to predict future demand use management judgment, expertise, and opinion to predict future demand  Time series statistical techniques that use historical demand data to predict future demand statistical techniques that use historical demand data to predict future demand  Regression methods attempt to develop a mathematical relationship between demand and factors that cause its behavior attempt to develop a mathematical relationship between demand and factors that cause its behavior

Copyright 2006 John Wiley & Sons, Inc Qualitative Methods   Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts   Delphi method involves soliciting forecasts about technological advances from experts

Copyright 2006 John Wiley & Sons, Inc Forecasting Process 6. Check forecast accuracy with one or more measures 4. Select a forecast model that seems appropriate for data 5. Develop/compute forecast for period of historical data 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data No Yes

Copyright 2006 John Wiley & Sons, Inc Time Series   Assume that what has occurred in the past will continue to occur in the future   Relate the forecast to only one factor - time   Include moving average exponential smoothing linear trend line

Copyright 2006 John Wiley & Sons, Inc Moving Average  Naive forecast demand the current period is used as next period’s forecast demand the current period is used as next period’s forecast  Simple moving average stable demand with no pronounced behavioral patterns stable demand with no pronounced behavioral patterns  Weighted moving average weights are assigned to most recent data

Copyright 2006 John Wiley & Sons, Inc Moving Average: Naïve Approach Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH Nov - FORECAST

Copyright 2006 John Wiley & Sons, Inc Simple Moving Average MA n = n i = 1  DiDiDiDi n where n =number of periods in the moving average D i =demand in period i

Copyright 2006 John Wiley & Sons, Inc month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1  DiDiDiDi 3 = = 110 orders for Nov ––– MOVINGAVERAGE

Copyright 2006 John Wiley & Sons, Inc month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 5 = 5 i = 1  DiDiDiDi 5 = = 91 orders for Nov ––––– MOVINGAVERAGE

Copyright 2006 John Wiley & Sons, Inc Smoothing Effects – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Actual Orders Month 5-month 3-month

Copyright 2006 John Wiley & Sons, Inc Weighted Moving Average WMA n = i = 1  Wi DiWi DiWi DiWi Di where W i = the weight for period i, between 0 and 100 percent  W i = 1.00  Adjusts moving average method to more closely reflect data fluctuations

Copyright 2006 John Wiley & Sons, Inc Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 WMA 3 = 3 i = 1  Wi DiWi DiWi DiWi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = orders November Forecast

Copyright 2006 John Wiley & Sons, Inc  Averaging method  Weights most recent data more strongly  Reacts more to recent changes  Widely used, accurate method Exponential Smoothing

Copyright 2006 John Wiley & Sons, Inc F t +1 =  D t + (1 -  )F t where: F t +1 =forecast for next period D t =actual demand for present period F t =previously determined forecast for present period  =weighting factor, smoothing constant Exponential Smoothing (cont.)

Copyright 2006 John Wiley & Sons, Inc Effect of Smoothing Constant 0.0  1.0 If  = 0.20, then F t +1 = 0.20  D t F t If  = 0, then F t +1 = 0  D t + 1 F t 0 = F t Forecast does not reflect recent data If  = 1, then F t +1 = 1  D t + 0 F t =  D t Forecast based only on most recent data

Copyright 2006 John Wiley & Sons, Inc F 2 =  D 1 + (1 -  )F 1 = (0.30)(37) + (0.70)(37) = 37 F 3 =  D 2 + (1 -  )F 2 = (0.30)(40) + (0.70)(37) = 37.9 F 13 =  D 12 + (1 -  )F 12 = (0.30)(54) + (0.70)(50.84) = Exponential Smoothing (α=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54

Copyright 2006 John Wiley & Sons, Inc FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3)(  = 0.5) 1Jan37–– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan– Exponential Smoothing (cont.)

Copyright 2006 John Wiley & Sons, Inc – – – – – – – 0 0 – ||||||||||||| Actual Orders Month Exponential Smoothing (cont.)  = 0.50  = 0.30

Copyright 2006 John Wiley & Sons, Inc AF t +1 = F t +1 + T t +1 where T = an exponentially smoothed trend factor T t +1 =  (F t +1 - F t ) + (1 -  ) T t where T t = the last period trend factor  = a smoothing constant for trend Adjusted Exponential Smoothing

Copyright 2006 John Wiley & Sons, Inc Adjusted Exponential Smoothing (β=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 T 3 =  (F 3 - F 2 ) + (1 -  ) T 2 = (0.30)( ) + (0.70)(0) = 0.45 AF 3 = F 3 + T 3 = = T 13 =  (F 13 - F 12 ) + (1 -  ) T 12 = (0.30)( ) + (0.70)(1.77) = 1.36 AF 13 = F 13 + T 13 = = 54.96

Copyright 2006 John Wiley & Sons, Inc Adjusted Exponential Smoothing: Example FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan –– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan–

Copyright 2006 John Wiley & Sons, Inc Adjusted Exponential Smoothing Forecasts – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Forecast (  = 0.50) Adjusted forecast (  = 0.30)

Copyright 2006 John Wiley & Sons, Inc y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x Linear Trend Line b = a = y - b x where n =number of periods x == mean of the x values y == mean of the y values  xy - nxy  x 2 - nx 2  x n  y n

Copyright 2006 John Wiley & Sons, Inc Least Squares Example x (PERIOD) y (DEMAND) xyx

Copyright 2006 John Wiley & Sons, Inc x = = 6.5 y = = b = = =1.72 a = y - bx = (1.72)(6.5) = (12)(6.5)(46.42) (6.5) 2  xy - nxy  x 2 - nx Least Squares Example (cont.)

Copyright 2006 John Wiley & Sons, Inc Linear trend line y = x Forecast for period 13 y = (13)= units – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Linear trend line

Copyright 2006 John Wiley & Sons, Inc Seasonal Adjustments  Repetitive increase/ decrease in demand  Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

Copyright 2006 John Wiley & Sons, Inc Seasonal Adjustment (cont.) Total DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1D1DDD1D1DD S 2 = = = 0.20 D2D2DDD2D2DD S 4 = = = 0.37 D4D4DDD4D4DD S 3 = = = 0.15 D3D3DDD3D3DD

Copyright 2006 John Wiley & Sons, Inc Seasonal Adjustment (cont.) SF 1 = (S 1 ) (F 5 ) = (0.28)(58.17) = SF 2 = (S 2 ) (F 5 ) = (0.20)(58.17) = SF 3 = (S 3 ) (F 5 ) = (0.15)(58.17) = 8.73 SF 4 = (S 4 ) (F 5 ) = (0.37)(58.17) = y = x = (4) = For 2005

Copyright 2006 John Wiley & Sons, Inc Forecast Accuracy   Forecast error difference between forecast and actual demand MAD mean absolute deviation MAPD mean absolute percent deviation Cumulative error Average error or bias

Copyright 2006 John Wiley & Sons, Inc Mean Absolute Deviation (MAD) where t = period number t = period number D t = demand in period t D t = demand in period t F t = forecast for period t F t = forecast for period t n = total number of periods n = total number of periods  = absolute value  D t - F t  n MAD =

Copyright 2006 John Wiley & Sons, Inc MAD Example –– PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t |   D t - F t  n MAD= = =

Copyright 2006 John Wiley & Sons, Inc Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD =  |D t - F t |  D t Cumulative error E =  e t Average error E = etetnnetetnnn

Copyright 2006 John Wiley & Sons, Inc Comparison of Forecasts FORECASTMADMAPDE(E) Exponential smoothing (  = 0.30) % Exponential smoothing (  = 0.50) % Adjusted exponential smoothing % (  = 0.50,  = 0.30) Linear trend line %––

Copyright 2006 John Wiley & Sons, Inc Forecast Control   Tracking signal monitors the forecast to see if it is biased high or low 1 MAD ≈ 0.8 б Control limits of 2 to 5 MADs are used most frequently Tracking signal = =  (D t - F t ) MADEMAD

Copyright 2006 John Wiley & Sons, Inc Tracking Signal Values ––– DEMANDFORECAST,ERROR  E = PERIODD t F t D t - F t  (D t - F t )MAD TS 3 = = Tracking signal for period 3 – TRACKINGSIGNAL

Copyright 2006 John Wiley & Sons, Inc Tracking Signal Plot 3  3  – 2  2  – 1  1  – 0  0  – -1  -1  – -2  -2  – -3  -3  – ||||||||||||| Tracking signal (MAD) Period Exponential smoothing (  = 0.30) Linear trend line

Copyright 2006 John Wiley & Sons, Inc Statistical Control Charts  = = = =  (D t - F t ) 2 n - 1  Using  we can calculate statistical control limits for the forecast error  Control limits are typically set at  3 

Copyright 2006 John Wiley & Sons, Inc Statistical Control Charts Errors – – – 0 0 – – – – ||||||||||||| Period UCL = +3  LCL = -3 

Copyright 2006 John Wiley & Sons, Inc Regression Methods   Linear regression a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation   Correlation a measure of the strength of the relationship between independent and dependent variables

Copyright 2006 John Wiley & Sons, Inc Linear Regression y = a + bx a = y - b x b = where a =intercept b =slope of the line x == mean of the x data y == mean of the y data  xy - nxy  x 2 - nx 2  x n  y n

Copyright 2006 John Wiley & Sons, Inc Linear Regression Example xy (WINS)(ATTENDANCE) xyx

Copyright 2006 John Wiley & Sons, Inc Linear Regression Example (cont.) x = = y = = b = = = 4.06 a = y - bx = (4.06)(6.125) =  xy - nxy 2  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

Copyright 2006 John Wiley & Sons, Inc ||||||||||| ,000 60,000 – 50,000 50,000 – 40,000 40,000 – 30,000 30,000 – 20,000 20,000 – 10,000 10,000 – Linear regression line, y = x Wins, x Attendance, y Linear Regression Example (cont.) y = x y = (7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins

Copyright 2006 John Wiley & Sons, Inc Correlation and Coefficient of Determination  Correlation, r  Measure of strength of relationship  Varies between and  Coefficient of determination, r 2  Percentage of variation in dependent variable resulting from changes in the independent variable

Copyright 2006 John Wiley & Sons, Inc Computing Correlation n  xy -  x  y [ n  x 2 - (  x ) 2 ] [ n  y 2 - (  y ) 2 ] r = Coefficient of determination r 2 = (0.947) 2 = r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947

Copyright 2006 John Wiley & Sons, Inc Multiple Regression Study the relationship of demand to two or more independent variables y =  0 +  1 x 1 +  2 x 2 … +  k x k where  0 =the intercept  1, …,  k =parameters for the independent variables x 1, …, x k =independent variables

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