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Chapter 12 Forecasting

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Lecture Outline Strategic Role of Forecasting in Supply Chain Management Components of Forecasting Demand Time Series Methods Forecast Accuracy Time Series Forecasting Using Excel Regression Methods Copyright 2011 John Wiley & Sons, Inc.12-2

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Forecasting Predicting the future Qualitative forecast methods subjective Quantitative forecast methods based on mathematical formulas Copyright 2011 John Wiley & Sons, Inc.12-3

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Supply Chain Management Accurate forecasting determines inventory levels in the supply chain Continuous replenishment supplier & customer share continuously updated data typically managed by the supplier reduces inventory for the company speeds customer delivery Variations of continuous replenishment quick response JIT (just-in-time) VMI (vendor-managed inventory) stockless inventory Copyright 2011 John Wiley & Sons, Inc.12-4

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The Effect of Inaccurate Forecasting Copyright 2011 John Wiley & Sons, Inc.12-5

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Forecasting Quality Management Accurately forecasting customer demand is a key to providing good quality service Strategic Planning Successful strategic planning requires accurate forecasts of future products and markets Copyright 2011 John Wiley & Sons, Inc.12-6

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Types of Forecasting Methods Depend on time frame demand behavior causes of behavior Copyright 2011 John Wiley & Sons, Inc.12-7

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Time Frame Indicates how far into the future is forecast Short- to mid-range forecast typically encompasses the immediate future daily up to two years Long-range forecast usually encompasses a period of time longer than two years Copyright 2011 John Wiley & Sons, Inc.12-8

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Demand Behavior Trend a gradual, long-term up or down movement of demand Random variations movements in demand that do not follow a pattern Cycle an up-and-down repetitive movement in demand Seasonal pattern an up-and-down repetitive movement in demand occurring periodically Copyright 2011 John Wiley & Sons, Inc.12-9

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Forms of Forecast Movement Copyright 2011 John Wiley & Sons, Inc Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Random movement

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Forecasting Methods Time series 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 Qualitative use management judgment, expertise, and opinion to predict future demand Copyright 2011 John Wiley & Sons, Inc.12-11

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Qualitative Methods Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts Delphi method involves soliciting forecasts about technological advances from experts Copyright 2011 John Wiley & Sons, Inc.12-12

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Forecasting Process Copyright 2011 John Wiley & Sons, Inc 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

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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 2011 John Wiley & Sons, Inc.12-14

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Moving Average Naive forecast demand in current period is used as next period’s forecast Simple moving average uses average demand for a fixed sequence of periods stable demand with no pronounced behavioral patterns Weighted moving average weights are assigned to most recent data Copyright 2011 John Wiley & Sons, Inc.12-15

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Moving Average: Naïve Approach Copyright 2011 John Wiley & Sons, Inc Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH Nov - FORECAST

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Simple Moving Average Copyright 2011 John Wiley & Sons, Inc MA n = n i = 1 DiDi n where n =number of periods in the moving average D i =demand in period i

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3-month Simple Moving Average Copyright 2011 John Wiley & Sons, Inc Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1 DiDi 3 = = 110 orders for Nov – MOVING AVERAGE

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5-month Simple Moving Average Copyright 2011 John Wiley & Sons, Inc MA 5 = 5 i = 1 DiDi 5 = = 91 orders for Nov Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH – MOVING AVERAGE

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Smoothing Effects Copyright 2011 John Wiley & Sons, Inc – 125 – 100 – 75 – 50 – 25 – 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Actual Orders Month 5-month 3-month

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Weighted Moving Average Copyright 2011 John Wiley & Sons, Inc Adjusts moving average method to more closely reflect data fluctuations WMA n = i = 1 W i D i where W i = the weight for period i, between 0 and 100 percent W i = 1.00 n

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Weighted Moving Average Example Copyright 2011 John Wiley & Sons, Inc MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 WMA 3 = 3 i = 1 W i D i = (0.50)(90) + (0.33)(110) + (0.17)(130) = orders November Forecast

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Exponential Smoothing Copyright 2011 John Wiley & Sons, Inc Averaging method Weights most recent data more strongly Reacts more to recent changes Widely used, accurate method

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Exponential Smoothing Copyright 2011 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

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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 = 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 Effect of Smoothing Constant Copyright 2011 John Wiley & Sons, Inc.12-25

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Exponential Smoothing (α=0.30) Copyright 2011 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) = PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54

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Exponential Smoothing Copyright 2011 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–

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Exponential Smoothing Copyright 2011 John Wiley & Sons, Inc – 60 – 50 – 40 – 30 – 20 – 10 – 0 – ||||||||||||| Actual Orders Month = 0.50 = 0.30

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Adjusted Exponential Smoothing Copyright 2011 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 0 ≤ ≤

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Adjusted Exponential Smoothing (β=0.30) Copyright 2011 John Wiley & Sons, Inc 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 = = 54.97

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Adjusted Exponential Smoothing Copyright 2011 John Wiley & Sons, Inc FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan –– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan–

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Adjusted Exponential Smoothing Forecasts Copyright 2011 John Wiley & Sons, Inc – 60 – 50 – 40 – 30 – 20 – 10 – 0 – ||||||||||||| Actual Demand Period Forecast ( = 0.50) Adjusted forecast ( = 0.30)

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Linear Trend Line Copyright 2011 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 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

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Least Squares Example Copyright 2011 John Wiley & Sons, Inc x (PERIOD) y (DEMAND) xyx

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Least Squares Example Copyright 2011 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

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Copyright 2011 John Wiley & Sons, Inc Linear trend line y = x Forecast for period 13 y = (13) = units 70 – 60 – 50 – 40 – 30 – 20 – 10 – ||||||||||||| Actual Demand Period Linear trend line

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Seasonal Adjustments Copyright 2011 John Wiley & Sons, Inc Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Seasonal factor = S i = DiDDiD

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Seasonal Adjustment Copyright 2011 John Wiley & Sons, Inc Total DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1DD1D S 2 = = = 0.20 D2DD2D S 4 = = = 0.37 D4DD4D S 3 = = = 0.15 D3DD3D

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Seasonal Adjustment Copyright 2011 John Wiley & Sons, Inc 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

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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 2011 John Wiley & Sons, Inc.12-40

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Mean Absolute Deviation (MAD) Copyright 2011 John Wiley & Sons, Inc where t = period number D t = demand in period t F t = forecast for period t n = total number of periods = absolute value D t - F t n MAD =

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Copyright 2011 John Wiley & Sons, Inc MAD Example –– PERIODDEMAND, D t F t ( =0.3)(D t - F t ) |D t - F t |

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MAD Calculation Copyright 2011 John Wiley & Sons, Inc D t - F t n MAD= = =

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Other Accuracy Measures Copyright 2011 John Wiley & Sons, Inc Mean absolute percent deviation (MAPD) MAPD = |D t - F t | D t Cumulative error E = e t Average error E = etnetn

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Comparison of Forecasts Copyright 2011 John Wiley & Sons, Inc FORECASTMADMAPDE(E) Exponential smoothing ( = 0.30) % Exponential smoothing ( = 0.50) % Adjusted exponential smoothing % ( = 0.50, = 0.30) Linear trend line %––

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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 Copyright 2011 John Wiley & Sons, Inc Tracking signal = = (D t - F t ) MAD E MAD

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Tracking Signal Values Copyright 2011 John Wiley & Sons, Inc ––– DEMANDFORECAST,ERROR E = PERIODD t F t D t - F t (D t - F t )MAD – TRACKING SIGNAL TS 3 = =

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Tracking Signal Plot Copyright 2011 John Wiley & Sons, Inc – 2 – 1 – 0 – -1 – -2 – -3 – ||||||||||||| Tracking signal (MAD) Period Exponential smoothing ( = 0.30) Linear trend line

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Statistical Control Charts Copyright 2011 John Wiley & Sons, Inc = (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

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Statistical Control Charts Copyright 2011 John Wiley & Sons, Inc Errors – – 6.12 – 0 – – – – ||||||||||||| Period UCL = +3 LCL = -3

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Time Series Forecasting Using Excel Excel can be used to develop forecasts: Moving average Exponential smoothing Adjusted exponential smoothing Linear trend line Copyright 2011 John Wiley & Sons, Inc.12-51

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Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts Copyright 2011 John Wiley & Sons, Inc =B5*(C11-C10)+ (1-B5)*D10 =C10+D10 =ABS(B10-E10) =SUM(F10:F20) =G22/11

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Demand and Exponentially Smoothed Forecast Copyright 2011 John Wiley & Sons, Inc Click on “Insert” then “Line”

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Data Analysis Option Copyright 2011 John Wiley & Sons, Inc.12-54

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Forecasting With Seasonal Adjustment Copyright 2011 John Wiley & Sons, Inc.12-55

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Forecasting With OM Tools Copyright 2011 John Wiley & Sons, Inc.12-56

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Regression Methods Linear regression 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 2011 John Wiley & Sons, Inc.12-57

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Linear Regression Copyright 2011 John Wiley & Sons, Inc 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

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Linear Regression Example Copyright 2011 John Wiley & Sons, Inc xy (WINS)(ATTENDANCE) xyx

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Linear Regression Example Copyright 2011 John Wiley & Sons, Inc 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

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Linear Regression Example Copyright 2011 John Wiley & Sons, Inc ||||||||||| ,000 – 50,000 – 40,000 – 30,000 – 20,000 – 10,000 – Linear regression line, y = x Wins, x Attendance, y y = (7) = 46.88, or 46,880 Attendance forecast for 7 wins

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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 2011 John Wiley & Sons, Inc.12-62

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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 = Computing Correlation Copyright 2011 John Wiley & Sons, Inc.12-63

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Regression Analysis With Excel Copyright 2011 John Wiley & Sons, Inc =INTERCEPT(B5:B12,A5:A12) =CORREL(B5:B12,A5:A12) =SUM(B5:B12)

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Regression Analysis with Excel Copyright 2011 John Wiley & Sons, Inc.12-65

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Regression Analysis With Excel Copyright 2011 John Wiley & Sons, Inc.12-66

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Multiple Regression Copyright 2011 John Wiley & Sons, Inc 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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Multiple Regression With Excel Copyright 2011 John Wiley & Sons, Inc r 2, the coefficient of determination Regression equation coefficients for x 1 and x 2

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Multiple Regression Example Copyright 2011 John Wiley & Sons, Inc y = 19, x x 2 y = 19, (7) (60,000) = 46,229.35

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Copyright 2011 John Wiley & Sons, Inc Copyright 2011 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.

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