1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Copyright 2006 John Wiley & Sons, Inc.11-10 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

11. Copyright 2006 John Wiley & Sons, Inc.11-11 Qualitative Methods   Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts   Delphi method involves soliciting forecasts about technological advances from experts

12. Copyright 2006 John Wiley & Sons, Inc.11-12 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

13. Copyright 2006 John Wiley & Sons, Inc.11-13 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

14. Copyright 2006 John Wiley & Sons, Inc.11-14 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

15. Copyright 2006 John Wiley & Sons, Inc.11-15 Moving Average: Naïve Approach Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH -1209010075110507513011090 Nov - FORECAST

16. Copyright 2006 John Wiley & Sons, Inc.11-16 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

17. Copyright 2006 John Wiley & Sons, Inc.11-17 3-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 = 90 + 110 + 130 3 = 110 orders for Nov –––103.388.395.078.378.385.0105.0110.0MOVINGAVERAGE

18. Copyright 2006 John Wiley & Sons, Inc.11-18 5-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 = 90 + 110 + 130+75+50 5 = 91 orders for Nov –––––99.085.082.088.095.091.0MOVINGAVERAGE

19. Copyright 2006 John Wiley & Sons, Inc.11-19 Smoothing Effects 150 150 – 125 125 – 100 100 – 75 75 – 50 50 – 25 25 – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Actual Orders Month 5-month 3-month

20. Copyright 2006 John Wiley & Sons, Inc.11-20 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

21. Copyright 2006 John Wiley & Sons, Inc.11-21 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) = 103.4 orders November Forecast

22. Copyright 2006 John Wiley & Sons, Inc.11-22  Averaging method  Weights most recent data more strongly  Reacts more to recent changes  Widely used, accurate method Exponential Smoothing

23. Copyright 2006 John Wiley & Sons, Inc.11-23 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.)

24. Copyright 2006 John Wiley & Sons, Inc.11-24 Effect of Smoothing Constant 0.0  1.0 If  = 0.20, then F t +1 = 0.20  D t + 0.80 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

25. Copyright 2006 John Wiley & Sons, Inc.11-25 F 2 =  D 1 + (1 -  )F 1 = (0.10)(120) + (0.90)(120) = 120 F 3 =  D 2 + (1 -  )F 2 = (0.10)(90) + (0.90)(120) = 117 F 11 =  D 10 + (1 -  )F 10 = (0.10)(90) + (0.90)(105.34) = 103.81 Exponential Smoothing (α=0.10) PERIODMONTHDEMAND 1Jan120 2Feb90 3Mar100 4Apr75 5May 110 6Jun50 7Jul 75 8Aug 130 9Sep 110 10Oct90

26. Copyright 2006 John Wiley & Sons, Inc.11-26 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

27. Copyright 2006 John Wiley & Sons, Inc.11-27 Least Squares Example x (PERIOD) y (DEMAND) xyx 2 11201201 2901804 31003009 47530016 511055025 65030036 77552549 8130104064 911099081 1090900100 559505205385

28. Copyright 2006 John Wiley & Sons, Inc.11-28 x = = 5.5 y = = 95 b = = = -0.2424 a = y - bx = 95 - (-0.2424)(5.5) = 96.3333 5205 - (10)(5.5)(95) 385 - 10(5.5) 2  xy - nxy  x 2 - nx 2 55 10 950 10 Least Squares Example (cont.)

29. Copyright 2006 John Wiley & Sons, Inc.11-29 Seasonal Adjustments  Repetitive increase / decrease in demand  Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

30. Copyright 2006 John Wiley & Sons, Inc.11-30 Seasonal Adjustment (cont.) 2002 12.68.66.317.545.0 2003 14.110.37.518.250.1 2004 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1D1DDD1D1DD 42.0148.7 S 2 = = = 0.20 D2D2DDD2D2DD 29.5148.7 S 4 = = = 0.37 D4D4DDD4D4DD 55.3148.7 S 3 = = = 0.15 D3D3DDD3D3DD 21.9148.7

31. Copyright 2006 John Wiley & Sons, Inc.11-31 Seasonal Adjustment (cont.) SF 1 = (S 1 ) (F 5 ) = (0.28)(58.17) = 16.28 SF 2 = (S 2 ) (F 5 ) = (0.20)(58.17) = 11.63 SF 3 = (S 3 ) (F 5 ) = (0.15)(58.17) = 8.73 SF 4 = (S 4 ) (F 5 ) = (0.37)(58.17) = 21.53 y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17 For 2005

32. Copyright 2006 John Wiley & Sons, Inc.11-32 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

33. Copyright 2006 John Wiley & Sons, Inc.11-33 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 =

34. Copyright 2006 John Wiley & Sons, Inc.11-34 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

35. Copyright 2006 John Wiley & Sons, Inc.11-35 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

36. Copyright 2006 John Wiley & Sons, Inc.11-36 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

37. Copyright 2006 John Wiley & Sons, Inc.11-37 Linear Regression Example xy (WINS)(ATTENDANCE) xyx 2 436.3145.216 640.1240.636 641.2247.236 853.0424.064 644.0264.036 745.6319.249 539.0195.025 747.5332.549 49346.72167.7311

38. Copyright 2006 John Wiley & Sons, Inc.11-38 Linear Regression Example (cont.) x = = 6.125 y = = 43.36 b = = = 4.06 a = y - bx = 43.36 - (4.06)(6.125) = 18.46 49 8 346.9 8  xy - nxy 2  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

39. Copyright 2006 John Wiley & Sons, Inc.11-39 ||||||||||| 012345678910 60,000 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 = 18.46 + 4.06 x Wins, x Attendance, y Linear Regression Example (cont.) y = 18.46 + 4.06 x y = 18.46 + 4.06(7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins

40. Copyright 2006 John Wiley & Sons, Inc.11-40 Correlation and Coefficient of Determination  Correlation, r  Measure of strength of relationship  Varies between -1.00 and +1.00  Coefficient of determination, r 2  Percentage of variation in dependent variable resulting from changes in the independent variable

41. Copyright 2006 John Wiley & Sons, Inc.11-41 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 = 0.897 r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947