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Chapter 8

Chapter 8. Forecasting. To Accompany Russell and Taylor, Operations Management, 4th Edition ,  2003 Prentice-Hall, Inc. All rights reserved. Forecasting. Predicting future events Usually demand behavior over a time frame Qualitative methods Based on subjective methods

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Chapter 8

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  1. Chapter 8 Forecasting To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

  2. Forecasting • Predicting future events • Usually demand behavior over a time frame • Qualitative methods • Based on subjective methods • Quantitative methods • Based on mathematical formulas

  3. Strategic Role of Forecasting • Focus on supply chain management • Short term role of product demand • Long term role of new products, processes, and technologies • Focus on Total Quality Management • Satisfy customer demand • Uninterrupted product flow with no defective items • Necessary for strategic planning

  4. Components of Forecasting Demand • Time Frame • Short-range, medium-range, long-range • Demand Behavior • Trends, cycles, seasonal patterns, random

  5. Time Frame • Short-range to medium-range • Daily, weekly monthly forecasts of sales data • Up to 2 years into the future • Long-range • Strategic planning of goals, products, markets • Planning beyond 2 years into the future

  6. Demand Behavior • Trend • gradual, long-term up or down movement • Cycle • up & down movement repeating over long time frame • Seasonal pattern • periodic oscillation in demand which repeats • Random movements follow no pattern

  7. Demand Demand Random movement Time (a) Trend Time (b) Cycle Demand Demand Time (c) Seasonal pattern Time (d) Trend with seasonal pattern Forms of Forecast Movement Figure 8.1

  8. Forecasting Methods • Time series • Regression or causal modeling • Qualitative methods • Management judgment, expertise, opinion • Use management, marketing, purchasing, engineering • Delphi method • Solicit forecasts from experts

  9. 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data 6. Check forecast accuracy with one or more measures 5. Develop/compute forecast for period of historical data 4. Select a forecast model that seems appropriate for data 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8a. Forecast over planning horizon Forecasting Process Figure 8.2

  10. Time Series Methods • Statistical methods using historical data • Moving average • Exponential smoothing • Linear trend line • Assume patterns will repeat • Naive forecasts • Forecast = data from last period Demand?

  11. Moving Average • Average several periods of data • Dampen, smooth out changes • Use when demand is stable with no trend or seasonal pattern

  12. n i= 1  Di MAn = n where n = number of periods in the moving average Di= demand in period i Moving Average • Average several periods of data • Dampen, smooth out changes • Use when demand is stable with no trend or seasonal pattern

  13. ORDERS MONTH PER MONTH Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Simple Moving Average Example 8.1

  14. 3 i= 1 ORDERS MONTH PER MONTH  Di MA3 = Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 3 90 + 110 + 130 3 = Simple Moving Average = 110 orders for Nov Example 8.1

  15. ORDERS THREE-MONTH MONTH PER MONTH MOVING AVERAGE Jan 120 – Feb 90 – Mar 100 – Apr 75 103.3 May 110 88.3 June 50 95.0 July 75 78.3 Aug 130 78.3 Sept 110 85.0 Oct 90 105.0 Nov – 110.0 Simple Moving Average Example 8.1

  16. 5 i= 1 ORDERS THREE-MONTH MONTH PER MONTH MOVING AVERAGE  Di MA5 = Jan 120 – Feb 90 – Mar 100 – Apr 75 103.3 May 110 88.3 June 50 95.0 July 75 78.3 Aug 130 78.3 Sept 110 85.0 Oct 90 105.0 Nov – 110.0 5 90 + 110 + 130 + 75 + 50 5 = Simple Moving Average = 91 orders for Nov Example 8.1

  17. ORDERS THREE-MONTH FIVE-MONTH MONTH PER MONTH MOVING AVERAGE MOVING AVERAGE Jan 120 – – Feb 90 – – Mar 100 – – Apr 75 103.3 – May 110 88.3 – June 50 95.0 99.0 July 75 78.3 85.0 Aug 130 78.3 82.0 Sept 110 85.0 88.0 Oct 90 105.0 95.0 Nov – 110.0 91.0 Simple Moving Average Example 8.1

  18. 150 – 125 – 100 – 75 – 50 – 25 – 0 – Orders | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Month Smoothing Effects Figure 8.2

  19. 150 – 125 – 100 – 75 – 50 – 25 – 0 – Orders Actual | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Month Smoothing Effects Figure 8.2

  20. 150 – 125 – 100 – 75 – 50 – 25 – 0 – Orders 3-month Actual | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Month Smoothing Effects Figure 8.2

  21. 150 – 125 – 100 – 75 – 50 – 25 – 0 – 5-month Orders 3-month Actual | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Month Smoothing Effects Figure 8.2

  22. Weighted Moving Average • Adjusts moving average method to more closely reflect data fluctuations

  23. Wi Di WMAn = i = 1 where Wi = the weight for period i, between 0 and 100 percent  Wi= 1.00 Weighted Moving Average • Adjusts moving average method to more closely reflect data fluctuations

  24. MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 Weighted Moving Average Example Example 8.2

  25. MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 November forecast 3 i = 1  WMA3 = Wi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders Weighted Moving Average Example Example 8.2

  26. Exponential Smoothing • Averaging method • Weights most recent data more strongly • Reacts more to recent changes • Widely used, accurate method

  27. Exponential Smoothing Ft +1 = Dt + (1 - )Ft where Ft +1 = forecast for next period Dt= actual demand for present period Ft= previously determined forecast for present period = weighting factor, smoothing constant • Averaging method • Weights most recent data more strongly • Reacts more to recent changes • Widely used, accurate method

  28. Effect of Smoothing Constant 0.0  1.0If = 0.20, then Ft +1 = 0.20Dt + 0.80 Ft If = 0, then Ft+1 = 0Dt + 1 Ft0 = FtForecast does not reflect recent data If = 1, then Ft +1 = 1Dt + 0 Ft=DtForecast based only on most recent data

  29. PERIOD MONTH DEMAND 1 Jan 37 2 Feb 40 3 Mar 41 4 Apr 37 5 May 45 6 Jun 50 7 Jul 43 8 Aug 47 9 Sep 56 10 Oct 52 11 Nov 55 12 Dec 54 Exponential Smoothing Example 8.3

  30. PERIOD MONTH DEMAND 1 Jan 37 2 Feb 40 3 Mar 41 4 Apr 37 5 May 45 6 Jun 50 7 Jul 43 8 Aug 47 9 Sep 56 10 Oct 52 11 Nov 55 12 Dec 54 F2 = D1 + (1 - )F1 = (0.30)(37) + (0.70)(37) = 37 F3 = D2 + (1 - )F2 = (0.30)(40) + (0.70)(37) = 37.9 F13 = D12 + (1 - )F12 = (0.30)(54) + (0.70)(50.84) = 51.79 Exponential Smoothing Example 8.3

  31. FORECAST, Ft + 1 PERIOD MONTH DEMAND ( = 0.3) 1 Jan 37 – 2 Feb 40 37.00 3 Mar 41 37.90 4 Apr 37 38.83 5 May 45 38.28 6 Jun 50 40.29 7 Jul 43 43.20 8 Aug 47 43.14 9 Sep 56 44.30 10 Oct 52 47.81 11 Nov 55 49.06 12 Dec 54 50.84 13 Jan – 51.79 Exponential Smoothing Example 8.3

  32. FORECAST, Ft + 1 PERIOD MONTH DEMAND ( = 0.3) ( = 0.5) 1 Jan 37 – – 2 Feb 40 37.00 37.00 3 Mar 41 37.90 38.50 4 Apr 37 38.83 39.75 5 May 45 38.28 38.37 6 Jun 50 40.29 41.68 7 Jul 43 43.20 45.84 8 Aug 47 43.14 44.42 9 Sep 56 44.30 45.71 10 Oct 52 47.81 50.85 11 Nov 55 49.06 51.42 12 Dec 54 50.84 53.21 13 Jan – 51.79 53.61 Exponential Smoothing Example 8.3

  33. 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Actual Orders | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Month Exponential Smoothing Forecasts Figure 8.3

  34. 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Actual Orders  = 0.30 | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Month Exponential Smoothing Forecasts Figure 8.3

  35. 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Actual  = 0.50 Orders  = 0.30 | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Month Exponential Smoothing Forecasts Figure 8.3

  36. Linear Trend Line y = a + bx where a = intercept (at period 0) b = slope of the line x = the time period y = forecast for demand for period x

  37. xy - nxy x2- nx2 b = a = y - b x where n = number of periods x = = mean of the x values y = = mean of the y values x n y n Linear Trend Line y = a + bx where a = intercept (at period 0) b = slope of the line x = the time period y = forecast for demand for period x

  38. x(PERIOD) y(DEMAND) 1 73 2 40 3 41 4 37 5 45 6 50 7 43 8 47 9 56 10 52 11 55 12 54 78 557 Least Squares Example Example 8.5

  39. x(PERIOD) y(DEMAND) xy x2 1 73 73 1 2 40 80 4 3 41 123 9 4 37 148 16 5 45 225 25 6 50 300 36 7 43 301 49 8 47 376 64 9 56 504 81 10 52 520 100 11 55 605 121 12 54 648 144 78 557 3867 650 Least Squares Example Example 8.5

  40. x(PERIOD) y(DEMAND) xy x2 557 12 78 12 1 73 37 1 2 40 80 4 3 41 123 9 4 37 148 16 5 45 225 25 6 50 300 36 7 43 301 49 8 47 376 64 9 56 504 81 10 52 520 100 11 55 605 121 12 54 648 144 78 557 3867 650 x = = 6.5 y = = 46.42 b = = = 1.72 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 xy - nxy x2 - nx2 3867 - (12)(6.5)(46.42) 650 - 12(6.5)2 Least Squares Example Example 8.5

  41. Linear trend line x(PERIOD) y(DEMAND) xy x2 y = 35.2 + 1.72x 557 12 78 12 1 73 37 1 2 40 80 4 3 41 123 9 4 37 148 16 5 45 225 25 6 50 300 36 7 43 301 49 8 47 376 64 9 56 504 81 10 52 520 100 11 55 605 121 12 54 648 144 78 557 3867 650 x = = 6.5 y = = 46.42 b = = = 1.72 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 xy - nxy x2 - nx2 3867 - (12)(6.5)(46.42) 650 - 12(6.5)2 Least Squares Example Example 8.5

  42. x(PERIOD) y(DEMAND) xy x2 Linear trend line 557 12 78 12 1 73 37 1 2 40 80 4 3 41 123 9 4 37 148 16 5 45 225 25 6 50 300 36 7 43 301 49 8 47 376 64 9 56 504 81 10 52 520 100 11 55 605 121 12 54 648 144 78 557 3867 650 x = = 6.5 y = = 46.42 b = = = 1.72 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 y = 35.2 + 1.72x Forecast for period 13 y = 35.2 + 1.72(13) xy - nxy x2 - nx2 3867 - (12)(6.5)(46.42) 650 - 12(6.5)2 y = 57.56 units Least Squares Example Example 8.5

  43. 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Actual Demand | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Period Linear Trend Line Example 8.5

  44. 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Actual Demand Linear trend line | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Period Linear Trend Line Example 8.5

  45. Forecast Accuracy • Error = Actual - Forecast • Find a method which minimizes error • Mean Absolute Deviation (MAD) • Mean Absolute Percent Deviation (MAPD) • Cumulative Error (E)

  46. Dt - Ft n MAD = Mean Absolute Deviation (MAD) where t = the period number Dt = demand in period t Ft = the forecast for period t n = the total number of periods  = the absolute value

  47. PERIOD DEMAND, DtFt ( =0.3) 1 37 37.00 2 40 37.00 3 41 37.90 4 37 38.83 5 45 38.28 6 50 40.29 7 43 43.20 8 47 43.14 9 56 44.30 10 52 47.81 11 55 49.06 12 54 50.84 557 MAD Example Example 8.7

  48. PERIOD DEMAND, DtFt ( =0.3) (Dt - Ft) |Dt - Ft| 1 37 37.00 – – 2 40 37.00 3.00 3.00 3 41 37.90 3.10 3.10 4 37 38.83 -1.83 1.83 5 45 38.28 6.72 6.72 6 50 40.29 9.69 9.69 7 43 43.20 -0.20 0.20 8 47 43.14 3.86 3.86 9 56 44.30 11.70 11.70 10 52 47.81 4.19 4.19 11 55 49.06 5.94 5.94 12 54 50.84 3.15 3.15 557 49.31 53.39 MAD Example Example 8.7

  49. PERIOD DEMAND, DtFt ( =0.3) (Dt - Ft) |Dt - Ft| 1 37 37.00 – – 2 40 37.00 3.00 3.00 3 41 37.90 3.10 3.10 4 37 38.83 -1.83 1.83 5 45 38.28 6.72 6.72 6 50 40.29 9.69 9.69 7 43 43.20 -0.20 0.20 8 47 43.14 3.86 3.86 9 56 44.30 11.70 11.70 10 52 47.81 4.19 4.19 11 55 49.06 5.94 5.94 12 54 50.84 3.15 3.15 557 49.31 53.39 • Dt - Ft n MAD = = = 4.85 53.39 11 MAD Example Example 8.7

  50. Forecast Control • Reasons for out-of-control forecasts • Change in trend • Appearance of cycle • Weather changes • Promotions • Competition • Politics

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