Forecasting

1. Forecasting

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. Forecasting • Predicting the Future • Qualitative forecast methods • subjective • Quantitative forecast methods • based on mathematical formulas

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 • 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

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. Types of Forecasting Methods • Depend on • time frame • demand behavior • causes of behavior

7. 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

8. 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

9. 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

10. Forecasting Methods • Qualitative • use management judgment, expertise, and opinion to predict future demand • 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

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. 1. Identify the purpose of forecast 2. Collect historical data 3. Plot data and identify patterns 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 7. Is accuracy of forecast acceptable? 8b. Select new forecast model or adjust parameters of existing model 10. Monitor results and measure forecast accuracy 9. Adjust forecast based on additional qualitative information and insight 8a. Forecast over planning horizon Forecasting Process No Yes

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. Moving Average • Naive forecast • demand the current period is used as next period’s forecast • Simple moving average • stable demand with no pronounced behavioral patterns • Weighted moving average • weights are assigned to most recent data

15. ORDERS MONTH PER MONTH Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 FORECAST - 120 90 100 75 110 50 75 130 110 90 Nov - Moving Average:Naïve Approach

16. n i= 1  Di MAn = n where n = number of periods in the moving average Di= demand in period i Simple Moving Average

17. 3 i= 1 ORDERS MONTH PER MONTH MOVING AVERAGE  Di MA3 = Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - – – – 103.3 88.3 95.0 78.3 78.3 85.0 105.0 3 = orders for Nov = 3-month Simple Moving Average

18. 5 i= 1 ORDERS MONTH PER MONTH MOVING AVERAGE  Di MA5 = Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - – – – – – 99.0 85.0 82.0 88.0 95.0 5 = = orders for Nov 5-month Simple Moving Average

19. 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

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

21. 3 i = 1  WMA3 = Wi Di November Forecast = = orders Weighted Moving Average Example MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90

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

23. Exponential Smoothing (cont.) 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

24. 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

25. 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 = = F3 = D2 + (1 - )F2 = = F13 = D12 + (1 - )F12 = = Exponential Smoothing (α=0.30)

26. 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 – Exponential Smoothing (cont.)

27. 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 (cont.)

28. Adjusted Exponential Smoothing AFt +1 = Ft +1 + Tt +1 where T = an exponentially smoothed trend factor Tt +1 = (Ft +1 - Ft) + (1 - ) Tt where Tt= the last period trend factor = a smoothing constant for trend

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 T3 = (F3 - F2) + (1 - ) T2 = = AF3 = F3 + T3 = = T13 = (F13 - F12) + (1 - ) T12 = = AF13 = F13 + T13 = = Adjusted Exponential Smoothing (β=0.30)

30. FORECAST TREND ADJUSTED PERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +1 1 Jan 37 37.00 – – 2 Feb 40 37.00 0.00 37.00 3 Mar 41 38.50 0.45 38.95 4 Apr 37 39.75 0.69 40.44 5 May 45 38.37 0.07 38.44 6 Jun 50 38.37 0.07 38.44 7 Jul 43 45.84 1.97 47.82 8 Aug 47 44.42 0.95 45.37 9 Sep 56 45.71 1.05 46.76 10 Oct 52 50.85 2.28 58.13 11 Nov 55 51.42 1.76 53.19 12 Dec 54 53.21 1.77 54.98 13 Jan – Adjusted Exponential Smoothing: Example

31. 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Adjusted forecast ( = 0.30) Actual Demand Forecast ( = 0.50) | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Period Adjusted Exponential Smoothing Forecasts

32. 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 b = slope of the line x = time period y = forecast for demand for period x

33. x(PERIOD) y(DEMAND) xy x2 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 Least Squares Example

34. x = = y = = b = = = a = y - bx = = xy - nxy x2 - nx2 Least Squares Example (cont.)

35. Linear trend line y = 35.2 + 1.72x Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units 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

36. Di D Seasonal factor = Si = Seasonal Adjustments Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast

37. DEMAND (1000’S PER QUARTER) YEAR 1 2 3 4 Total 2003 12.6 8.6 6.3 17.5 2004 14.1 10.3 7.5 18.2 2005 15.3 10.6 8.1 19.6 Total D1 D D2 D D4 D D3 D S1 = = = S2 = = = S4 = = = S3 = = = Seasonal Adjustment (cont.)

38. For 2006 y = = = SF1 = (S1) (F5) = = SF2 = (S2) (F5) = = SF3 = (S3) (F5) = = SF4 = (S4) (F5) = = Seasonal Adjustment (cont.)

39. 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

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

41. 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

42. Mean absolute percent deviation (MAPD) MAPD = |Dt - Ft| Dt Cumulative error E = et et n Average error E = Other Accuracy Measures

43. FORECAST MAD MAPD E (E) Exponential smoothing (= 0.30) 4.85 9.6% 49.31 4.48 Exponential smoothing (= 0.50) 4.04 8.5% 33.21 3.02 Adjusted exponential smoothing 3.81 7.5% 21.14 1.92 (= 0.50, = 0.30) Linear trend line 2.29 4.9% – – Comparison of Forecasts

44. (Dt - Ft) MAD E MAD Tracking signal = = 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

45. DEMAND FORECAST, ERROR E = PERIOD DtFtDt - Ft(Dt - Ft) MAD TRACKING SIGNAL 1 37 37.00 – – – 2 40 37.00 3.00 3.00 3.00 3 41 37.90 3.10 6.10 3.05 4 37 38.83 -1.83 4.27 2.64 5 45 38.28 6.72 10.99 3.66 6 50 40.29 9.69 20.68 4.87 7 43 43.20 -0.20 20.48 4.09 8 47 43.14 3.86 24.34 4.06 9 56 44.30 11.70 36.04 5.01 10 52 47.81 4.19 40.23 4.92 11 55 49.06 5.94 46.17 5.02 12 54 50.84 3.15 49.32 4.85 – 1.00 2.00 1.62 3.00 4.25 5.01 6.00 7.19 8.18 9.20 10.17 Tracking Signal Values

46. Exponential smoothing ( = 0.30) Linear trend line Tracking Signal Plot 3 – 2 – 1 – 0 – -1 – -2 – -3 – Tracking signal (MAD) | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 Period

47.  = (Dt - Ft)2 n - 1 Statistical Control Charts Using  we can calculate statistical control limits for the forecast error Control limits are typically set at  3

48. 18.39– 12.24– 6.12– 0– -6.12– -12.24– -18.39– UCL = +3 Errors LCL = -3 | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 Period Statistical Control Charts

49. 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

50. 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 x2- nx2 x n y n Linear Regression