1. 15-1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Forecasting Chapter 15

2. 15-2 ■Forecasting Components ■Time Series Methods ■Forecast Accuracy ■Time Series Forecasting Using Excel ■Time Series Forecasting Using QM for Windows ■Regression Methods Chapter Topics Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3. 15-3 ■A variety of forecasting methods are available for use depending on the time frame of the forecast and the existence of patterns. Time Frames:  Short-range (one to two months)  Medium-range (two months to one or two years)  Long-range (more than one or two years) Patterns:  Trend  Random variations  Cycles  Seasonal Patterns Forecasting Components Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

4. 15-4 Time Horizon in Forecasting Short-term forecasts (days or weeks) are required for inventory management, production plans and resource requirements planning. Medium-term forecasts (weeks and months) are required for estimating product family sales, resource requirements in aggregate production planning. Long-term forecasts (Months and years) are required for estimating capacity needs, growth trends in strategic planning.

5. 15-5 Trend - A long-term movement of the item being forecast. Random variations - movements that are not predictable and follow no pattern. Cycle - A movement, up or down, that repeats itself over a lengthy time span. Seasonal pattern - Oscillating movement in demand that occurs periodically in the short run and is repetitive. Forecasting Components Patterns (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

6. 15-6 Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend w/Season Forecasting Components Patterns (2 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

7. 15-7 Forecasting Components Forecasting Methods Times Series - Statistical techniques that use historical data to predict future behavior. Regression Methods - Regression (or causal ) methods that attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does. Qualitative Methods - Methods using judgment, expertise and opinion to make forecasts. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

8. 15-8 Forecasting Components Qualitative Methods “Jury of executive opinion,” a qualitative technique, is the most common type of forecast for long-term strategic planning.  Performed by individuals or groups within an organization, sometimes assisted by consultants and other experts, whose judgments and opinions are considered valid for the forecasting issue.  Usually includes specialty functions such as marketing, engineering, purchasing, etc. in which individuals have experience and knowledge of the forecasted item. Supporting techniques include the Delphi Method, market research, surveys, etc. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

9. 15-9 Time Series Methods Overview Statistical techniques that make use of historical data collected over a long period of time. Methods assume that what has occurred in the past will continue to occur in the future. Forecasts based on only one factor - time. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

10. 15-10 Time-Series Methods  Time-Series Forecasting  Moving Averages  Exponential Smoothing  Exponential Smoothing with Trend Adjustment  Trend Projections using regression  Trend Projections with seasonal pattern using regression Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

11. 15-11 Time Series Methods Moving Average (1 of 5) Moving average uses values from the recent past to develop forecasts. This dampens or smoothes random increases and decreases. Useful for forecasting relatively stable items that do not display any trend or seasonal pattern. Formula for: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

12. 15-12 Example: Instant Paper Clip Supply Company forecast of orders for the month of November. Month JuneJulyAugustSeptemberOctober Order 50 75 130 110 90 Three-month moving average: Five-month moving average: Time Series Methods Moving Average (2 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

13. 15-13 Table 15.2 Three- and Five-Month Moving Averages Time Series Methods Moving Average (3 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

14. 15-14 Figure 15.2 Three- and Five-Month Moving Averages Time Series Methods Moving Average (4 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

15. 15-15 Time Series Methods Moving Average (5 of 5) Longer-period moving averages react more slowly to changes in demand than do shorter-period moving averages. The appropriate number of periods to use often requires trial-and- error experimentation. Disadvantage: Moving average does not react well to changes (trends, seasonal effects, etc.) Advantage: Easy to use and inexpensive. Good for short-term forecasting. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

16. 15-16 In a weighted moving average, user defined weights are assigned to the most recent data. Determining precise weights and number of periods requires trial- and-error experimentation. Time Series Methods Weighted Moving Average Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

17. 15-17 Exponential smoothing weights recent past data more strongly than more distant data. Two forms: simple exponential smoothing and adjusted exponential smoothing. Simple exponential smoothing: F t + 1 =  D t + (1 -  )F t where: F t + 1 = the forecast for the next period D t = actual demand in the present period F t = forecasted demand for the present period  = a weighting factor (smoothing constant). Time Series Methods Exponential Smoothing (1 of 11) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

18. 15-18 The most commonly used values of  are between 0.10 and 0.50. Determination of  is usually judgmental and subjective and often based on trial-and -error experimentation. Exponential smoothing is a sophisticated weighted average. Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast and the actual value of the series at that point. F t + 1 = F t +  (D t – F t ) Time Series Methods Exponential Smoothing (2 of 11) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

19. 15-19 Example: PM Computer Services (see Table 15.4). Exponential smoothing forecasts using smoothing constant of.30. Forecast for period 2 (February): F 2 =  D 1 + (1-  )F 1 = (.30)(37) + (.70)(37) = 37 units Forecast for period 3 (March): F 3 =  D 2 + (1-  )F 2 = (.30)(40) + (.70)(37) = 37.9 units Time Series Methods Exponential Smoothing (3 of 11) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

20. 15-20 Table 15.4 Exponential Smoothing Forecasts,  =.30 and  =.50 Time Series Methods Exponential Smoothing (4 of 11) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

21. 15-21 The forecast that uses the higher smoothing constant (.50) reacts more strongly to changes in demand than does the forecast with the lower constant (.30). Both forecasts lag behind actual demand. Both forecasts tend to be consistently lower than actual demand. Low smoothing constants are appropriate for stable data without trend; higher constants appropriate for data with trends. Time Series Methods Exponential Smoothing (5 of 11) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

22. 15-22 Figure 15.3 Exponential Smoothing Forecasts Time Series Methods Exponential Smoothing (6 of 11) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

23. 15-23 ■ When demand displays an obvious trend over time, a least squares regression method, can be used to forecast the demand. ■ Formula: Time Series Methods Linear Trend Line (1 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

24. 15-24 Example: PM Computer Services (see Table 15.6) Time Series Methods Linear Trend Line (2 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

25. 15-25 Table 15.6 Least Squares Calculations Time Series Methods Linear Trend Line (3 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

26. 15-26 Figure 15.5 Linear Trend Line Time Series Methods Linear Trend (5 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

27. 15-27 Forecasts will always deviate from actual values. Difference between forecasts and actual values referred to as forecast error. We would like forecast error to be as small as possible. If error is large, either technique being used is the wrong one, or parameters need adjusting. Measures of forecast errors:  Mean Absolute deviation (MAD)  Mean absolute percentage deviation (MAPD)  Cumulative error (E bar)  Average error, or bias (E) Forecast Accuracy Overview Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

28. 15-28 MAD is the average absolute difference between the forecast and actual demand. Most popular and simplest-to-use measures of forecast error. Formula: Forecast Accuracy Mean Absolute Deviation (1 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

29. 15-29 Example: PM Computer Services (see Table 15.8). Compare accuracies of different forecasts using MAD: Forecast Accuracy Mean Absolute Deviation (2 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

30. 15-30 Table 15.8 Computational Values for MAD and error Forecast Accuracy Mean Absolute Deviation (3 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

31. 15-31 The lower the value of MAD relative to the magnitude of the data, the more accurate the forecast. When viewed alone, MAD is difficult to assess. Must be considered in light of magnitude of the data. Forecast Accuracy Mean Absolute Deviation (4 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

32. 15-32 Can be used to compare accuracy of different forecasting techniques working on the same set of demand data (PM Computer Services): Exponential smoothing (  =.30): MAD = 53.41/11=4.85 Exponential smoothing (  =.50): MAD = 4.04 Linear trend line: MAD = 2.29 Linear trend line has lowest MAD; increasing  from.30 to.50 improved smoothed forecast. Forecast Accuracy Mean Absolute Deviation (5 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

33. 15-33 A variation on MAD is the mean absolute percent deviation (MAPD). Measures absolute error as a percentage of demand rather than per period. Eliminates problem of interpreting the measure of accuracy relative to the magnitude of the demand and forecast values. Formula: Forecast Accuracy Mean Absolute Deviation (6 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

34. 15-34 MAPD for other two forecasts: Exponential smoothing (  =.50): MAPD = 8.5% Linear trend: MAPD = 4.9% Forecast Accuracy Mean Absolute Deviation (7 of 7) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Again, Linear trend line has lowest MAPD; and increasing  from.30 to.50 improves smoothed forecast.

35. 15-35 Cumulative error is the sum of the forecast errors (E =  e t ). A relatively large positive value indicates forecast is biased low, a large negative value indicates forecast is biased high. If majority of errors are positive, then forecasted values will be consistently low; and vice versa. Cumulative error for PM Computer Services for  =.30 can be read directly from Table 15.8: E =  e t = 49.31 indicating that forecasts are frequently below the actual demand. Cumulative error for PM Computer Services for  =.50 is E = 33.21 Forecast Accuracy Cumulative Error (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

36. 15-36 Average error (bias) is the per period average of cumulative error. A large positive value of average error indicates a forecast is biased low; a large negative error indicates it is biased high. Average error for exponential smoothing forecast for  =.30 : Forecast Accuracy Average Error Bias Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

37. 15-37 Results consistent for all forecasts:  Larger value of alpha is preferable.  Adjusted forecast is more accurate than exponential smoothing.  Linear trend is more accurate than all the others. Table 15.9 Comparison of Forecasts for PM Computer Services Forecast Accuracy Example Forecasts by Different Measures Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

38. 15-38 Time series techniques relate a single variable being forecast to time. Regression is a forecasting technique that measures the relationship of one variable to one or more other variables. Simplest form of regression is linear regression. Regression Methods Overview Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

39. 15-39 Linear regression relates demand (dependent variable ) to an independent variable. Regression Methods Linear Regression Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

40. 15-40 EXAMPLE: The State University athletic department The State University athletic department wants to develop its budget for the coming year, using a forecast for football attendance. Football attendance accounts for the largest portion of its revenues, and the athletic director believes attendance is directly related to the number of wins by the team. The business manager has accumulated total annual attendance figures for the past 8 years: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

41. 15-41 State University Athletic Department. Regression Methods Linear Regression Example (1 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

42. 15-42 Regression Methods Linear Regression Example (2 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

43. 15-43 Figure 15.6 Linear Regression Line Regression Methods Linear Regression Example (3 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

44. 15-44 Problem Statement: For data below, develop an exponential smoothing forecast using  = 0.40. Evaluate the accuracy of the forecasts using MAD and cumulative error. Example Problem Solution Computer Software Firm (1 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

45. 15-45 Step 1: Compute the Exponential Smoothing Forecast. F t + 1 = F t +  (D t – F t ) Example Problem Solution Computer Software Firm (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

46. 15-46 Example Problem Solution Computer Software Firm (3 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

47. 15-47 Step 2: Compute the MAD Values MAD= 41.97/7 = 5.99 Step 3: Compute the Cumulative Error. E(F t ) = 35.97 Example Problem Solution Computer Software Firm (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

48. 15-48 For the following data: Develop a linear regression model Determine a forecast for lumber given 10 building permits in the next quarter. Example Problem Solution Building Products Store (1 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

49. 15-49 Example Problem Solution Building Products Store (2 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

50. 15-50 Step 1: Compute the Components of the Linear Regression Equation. Example Problem Solution Building Products Store (3 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

51. 15-51 Step 2: Develop the Linear regression equation. y = a + bx, y = 1.36 + 1.25x Example Problem Solution Building Products Store (4 of 5) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Step 3: Calculate the forecast for x = 10 permits. Y = a + bx = 1.36 + 1.25(10) = 13.86 or 1,386 board ft