1. Forecasting
Chapter 15

2. Chapter Topics Forecasting Components Time Series Methods
Forecast Accuracy
Time Series Forecasting Using Excel
Time Series Forecasting Using QM for Windows
Regression Methods
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3. Forecasting Components
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 pattern
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4. Forecasting Components Patterns (1 of 2)
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.
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5. Forecasting Components Patterns (2 of 2)
Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend w/Season
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6. 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.
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7. 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.
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8. 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.
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9. 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:
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10. Time Series Methods Moving Average (2 of 5)
Example: Instant Paper Clip Supply Company forecast of orders for the month of November.
Three-month moving average:
Five-month moving average:
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11. Time Series Methods Moving Average (3 of 5)
Table Three- and Five-Month Moving Averages
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12. Time Series Methods Moving Average (4 of 5)
Figure Three- and Five-Month Moving Averages
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13. 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.
Moving average does not react well to changes (trends, seasonal effects, etc.) but is easy to use and inexpensive.
Good for short-term forecasting.
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14. Weighted Moving Average
Time Series Methods
Weighted Moving Average
In a weighted moving average, weights are assigned to the most recent data.
Determining precise weights and number of periods requires trial-and-error experimentation.
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15. Exponential Smoothing (1 of 11)
Time Series Methods
Exponential Smoothing (1 of 11)
Exponential smoothing weights recent past data more strongly than more distant data.
Two forms: simple exponential smoothing and adjusted exponential smoothing.
Simple exponential smoothing:
Ft + 1 = Dt + (1 - )Ft
where: Ft + 1 = the forecast for the next period
Dt = actual demand in the present period
Ft = the previously determined forecast for the present period
 = a weighting factor (smoothing constant).
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16. Exponential Smoothing (2 of 11)
Time Series Methods
Exponential Smoothing (2 of 11)
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.
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17. Exponential Smoothing (3 of 11)
Time Series Methods
Exponential Smoothing (3 of 11)
Example: PM Computer Services (see Table 15.4).
Exponential smoothing forecasts using smoothing constant of .30.
Forecast for period 2 (February):
F2 =  D1 + (1- )F1 = (.30)(.37) + (.70)(.37) = 37 units
Forecast for period 3 (March):
F3 =  D2 + (1- )F2 = (.30)(.40) + (.70)(37) = 37.9 units
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18. Exponential Smoothing (4 of 11)
Time Series Methods
Exponential Smoothing (4 of 11)
Table Exponential Smoothing Forecasts,  = .30 and  = .50
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19. Exponential Smoothing (5 of 11)
Time Series Methods
Exponential Smoothing (5 of 11)
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.
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20. Exponential Smoothing (6 of 11)
Time Series Methods
Exponential Smoothing (6 of 11)
Figure Exponential Smoothing Forecasts
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21. Exponential Smoothing (7 of 11)
Time Series Methods
Exponential Smoothing (7 of 11)
Adjusted exponential smoothing: exponential smoothing with a trend adjustment factor added.
Formula:
AFt + 1 = Ft Tt+1
where: T = an exponentially smoothed trend factor
Tt (Ft Ft) + (1 - )Tt
Tt = the last period trend factor
 = smoothing constant for trend ( a value between zero and one).
Reflects the weight given to the most recent trend data.
Determined subjectively.
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22. Exponential Smoothing (8 of 11)
Time Series Methods
Exponential Smoothing (8 of 11)
Example: PM Computer Services exponential smoothed
forecasts with  = .50 and  = .30 (see Table 15.5).
Adjusted forecast for period 3:
T3 = (F3 - F2) + (1 - )T2
= (.30)( ) + (.70)(0) = 0.45
AF3 = F3 + T3 = = 38.95
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23. Exponential Smoothing (9 of 11)
Time Series Methods
Exponential Smoothing (9 of 11)
Table Adjusted Exponentially Smoothed Forecast Values
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24. Exponential Smoothing (10 of 11)
Time Series Methods
Exponential Smoothing (10 of 11)
Adjusted forecast is consistently higher than the simple exponentially smoothed forecast.
It is more reflective of the generally increasing trend of the data.
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25. Exponential Smoothing (11 of 11)
Time Series Methods
Exponential Smoothing (11 of 11)
Figure Adjusted Exponentially Smoothed Forecast
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26. Time Series Methods Linear Trend Line (1 of 5)
When demand displays an obvious trend over time, a least squares regression line , or linear trend line, can be used to forecast.
Formula:
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27. Time Series Methods Linear Trend Line (2 of 5)
Example: PM Computer Services (see Table 15.6)
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28. Least Squares Calculations
Time Series Methods
Linear Trend Line (3 of 5)
Table 15.6
Least Squares Calculations
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29. Time Series Methods Linear Trend Line (4 of 5)
A trend line does not adjust to a change in the trend as does the exponential smoothing method.
This limits its use to shorter time frames in which trend will not change.
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30. Time Series Methods Linear Trend (5 of 5)
Figure Linear Trend Line
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31. Seasonal Adjustments (1 of 4)
Time Series Methods
Seasonal Adjustments (1 of 4)
A seasonal pattern is a repetitive up-and-down movement in demand.
Seasonal patterns can occur on a quarterly, monthly, weekly, or daily basis.
A seasonally adjusted forecast can be developed by multiplying the normal forecast by a seasonal factor.
A seasonal factor can be determined by dividing the actual demand for each seasonal period by total annual demand:
Si =Di/D
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32. Seasonal Adjustments (2 of 4)
Time Series Methods
Seasonal Adjustments (2 of 4)
Seasonal factors lie between zero and one and represent the portion of total annual demand assigned to each season.
Seasonal factors are multiplied by annual demand to provide adjusted forecasts for each period.
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33. Table 15.7 Demand for Turkeys at Wishbone Farms
Time Series Methods
Seasonal Adjustments (3 of 4)
Example: Wishbone Farms
Table Demand for Turkeys at Wishbone Farms
S1 = D1/ D = 42.0/148.7 = 0.28
S2 = D2/ D = 29.5/148.7 = 0.20
S3 = D3/ D = 21.9/148.7 = 0.15
S4 = D4/ D = 55.3/148.7 = 0.37
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34. Seasonal Adjustments (4 of 4)
Time Series Methods
Seasonal Adjustments (4 of 4)
Multiply forecasted demand for entire year by seasonal factors to determine quarterly demand.
Forecast for entire year (trend line for data in Table 15.7):
y = x = (4) = 58.17
Seasonally adjusted forecasts:
SF1 = (S1)(F5) = (.28)(58.17) = 16.28
SF2 = (S2)(F5) = (.20)(58.17) = 11.63
SF3 = (S3)(F5) = (.15)(58.17) = 8.73
SF4 = (S4)(F5) = (.37)(58.17) = 21.53
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35. Forecast Accuracy Overview
Forecasts will always deviate from actual values.
Difference between forecasts and actual values referred to as forecast error.
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)
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36. Mean Absolute Deviation (1 of 7)
Forecast Accuracy
Mean Absolute Deviation (1 of 7)
MAD is the average absolute difference between the forecast and actual demand.
Most popular and simplest-to-use measures of forecast error.
Formula:
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37. Mean Absolute Deviation (2 of 7)
Forecast Accuracy
Mean Absolute Deviation (2 of 7)
Example: PM Computer Services (see Table 15.8).
Compare accuracies of different forecasts using MAD:
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38. Mean Absolute Deviation (3 of 7)
Forecast Accuracy
Mean Absolute Deviation (3 of 7)
Table Computational Values for MAD and error
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39. Mean Absolute Deviation (4 of 7)
Forecast Accuracy
Mean Absolute Deviation (4 of 7)
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.
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40. Mean Absolute Deviation (5 of 7)
Forecast Accuracy
Mean Absolute Deviation (5 of 7)
Can be used to compare accuracy of different forecasting techniques working on the same set of demand data (PM Computer Services):
Exponential smoothing ( = .50): MAD = 4.04
Adjusted exponential smoothing ( = .50,  = .30): MAD = 3.81
Linear trend line: MAD = 2.29
Linear trend line has lowest MAD; increasing  from .30 to .50 improved smoothed forecast.
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41. Mean Absolute Deviation (6 of 7)
Forecast Accuracy
Mean Absolute Deviation (6 of 7)
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:
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42. Mean Absolute Deviation (7 of 7)
Forecast Accuracy
Mean Absolute Deviation (7 of 7)
MAPD for other three forecasts:
Exponential smoothing ( = .50): MAPD = 8.5%
Adjusted exponential smoothing ( = .50,  = .30):
MAPD = 8.1%
Linear trend: MAPD = 4.9%
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43. Forecast Accuracy Cumulative Error (1 of 2)
Cumulative error is the sum of the forecast errors (E =et).
A relatively large positive value indicates forecast is biased low, a large negative value indicates forecast is biased high.
If preponderance of errors are positive, forecast is consistently low; and vice versa.
Cumulative error for trend line is always almost zero, and is therefore not a good measure for this method.
Cumulative error for PM Computer Services can be read directly from Table 15.8.
E =  et = indicating forecasts are frequently below actual demand.
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44. Forecast Accuracy Cumulative Error (2 of 2)
Cumulative error for other forecasts:
Exponential smoothing ( = .50): E = 33.21
Adjusted exponential smoothing ( = .50,  =.30):
E = 21.14
Average error (bias) is the per period average of cumulative error.
Average error for exponential smoothing forecast:
A large positive value of average error indicates a forecast is biased low; a large negative error indicates it is biased high.
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45. Table 15.9 Comparison of Forecasts for PM Computer Services
Forecast Accuracy
Example Forecasts by Different Measures
Table Comparison of Forecasts for PM Computer Services
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.
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46. Time Series Forecasting Using Excel (1 of 4)
Exhibit 15.1
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47. Time Series Forecasting Using Excel (2 of 4)
Exhibit 15.2
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48. Time Series Forecasting Using Excel (3 of 4)
Exhibit 15.3
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49. Time Series Forecasting Using Excel (4 of 4)
Exhibit 15.4
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50. Exponential Smoothing Forecast with Excel QM
Exhibit 15.5
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51. Time Series Forecasting Solution with QM for Windows (1 of 2)
Exhibit 15.6
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52. Time Series Forecasting Solution with QM for Windows (2 of 2)
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Exhibit 15.7

53. Regression Methods Overview
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.
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54. Regression Methods Linear Regression
Linear regression relates demand (dependent variable ) to an independent variable.
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55. Linear Regression Example (1 of 3)
Regression Methods
Linear Regression Example (1 of 3)
State University Athletic Department.
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56. Linear Regression Example (2 of 3)
Regression Methods
Linear Regression Example (2 of 3)
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57. Linear Regression Example (3 of 3)
Regression Methods
Linear Regression Example (3 of 3)
Figure 15.6
Linear Regression Line
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58. Regression Methods Correlation (1 of 2)
Correlation is a measure of the strength of the relationship between independent and dependent variables.
Formula:
Value lies between +1 and -1.
Value of zero indicates little or no relationship between variables.
Values near 1.00 and indicate strong linear relationship.
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59. Regression Methods Correlation (2 of 2)
Value for State University example:
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60. Coefficient of Determination
Regression Methods
Coefficient of Determination
The Coefficient of determination is the percentage of the variation in the dependent variable that results from the independent variable.
Computed by squaring the correlation coefficient, r.
For State University example:
r = .948, r2 = .899
This value indicates that 89.9% of the amount of variation in attendance can be attributed to the number of wins by the team, with the remaining 10.1% due to other, unexplained, factors.
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61. Regression Analysis with Excel (1 of 6)
Exhibit 15.8
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62. Regression Analysis with Excel (2 of 6)
Exhibit 15.9
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63. Regression Analysis with Excel (3 of 6)
Exhibit 15.10
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64. Regression Analysis with Excel (4 of 6)
Exhibit 15.11
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65. Regression Analysis with Excel (5 of 6)
Exhibit 15.12
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66. Regression Analysis with Excel (6 of 6)
Exhibit 15.13
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67. Multiple Regression with Excel (1 of 4)
Multiple regression relates demand to two or more independent variables.
General form:
y = 0 +  1x1 +  2x  kxk
where  0 = the intercept
  k = parameters representing contributions of the independent variables
x xk = independent variables
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68. Multiple Regression with Excel (2 of 4)
State University example:
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69. Multiple Regression with Excel (3 of 4)
Exhibit 15.14
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70. Multiple Regression with Excel (4 of 4)
Exhibit 15.15
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71. Example Problem Solution Computer Software Firm (1 of 4)
Problem Statement:
For data below, develop an exponential smoothing forecast using  = .40, and an adjusted exponential smoothing forecast using  = .40 and  = .20.
Compare the accuracy of the forecasts using MAD and cumulative error.
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72. Example Problem Solution Computer Software Firm (2 of 4)
Step 1: Compute the Exponential Smoothing Forecast.
Ft+1 =  Dt + (1 - )Ft
Step 2: Compute the Adjusted Exponential Smoothing
Forecast
AFt+1 = Ft +1 + Tt+1
Tt+1 = (Ft +1 - Ft) + (1 - )Tt
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73. Example Problem Solution Computer Software Firm (3 of 4)
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74. Example Problem Solution Computer Software Firm (4 of 4)
Step 3: Compute the MAD Values
Step 4: Compute the Cumulative Error.
E(Ft) = 35.97
E(AFt) = 30.60
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75. Example Problem Solution Building Products Store (1 of 5)
For the following data:
Develop a linear regression model
Determine the strength of the linear relationship using correlation.
Determine a forecast for lumber given 10 building permits in the next quarter.
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76. Example Problem Solution Building Products Store (2 of 5)
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77. Example Problem Solution Building Products Store (3 of 5)
Step 1: Compute the Components of the Linear Regression Equation.
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78. Example Problem Solution Building Products Store (4 of 5)
Step 2: Develop the Linear regression equation.
y = a + bx, y = x
Step 3: Compute the Correlation Coefficient.
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79. Y = a + bx = 1.36 + 1.25(10) = 13.86 or 1,386 board ft
Example Problem Solution
Building Products Store (5 of 5)
Step 4: Calculate the forecast for x = 10 permits.
Y = a + bx = (10) = or 1,386 board ft
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80. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall