1. Introduction to Management Science
8th Edition by
Bernard W. Taylor III
Chapter 5
Forecasting
Chapter 5 - Forecasting

2. Chapter Topics Forecasting Components Time Series Methods
Forecast Accuracy
Time Series Forecasting Using Excel
Time Series Forecasting Using QM for Windows
Regression Methods
Chapter 5 - Forecasting

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
Chapter 5 - Forecasting

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.
Chapter 5 - Forecasting

5. Forecasting Components Patterns (2 of 2)
trend-line
Figure 5.1
Forms of Forecast Movement: (a) Trend, (b) Cycle, (c) Seasonal Pattern, (d) Trend with Seasonal Pattern
Chapter 5 - Forecasting

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.
Chapter 5 - Forecasting

7. Forecasting Components Qualitative Methods
Qualitative methods, the “jury of executive opinion,” is the most common type of forecasting method for long-term strategic planning.
Performed by individuals or groups within an organization, sometimes assisted by consultants and other experts, whose judgments and opinion 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.
Chapter 5 - Forecasting

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.
Chapter 5 - Forecasting

9. Time Series Methods Moving Average (1 of 5)
Moving average uses values from the recent past to develop forecasts.
This dampens or smoothes out random increases and decreases.
Useful for forecasting relatively stable items that do not display any trend or seasonal pattern.
Formula for:
Chapter 5 - Forecasting

10. Time Series Methods Moving Average (2 of 5)
Example: Instant Paper Clip Supply Company forecast of orders for the next month.
Three-month moving average:
Five-month moving average:
Chapter 5 - Forecasting

11. Three- and Five-Month Moving Averages
Time Series Methods
Moving Average (3 of 5)
Figure 5.2
Three- and Five-Month Moving Averages
Chapter 5 - Forecasting

12. Three- and Five-Month Moving Averages
Time Series Methods
Moving Average (4 of 5)
Figure 5.2
Three- and Five-Month Moving Averages
Chapter 5 - Forecasting

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.
Chapter 5 - Forecasting

14. Weighted Moving Average (1 of 2)
Time Series Methods
Weighted Moving Average (1 of 2)
In a weighted moving average, weights are assigned to the most recent data.
Formula:
Chapter 5 - Forecasting

15. Weighted Moving Average (2 of 2)
Time Series Methods
Weighted Moving Average (2 of 2)
Determining precise weights and number of periods requires trial-and-error experimentation.
Chapter 5 - Forecasting

16. 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)
use F1 = D1.
Chapter 5 - Forecasting

17. Exponential Smoothing (2 of 11)
Time Series Methods
Exponential Smoothing (2 of 11)
The most commonly used values of  are between .10 and .50.
Determination of  is usually judgmental and subjective and often based on trial-and -error experimentation.
Chapter 5 - Forecasting

18. Exponential Smoothing (3 of 11)
Time Series Methods
Exponential Smoothing (3 of 11)
Example: PM Computer Services (see Table 5.4).
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
Chapter 5 - Forecasting

19. Exponential Smoothing Forecasts,  = .30 and  = .50
Time Series Methods
Exponential Smoothing (4 of 11)
Using
F1 = D1
Table 5.4
Exponential Smoothing Forecasts,  = .30 and  = .50
Chapter 5 - Forecasting

20. 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.
Chapter 5 - Forecasting

21. Exponential Smoothing Forecasts
Time Series Methods
Exponential Smoothing (6 of 11)
Figure 5.3
Exponential Smoothing Forecasts
Chapter 5 - Forecasting

22. 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: Tt = an exponentially smoothed trend factor:
Tt + 1 = (Ft Ft) + (1 - )Tt
Tt = the last (previous) period’s trend factor
 = smoothing constant for trend ( a value between zero and one).
Reflects the weight given to the most recent trend data.
Determined subjectively.
Chapter 5 - Forecasting

23. 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 5.5).
Start with T2 = 0.00
Adjusted forecast for period 3:
T3 = (F3 - F2) + (1 - )T2
= (.30)( ) + (.70)(0) = 0.45
AF3 = F3 + T3 = = 38.95
Chapter 5 - Forecasting

24. Exponential Smoothing (9 of 11)
Time Series Methods
Exponential Smoothing (9 of 11)
Tt + 1 = (Ft Ft) + (1 - )Tt
Table 5.5
Adjusted Exponentially Smoothed Forecast Values
Chapter 5 - Forecasting

25. 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.
Chapter 5 - Forecasting

26. Adjusted Exponentially Smoothed Forecast
Time Series Methods
Exponential Smoothing (11 of 11)
Figure 5.4
Adjusted Exponentially Smoothed Forecast
Chapter 5 - Forecasting

27. 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:
Chapter 5 - Forecasting

28. Time Series Methods Linear Trend Line (2 of 5)
Example: PM Computer Services (see Table 5.6)
Chapter 5 - Forecasting

29. Time Series Methods Linear Trend Line (3 of 5) Table 5.6
Least Squares Calculations
Chapter 5 - Forecasting

30. 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.
Chapter 5 - Forecasting

31. Time Series Methods Linear Trend Line (5 of 5) Figure 5.5
Chapter 5 - Forecasting

32. 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 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
Chapter 5 - Forecasting

33. 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.
Chapter 5 - Forecasting

34. Demand for Turkeys at Wishbone Farms
Time Series Methods
Seasonal Adjustments (3 of 4)
Example: Wishbone Farms
Table 5.7
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
Chapter 5 - Forecasting

35. 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 5.7):
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
Note the potential for confusion: the Si are “seasonal factors” (fractions),
whereas the SFi are “seasonally adjusted forecasts” (commodity values)!
Chapter 5 - Forecasting

36. 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)
Chapter 5 - Forecasting

37. 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:
Chapter 5 - Forecasting

38. Mean Absolute Deviation (2 of 7)
Forecast Accuracy
Mean Absolute Deviation (2 of 7)
Example: PM Computer Services (see Table 5.8).
Compare accuracies of different forecasts using MAD:
Chapter 5 - Forecasting

39. Computational Values for MAD
Forecast Accuracy
Mean Absolute Deviation (3 of 7)
Table 5.8
Computational Values for MAD
Chapter 5 - Forecasting

40. 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.
Chapter 5 - Forecasting

41. 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.
Chapter 5 - Forecasting

42. 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:
Chapter 5 - Forecasting

43. 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%
Chapter 5 - Forecasting

44. 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 5.8.
E =  et = indicating forecasts are frequently below actual demand.
Chapter 5 - Forecasting

45. 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.
Chapter 5 - Forecasting

46. Comparison of Forecasts for PM Computer Services
Forecast Accuracy
Example Forecasts by Different Measures
Table 5.9
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 forecasts.
Linear trend is more accurate than all the others.
Chapter 5 - Forecasting

47. Time Series Forecasting Using Excel (1 of 4)
Exhibit 5.1
Chapter 5 - Forecasting

48. Time Series Forecasting Using Excel (2 of 4)
Exhibit 5.2
Chapter 5 - Forecasting

49. Time Series Forecasting Using Excel (3 of 4)
Exhibit 5.3
Chapter 5 - Forecasting

50. Time Series Forecasting Using Excel (4 of 4)
Exhibit 5.4
Chapter 5 - Forecasting

51. Exponential Smoothing Forecast with Excel QM
Exhibit 5.5
Chapter 5 - Forecasting

52. Time Series Forecasting Solution with QM for Windows (1 of 2)
Exhibit 5.6
Chapter 5 - Forecasting

53. Time Series Forecasting Solution with QM for Windows (2 of 2)
Exhibit 5.7
Chapter 5 - Forecasting

54. 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.
Chapter 5 - Forecasting

55. Regression Methods Linear Regression
Linear regression relates demand (dependent variable ) to an independent variable.
Linear function
Chapter 5 - Forecasting

56. Linear Regression Example (1 of 3)
Regression Methods
Linear Regression Example (1 of 3)
State University athletic department.
Chapter 5 - Forecasting

57. Linear Regression Example (2 of 3)
Regression Methods
Linear Regression Example (2 of 3)
Chapter 5 - Forecasting

58. Linear Regression Example (3 of 3)
Regression Methods
Linear Regression Example (3 of 3)
Figure 5.6
Linear Regression Line
Chapter 5 - Forecasting

59. 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: correlation and anti-correlation.
Chapter 5 - Forecasting

60. Regression Methods Correlation (2 of 2)
Value for State University example:
Chapter 5 - Forecasting

61. 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.
Chapter 5 - Forecasting

62. Regression Analysis with Excel (1 of 7)
Exhibit 5.8
Chapter 5 - Forecasting

63. Regression Analysis with Excel (2 of 7)
Exhibit 5.9
Chapter 5 - Forecasting

64. Regression Analysis with Excel (3 of 7)
Exhibit 5.10
Chapter 5 - Forecasting

65. Regression Analysis with Excel (4 of 7)
Exhibit 5.11
Chapter 5 - Forecasting

66. Regression Analysis with Excel (5 of 7)
Exhibit 5.12
Chapter 5 - Forecasting

67. Regression Analysis with Excel (6 of 7)
Exhibit 5.13
Chapter 5 - Forecasting

68. Regression Analysis with Excel (7 of 7)
Exhibit 5.14
Chapter 5 - Forecasting

69. Regression Analysis with QM for Windows
Exhibit 5.15
Chapter 5 - Forecasting

70. 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
Chapter 5 - Forecasting

71. Multiple Regression with Excel (2 of 4)
State University example:
Chapter 5 - Forecasting

72. Multiple Regression with Excel (3 of 4)
Exhibit 5.16
Chapter 5 - Forecasting

73. Multiple Regression with Excel (4 of 4)
Exhibit 5.17
Chapter 5 - Forecasting

74. 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.
Chapter 5 - Forecasting

75. 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
Chapter 5 - Forecasting

76. Example Problem Solution Computer Software Firm (3 of 4)
Chapter 5 - Forecasting

77. 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
Chapter 5 - Forecasting

78. Example Problem Solution Building Products Store (1 of 5)
Problem Statement:
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.
Chapter 5 - Forecasting

79. Example Problem Solution Building Products Store (2 of 5)
Chapter 5 - Forecasting

80. Example Problem Solution Building Products Store (3 of 5)
Step 1: Compute the Components of the Linear Regression
Equation.
Chapter 5 - Forecasting

81. 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.
Chapter 5 - Forecasting

82. 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
Chapter 5 - Forecasting

83. Chapter 5 - Forecasting