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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

5. Forecasting Components Patterns (2 of 2)
Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend with Season
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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, and technological forecasting.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

9. Time Series Methods Moving Average (1 of 6)
Moving average uses values from the recent past to develop forecasts.
This dampens random increases and decreases.
Useful for forecasting relatively stable items that do not display any trend or seasonal pattern.
Formula for moving average (MA):
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

10. Time Series Methods Moving Average (2 of 6)
Example: Instant Paper Clip Supply Company wants to forecast orders for the month of November. Develop three-month and five-month moving averages using the data.
Table 15.1 Orders for 10-month period
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

11. Time Series Methods Moving Average (3 of 6)
Example: Instant Paper Clip Supply Company wants to forecast orders for the month of November.
Three-month moving average:
Five-month moving average:
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

12. Time Series Methods Moving Average (4 of 6)
Table Three- and 5-month moving averages
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

13. Time Series Methods Moving Average (5 of 6)
Figure Three- and 5-month moving averages
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

14. Time Series Methods Moving Average (6 of 6)
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.
A moving average does not react well to changes (trends, seasonal effects, etc.) but is easy to use and inexpensive.
Good for short-term forecasting.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

15. 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 the number of periods requires trial-and-error experimentation.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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).
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

17. 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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

18. 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) + (1-.30)(.37) = 37 units
Forecast for period 3 (March):
F3 =  D2 + (1- )F2 = (.30)(.40) + (1-.30)(37) = 37.9 units
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

19. Exponential Smoothing (4 of 11)
Time Series Methods
Exponential Smoothing (4 of 11)
Table Exponential smoothing forecasts,  = .30 and  = .50
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

21. Exponential Smoothing (6 of 11)
Time Series Methods
Exponential Smoothing (6 of 11)
Figure Exponential smoothing forecasts
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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:
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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

23. Exponential Smoothing (8 of 11)
Time Series Methods
Exponential Smoothing (8 of 11)
Example: PM Computer Services exponentially smoothed
forecasts with  = .50 and  = .30 (see Table 15.5 next slide).
Adjusted forecast for period 3:
T3 = (F3 - F2) + (1 - )T2
= (.30)( ) + (.70)(0) = 0.45
AF3 = F3 + T3 = = 38.95
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

24. Exponential Smoothing (9 of 11)
Time Series Methods
Exponential Smoothing (9 of 11)
Table Adjusted exponentially smoothed forecast values
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

25. Exponential Smoothing (10 of 11)
Time Series Methods
Exponential Smoothing (10 of 11)
The adjusted forecast is consistently higher than the simple exponentially smoothed forecast.
It is more reflective of the generally increasing trend of the data.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

26. Exponential Smoothing (11 of 11)
Time Series Methods
Exponential Smoothing (11 of 11)
Figure Adjusted exponentially smoothed forecast
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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:
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

28. Time Series Methods Linear Trend Line (2 of 5)
Example: PM Computer Services (see Table 15.6)
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

29. Time Series Methods Linear Trend Line (3 of 5)
Table 15.6 Least squares calculations
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 the trend will not change.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

31. Time Series Methods Linear Trend (5 of 5)
Figure Linear trend line
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

34. 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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

35. Seasonal Adjustments (4 of 4)
Time Series Methods
Seasonal Adjustments (4 of 4)
Multiply forecasted demand for an entire year by seasonal factors to determine the 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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

36. Forecast Accuracy Overview
Forecasts will always deviate from actual values.
Difference between forecasts and actual values are referred to as forecast error.
We would like forecast error to be as small as possible.
If forecast error is large, either the technique being used is the wrong one, or the 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)
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
The most popular and simplest-to-use measures of forecast error.
Formula:
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

38. 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:
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

39. Mean Absolute Deviation (3 of 7)
Forecast Accuracy
Mean Absolute Deviation (3 of 7)
Table Computational values for MAD and error
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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.
MAD must be considered in light of magnitude of the data.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

41. Mean Absolute Deviation (5 of 7)
Forecast Accuracy
Mean Absolute Deviation (5 of 7)
Can be used to compare the 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
The linear trend line has the lowest MAD; increasing  from .30 to .50 improved the smoothed forecast.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 the absolute error as a percentage of demand rather than per period.
Eliminates the problem of interpreting the measure of accuracy relative to the magnitude of the demand and forecast values.
Formula:
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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%
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 the forecast is biased low, a large negative value indicates the forecast is biased high.
If the preponderance of errors are positive, the forecast is consistently low; and vice versa.
The cumulative error for a trend line is always almost zero, and is therefore not a good measure for this method.
The cumulative error for PM Computer Services can be read directly from Table 15.8.
E =  et = 49.31, indicating the forecasts are frequently below actual demand.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 the 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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

46. Example Forecasts by Different Measures
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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

47. Time Series Forecasting Using Excel (1 of 4)
=B3*B8+(1-B3)*C8
=C9+D9
=B9-E9
=ABS(B9-E9)
=G21/11
=SUM(F9:F20)
Exhibit 15.1
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

48. Time Series Forecasting Using Excel (2 of 4)
To access this window, click on “Data” on the toolbar ribbon and then the “Data Analysis” add-in
Exhibit 15.2
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

49. Time Series Forecasting Using Excel (3 of 4)
Demand values
a = 0.5
Cells in which the forecasted values will be placed
Exhibit 15.3
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

50. Time Series Forecasting Using Excel (4 of 4)
Exhibit 15.4
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

51. Exponential Smoothing Forecast with Excel QM
Click “Add-Ins” to access forecasting macros
Input problem data in cells B7 and B10:B21
Exhibit 15.5
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

52. Time Series Forecasting Solution with QM for Windows (1 of 2)
Exhibit 15.6
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

53. Time Series Forecasting Solution with QM for Windows (2 of 2)
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
Exhibit 15.7

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.
The simplest form of regression is linear regression.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

55. Regression Methods Linear Regression
Linear regression relates demand (dependent variable ) to an independent variable.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

56. Linear Regression Example (1 of 3)
Regression Methods
Linear Regression Example (1 of 3)
State University Athletic Department.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

57. Linear Regression Example (2 of 3)
Regression Methods
Linear Regression Example (2 of 3)
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

58. Linear Regression Example (3 of 3)
Regression Methods
Linear Regression Example (3 of 3)
Figure 15.6
Linear regression line
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 a strong linear relationship.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

60. Regression Methods Correlation (2 of 2)
Value for State University example:
Since the value is close to one, we have evidence of a strong linear relationship.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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 the 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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

62. Regression Analysis with Excel (1 of 6)
=INTERCEPT(B5:B12,A5:A12)
=CORREL(B5:B12,A5:A12)
Exhibit 15.8
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

63. Regression Analysis with Excel (2 of 6)
Click on “Insert” to access “Charts”
Click on “Scatter”
Exhibit 15.9
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

64. Regression Analysis with Excel (3 of 6)
Exhibit 15.10
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

65. Regression Analysis with Excel (4 of 6)
Exhibit 15.11
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

66. Regression Analysis with Excel (5 of 6)
Exhibit 15.12
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

67. Regression Analysis with QM for Windows (6 of 6)
Exhibit 15.13
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

68. 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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

69. Multiple Regression with Excel (2 of 4)
State University example revisited; does the addition of promotional and advertising expenditures to wins improve the prediction of attendance?
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

70. Multiple Regression with Excel (3 of 4)
r2, the coefficient of determination
Regression equation coefficients for x1 and x2
Exhibit 15.14
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

71. Multiple Regression with Excel (4 of 4)
Includes x1 and x2 columns
Exhibit 15.15
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

72. Example Problem Solution Computer Software Firm (1 of 4)
Problem Statement:
For the 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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

73. 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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

74. Example Problem Solution Computer Software Firm (3 of 4)
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

75. 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
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

76. 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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

77. Example Problem Solution Building Products Store (2 of 5)
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

78. Example Problem Solution Building Products Store (3 of 5)
Step 1: Compute the Components of the Linear Regression Equation.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

79. 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.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

80. 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
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

81. Printed in the United States of America.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.
Printed in the United States of America.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall