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**Page 24**- The discussion of evaluation measures does not make clear exactly what elements
in a value tree (hierarchy) have evaluation measures associated with them. From
the definition of a value tree on pages 12 and 13 (particularly the discussion
of "layers" or "tiers" on page 13), it follows that when the performance is
known for an alternative with respect to the evaluation considerations most
distant from the root of the tree, then it is know for the entire tree.
Therefore, it is only necessary to develop evaluation measures
for the "leaves" at the end of each "branch" of the value tree.
As an example, for the value tree shown in Figure 2.1, it is only necessary to develop evaluation measures for software outlay; training, maintenance, and upgrades; hardware outlay; technical graphics; tables; automation and customization; interoperability; layout, editing, and formatting; long documents and proofing; marketing graphics; printing and mail merge; and interface. That is, a total of twelve evaluation measures are needed for this value tree. Evaluation measures are not needed for purchase best value software; cost; suitability for use; production, R&D, and engineering; finance and administration; or marketing because these considerations each consist of other elements lower in the hierarchy that have evaluation measures associated with them. [February 24, 1998]

**Pages 50-51**- Options analysis approaches have been applied to the type of
sequencing
alternatives discussed in Section 3.4. For further information, see
T. W.
Faulkner, "Applying 'Options Thinking' to R&D Valuation,"
*Research Technology Management*, Vol. 39, No. 3, pp. 50-56 (May-June 1996). For a more theoretical discussion, see J. E. Smith and R. F. Nau, "Valuing Risky Projects: Option Pricing Theory and Decision Analysis,"*Management Science*, Vol. 41, No. 5, pages 795-816 (May 1995). [September 24, 1997] **Pages 54-55**- The example in Section 4.1 includes two evaluation measures with constructed scales. For both of these, the data in Table 4.1 includes cases where the scores are intermediate between levels for the evaluation measure scales that are defined on page 54. There is no discussion about how such intermediate scores should be determined or what these intermediate scores mean. Such intermediate scores have the meaning that the alternative with an intermediate score has a single dimensional value that is intermediate between the values for the two defined evaluation measure scores on either side of the intermediate score. For example, the score of 0.5 for the Low Quality/Low Cost alternative on the Productivity Enhancement evaluation measure means that this alternative has a single dimensional value with respect to Productivity Enhancement that is intermediate between the values for the zero and one levels defined on page 54. More specifically, since the score of 0.5 is exactly half way between the defined levels of zero and one, then the Low Quality/Low Cost alternative has a single dimensional value on Productivity Enhancement that exactly half way between the single dimensional values for the zero and one levels. The calculation procedure to determine single dimensional values is reviewed in Sections 4.2 and 4.3. [January 26, 2005]
**Pages 68-72**- The discussion in Section 4.4 does not explicitly address the question of how a
hierarchical value structure is used in the determination of weights. With the
procedure that is presented in Section 4.2, the hierarchical structure is not
explicitly used in the determination of weights. That is, the various
evaluation measures are addressed in the procedure to determine weights without
considering which layer each evaluation measure belongs to in the value tree.
Specifically, this procedure does not require determination of weights for evaluation considerations that do not have evaluation measures associated with them. For example, in the value tree shown in Figure 2.1 (page 14), it is not necessary to determine weights for cost; suitability for use; production, R&D, and engineering; finance and administration; or marketing. (If you wish to associate a weight with one of these considerations, then a reasonable method of doing this is to add up the weights that have been determined for the evaluation measures below this consideration.)

Other procedures for determining weights have been proposed that explicitly consider the hierarchical structure of the value tree. For more information about differences that can result from using different weight assessment procedures, see the following: 1) W. G. Stillwell, D. von Winterfeldt, and R. S. John, "Comparing Hierarchical and Nonhierarchical Weighting Methods for Eliciting Multiattribute Value Models,"

*Management Science*, Vol. 33, No. 4, pp. 442-450 (April 1987), and 2) M. Weber, R. Eisenführ, and D. von Winterfeldt, "The Effects of Splitting Attributes on Weights in Multiattribute Utility Measurement,"*Management Science*, Vol. 34, No. 4, pp. 431-445 (April 1988). [February 24, 1998]A simplified version of the weight assessment procedure presented in Section 4.4, called the Swing Weight Matrix Method, is presented in the context of specific applications by P. L. Ewing Jr., W. Tarantino, and G. S. Parnell, "Use of Decision Analysis in the Army Base Realignment and Closure (BRAC) 2005 Military Value Analysis,"

*Decision Analysis*, Vol. 3, No. 1, pp. 33-49 (March 2006), and T. Trainor, G. S. Parnell, B. Kwinn, J. Brence, E. Tollefson, and P. Downes, "The US Army Uses Decision Analysis in Designing Its US Installation Regions,"*Interfaces*, Vol. 37, No. 3, pp. 253-264, May-June 2007. [October 8, 2012] **Pages 75-96**- Consult Excel 97 Display Bug for a discussion of a bug in Excel 97 that impacts some of the spreadsheets in Sections 4.7 and 4.8. [January 2, 1999]
**Page 78**- The discussion of the arguments for the piecewise linear single
dimensional
value function ValuePL(
*x*,*X*-list,*V*-list) does not explicitly state the order in which the elements of*X*-list and*V*-list should be entered. These should be entered so that the elements of*X*-list are monotonically increasing regardless of whether the single dimensional value function is monotonically increasing, monotonically decreasing, or non monotonic. For example, suppose a monotonically decreasing piecewise linear single dimensional value function is specified by three evaluation measure levels 10, 16, and 20, with corresponding single dimensional values 1, 0.7, and 0. Then the*X*-list should be in the order 10, 16, and 20, and the*V*-list should be in the order 1, 0.7, and 0. ValuePL does not do much error checking, and it will usually not detect an incorrect entry order for arguments. [August 21, 1996] **Page 80**- To insert a Visual Basic module in Excel 97, first select the following menu sequence: Tools, Macro, Visual Basic Editor. This opens the Visual Basic editor. Then, to create the Visual Basic module, select the following menu sequence in the Visual Basic editor: Insert, Module. In the window that is opened, enter the code shown in Figure 4.5. To return to the Excel spreadsheet, select the Excel icon from the Windows Taskbar. The Visual Basic module you have created will not appear among the worksheet tabs at the bottom of the Excel Window, but this module will automatically be saved with your spreadsheet. [June 20, 1997]
**Page 81**- Consult Excel 97 Display Bug for a discussion of a bug in Excel 97. One way to work around this bug requires modifying the function definitions in Figure 4.5, as discussed on that web page. [January 2, 1999]
**Page 97**- Consult Excel 97 Display Bug for a discussion of a bug in Excel 97. One way to work around this bug requires modifying the function definition in Figure 4.12, as discussed on that web page. [January 2, 1999]
**Page 100**- The solution in the
*Instructor's Manual*for Exercise 4.3 has a slight error. The decimal value shown for the Efficiency weight is not the same as the fraction value, and the fraction value is the correct one. [June 18, 1997] **Page 101**- In Exercise 4.5, part iii, delete the last sentence. ("Assume that, while you are varying this weight, the ratio of the other two weights remains constant.") There are only two evaluation measures in this exercise. [March 26, 1997]
**Pages 101-103**- The solution in the
*Instructor's Manual*for Exercise 4.6 has a slight error. Specifically, in rows 23 and 29 of the Figure 4.2 spreadsheet in the*Instructor's Manual*, the words in parentheses should be "Operational Ease" rather than "Cost." [January 14, 1998] **Page 103**- In Exercise 4.7, six lines from the bottom of the page, "increasing accuracy from 95 percent to 99 percent" should be "increasing uptime from 95 percent to 99 percent." [March 26, 1997]
**Pages 107-116**- For an extended discussion of the historical development of ideas
about
uncertainty, see P. L. Bernstein,
*Against the Gods: The Remarkable Story of Risk*, Wiley, New York, 1996. See especially Chapter 16, "The Failure of Invariance," which contains additional examples of reasoning difficulties about uncertainty. [January 22, 1997] **Page 117**- In the seventh line from the bottom of the page, "the uncertainty quantity" should be "the uncertain quantity." [January 2, 1999]
**Page 138**- The accuracy of the exponential utility function as an approximation to
other
utility functions is studied
in C. W. Kirkwood, "Approximating Risk
Aversion in Decision Analysis
Applications,"
*Decision Analysis*, Vol. 1, No. 1, pp. 55-72 (March, 2004). [April 10, 2007] **Pages 138-141**- The accuracy of several methods for determining utilities is studied in
H.
Bleichrodt, J. M. Abbellan-Perpiñan, J. L. Pinto-Prades, and
I.
Mendez-Martinez, "Resolving Inconsistencies in Utility Measurement Under
Risk:
Tests of Generalizations of Expected Utility,"
*Management Science*, Vol. 53, No. 3, pp. 469-482 (March 2007). [April 10, 2007] **Pages 138-143**- For an extended example of the use of exponential utility functions, see M.
R.
Walls, G. T. Morahan, and J. S. Dyer, "Decision Analysis of
Exploration
Opportunities in the Onshore US at Phillips Petroleum Company,"
*Interfaces*, Vol. 25, No. 6, pp. 39-56 (November-December 1995). [September 24, 1997] **Pages 142-143**- For a more complete discussion of the impact of organizational size on
risk
attitude, see M. R. Walls and J. S. Dyer, "Risk Propensity and
Firm
Performance: A Study of the Petroleum Exploration Industry,"
*Management Science*, Vol. 42, No. 7, pp. 1004-1021 (July 1996). Their empirical work indicates that risk tolerance does increase with increasing organizational size as specified by Howard's rules of thumb, but that the increase is not in the simple linear manner indicated by the rules of thumb. [September 3, 1996]See also J. Eric Bickel, "Some Determinants of Corporate Risk Aversion,"

*Decision Analysis*, Vol. 3, No. 4, pp. 233-251 (December 2006) for further consideration of rationales for corporate attitudes toward risk taking. Bickel concludes that he is unable to fully support the degree of corporate risk aversion reported in the decision analysis literature. [October 8, 2012] **Pages 147, 149**- The spreadsheets shown in Figures 6.4 and 6.5 can be simplified by using
the
Excel SUMPRODUCT function. If you will be doing a substantial number
of
certainty equivalent calculations, then it may be worthwhile to define a
Visual
Basic function that implements equations 6.4 and 6.5 on page 143.Download the Excel spreadsheet EXPCE.XLS (19,968 bytes) for examples demonstrating the use of SUMPRODUCT and a
specially
defined Visual Basic function. (
**Note:**When you click on the "Download the Excel spreadsheet EXPCE.XLS" link above, your browser may attempt to display this file on the screen, and the display may be garbage. If the display is garbage, then select the "Save As" option from the "File" menu to save the spreadsheet to your hard disk. You can then load the spreadsheet into Excel.) [March 25, 1997] **Page 161**- In equation (7.2), the x-sub-i should be x-sub-1. [June 20, 1997]
**Page 164**- In the first line of equation (7.3), the rho without a subscript should be rho-sub-m. [June 30, 1997]
**Page 165**- In the first line of equation (7.5), the rightmost right parenthesis should be deleted. [June 30, 1997]
**Page 166**- In the third line of the equation on this page (which begins with a plus sign), the left bracket and the 0.67 that follows this bracket should be deleted. [June 20, 1997]
**Page 173**- Consult Excel 97 Display Bug for a discussion of a bug in Excel 97. One way to work around this bug requires modifying the function definition in Figure 7.5, as discussed on that web page. [January 2, 1999]
**Pages 182-190**- Consult Excel 97 Display Bug for a discussion of a bug in Excel 97 that impacts the spreadsheet in Section 7.7. [January 2, 1999]
**Pages 200-206**- Section 8.1 does not present a theoretical basis for the benefit/cost
approach. The theoretical basis for the approach is presented in H. Everett
III, "Generalized Lagrange Multiplier Method for Solving Problems of Optimum
Allocation of Resources,"
*Operations Research*, Vol. 11, No. 3, pp. 399-417 (May/June 1963). See also A. Charnes and W. W. Cooper, "A Note on the 'Fail-Safe' Properties of the 'Generalized Lagrange Multiplier Method,'"*Operations Research*, Vol. 13, No. 4, pp. 674-677 (July/August 1965), and H. Everett, III, "Comments on Preceding Note,"*Operations Research*, Vol. 13, No. 4, pp. 677-678 (July/August 1965). [September 30, 1996] **Pages 200-211**- The analysis procedures in Sections 8.1 and 8.2 implicitly assume that the
value of
*not*selecting any project is zero. (Another way of saying this is that not selecting a project is assumed to be equivalent in a value sense to selecting a project that has the worst possible score on each of the evaluation measures.) The following example shows how to analyze decisions where not selecting a project has some value.Suppose that you own three fast food restaurants that are run down but functional. You have a budget of 250 thousand dollars to renovate one or more of the restaurants. You develop evaluation measures and a multiobjective value function to score the current conditions of the restaurants and what their conditions would be if they were renovated. The cost of renovating each restaurant, as well as the current and renovated values, are as follows:

**Value****Project****Cost****Renovated****Current****Increment**Restaurant 1 200 0.55 0.30 0.25 Restaurant 2 120 0.40 0.25 0.15 Restaurant 3 100 0.30 0.25 0.05 The two competitive combinations of projects that could be completed within the budget are to either renovate only Restaurant 1, or to renovate both Restaurants 2 and 3. Assuming that the values of projects add, then it may appear that the combination of renovating Restaurants 2 and 3 should be selected since this has a value of 0.40+0.30=0.70 versus 0.55 for renovating Restaurant 1. However, this is not the complete story. The fourth column of the table shows the current values of the three restaurants, and the right-most column shows the difference between the renovated and current values. The value increment from renovating Restaurant 1 is greater than the sum of the value increments from renovating Restaurants 2 and 3 (0.25 versus 0.15+0.05=0.20). It can be proved that value increments should be used in selecting the best combination of projects, and hence Restaurant 1 should be renovated. If not selecting a particular project has a cost, then that cost needs to be taken into account. This does not change the value associated with selecting a particular set of projects, but it might make some combinations of projects infeasible. See this link for a presentation of the theory for addressing portfolios where not selecting a project may have a value or cost. This is discussed further in R. T. Clemen and J. E. Smith, "On the Choice of Baselines in Multiattribute Portfolio Analysis: A Cautionary Note,"

*Decision Analysis,*Vol. 6, No. 4, pp. 256-262 (December 2009). [March 10, 2009; March 19, 2009; January 9, 2010] **Pages 223-224**- The solution in the
*Instructor's Manual*for Exercise 8.2 is incorrect. That solution assumes that the cost for Digital Display B is 450, but the cost specified in the exercise is 490. The changes needed to correct the solution are as follows: - In the part (i) solution, the last three lines of the table in Figure 8.2
of the
*Instructor's Manual*are incorrect. - The solution to part (ii) that is shown in Figure 8.3 of the
*Instructor's Manual*is incorrect. There are two different optimal solutions to part (ii): For one of these, the decision variable values for projects 1, 2, 6, 10, and 11 need to be reversed from the values shown in Figure 8.3 of the*Instructor's Manual*, and for the other solution, the decision variable values for projects 2, 4, and 5 need to be reversed from the values shown in Figure 8.3. The total Benefit should be reduced by 0.03 from that shown in Figure 8.3. - All the discussion and figures should be revised to reflect the corrected cost for Digital Display B, as well as the corrections listed above. [June 24, 1997]
**Page 241**- In addition to the Dyer and Sarin (1979) reference in the last paragraph
on
this page, see J. M. Deichtmann and F. Sainfort, "On the Difference Between
the
Cardinalities of Measurable Value Functions and von Neumann-Morgenstern
Utility
Functions,"
*Operations Research*, Vol. 45, No. 2, pp. 307-308 (March/April 1997). This paper presents an additional technical condition that is needed for the measurable value function decomposition theorem to hold. [May 19, 1997] **Page 242**- In the second paragraph, second line, "that we that" should read "that we have." [September 17, 2006]
**Pages 249-259**- Several proofs on these pages implicitly assume that the outcome space is
a
whole product set over the evaluation measures. Situations where the
outcome
space is only a subset of a product space are investigated in F.
Sainfort and
J. M. Deichtmann, "Decomposition of Utility Functions on Subsets
of Product
Sets,"
*Operations Research*, Vol. 44, No. 4, pp. 609-616 (July/August 1996). [September 30, 1996] **Page 258**- In the left hand side of (9.41.1), the "x" in u(x) is not defined. This
should
be u(x
_{1}, x_{2}, ..., x_{n}). [March 10, 2001] **Pages 259-260**- An additional reference comparing the Analytic Hierarchy Process
with
multiattribute value approaches is A. A. Salo and Raimo P. Hamalainen, "On
the
Measurement of Preferences in the Analytic Hierarchy Process,"
*Journal of Multi-Criteria Decision Analysis*, Vol. 6, No. 6, pp. 309-319 (November 1997). There are also six useful discussion articles on pages 320-343 of the same issue by M. Weber; H. A. Donegan; B. Schoner, E. U. Choo, and W. C. Wedley; T. L. Saaty; V. Belton and T. Gear; and A. Stam; as well as a rejoinder by the authors. [January 9, 1998] **Pages 285-298**- For a detailed discussion of various approaches to scenario planning,
including
numerous examples, see Gill Ringland,
*Scenario Planning: Managing for the Future*, Wiley, Chichester, England, 1998. [April 16, 1998] **Pages 291-293**- For a more detailed discussion of inadvertent intrusion into the
Waste
Isolation Pilot Project, see Martin J. Pasqualetti, "Landscape Permanence
and
Nuclear Warnings,"
*The Geographical Review*, Vol. 87, No. 1, pp. 73-91 (January 1997). [March 10, 2001; January 26, 2005]

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