Logical Decisions - Classweb

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Each cell in the matrix represents the ratio of the row alternative's performance on the measure to the column alternative's performance. You complete the AHP assessment process by entering performance ratios into the proper cells. You will be done when each cell has the correct performance ratio. Your task is not quite as bad as it seems. Since the cells on the diagonal of the matrix compare the performance of each alternative to itself, the performance ratios in those cells must all be one. You don't have to enter these obvious ratios. LDW uses the diagonal cells to show the computed utilities for the alternatives instead of the forced 1.0 ratios. In addition, the ratio of a row to a column alternative must be the inverse of the ratio of the column alternative to the row alternative. For example, suppose alternative A is in row and column 1 of the matrix and alternative B is in row and column 2. If A's performance on the measure is twice as good as B's then the cell for row 1 and column 2 should have the ratio 2.0. Similarly, the cell for row 2 and column 1 should have the ratio 0.5, since it is the ratio of B's performance to A's. These ratios are inextricably linked, so when you enter the ratio for one cell, LDW automatically enters its inverse in the corresponding cell on the other side of the matrix. This means you only have to enter as many ratios as there are cells above the diagonal row in the matrix to complete your assessment. Each time you enter a ratio, LDW marks the cell in blue and updates the level in the corresponding cell on the other side of the diagonal. LDW also marks this cell in blue. You will have completed your assessment when all the cells in the matrix are marked in blue. The developers of the AHP method have provided some cues to help you set the performance ratios. They have defined the following five terms along with a corresponding performance ratio: Ratio Term Explanation 9-28 Section 9 -- In Depth
1 Equal Importance Two activities contribute equally to the objective. 3 Moderate Importance Experience and judgment slightly favor one activity over another. 5 Essential or Strong Experience and judgment Importance strongly favor one activity over another. 7 Demonstrated Importance An activity is strongly favored and its dominance is demonstrated in practice. 9 Extreme Importance The evidence favoring one activity over another is of the highest possible order of affirmation. In the traditional AHP approach, you can only enter one of these ratios or one of the intermediate ratios 2,4,6, or 8. LDW does not impose these restrictions. You can enter any ratio you want. However, if you use the AHP dialog box to select a ratio, you are restricted to one of these nine ratios. To compute the utilities for the alternatives from the ratios, the AHP method uses computations based on linear algebra. This method results in consistent utilities if you have entered completely consistent ratios and results in "best fit" utilities if your ratios are not completely consistent. The utility for each alternative is generally very close to the geometric mean of the ratios in its matrix row. The geometric mean is the nth root of the product of the ratios, where n is the number of alternatives. The utilities are computed for each row and the means are then normalized to sum to one. Instead of waiting till you have entered all the needed ratios, LDW computes the utilities for the alternatives each time you enter a new ratio. (You can turn off this computation by unchecking the AHP::Estimate Ratios option.) LDW uses all the ratios you have entered so far as the basis for its estimates. LDW uses a simple iterative procedure to estimate the ratios you haven't entered yet based on those you have. Thus, there is Section 9 -- In Depth 9-29
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Logical Decisions Decision Support
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Table of Contents Table of Contents
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Assessing Weights with Weight Ratio
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Assessing Interactions Between Meas
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Introduction Real decisions aren't
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S E C T I O N Requirements and Inst
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"Logical Decisions". This program g
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Quick Start Introduction This secti
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Defining goals and measures. In LDW
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Figure 3-1. The SUF for "Years of E
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weights of the measures. All of the
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S E C T I O N Basic Tutorial 4
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Figure 4-1. Tutorial overview. 4-2
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Now lets make sure the alternatives
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Assume you have decided that you wi
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Next we will enter the measures for
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Defining Preferences The alternativ
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1. Select the Assess::Common Units
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almost equally unacceptable, while
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1. Select the Assess::Common Units
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When you do this, the tradeoff grap
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1. Select "Performance" and "Price"
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8. Click on the "Equal" button to t
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Figure 4-11. Display generated by R
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Figure 4-13. Overall ranking for tr
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Figure 4-15. Graph showing sensitiv
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You can see the completed introduct
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Advanced Tutorial This tutorial sec
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Probabilities There is a problem wi
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This information indicates that the
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A uniform distribution is defined b
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On the left is a list of the possib
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Figure 5-2. Example of Results::Unc
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screen a large database for the alt
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9. LDW will ask if you want to appe
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commit to buying their truck before
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see that the rankings for all the a
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S E C T I O N Using LDW 1: Structur
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The Edit::Insert option. The Insert
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! Summary -- view a dialog box that
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structure like an organization char
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If you check the Show Assessment St
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saves it for later pasting. When yo
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You can create a new Matrix view by
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The quick entry view shows the alte
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Structuring Goals The goals in an L
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these two fields to describe each m
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the hierarchy. In the Matrix view,
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! Point Estimate -- use a single nu
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Figure 6-12. Example of a measure l
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Figure 6-14. Example of a measure l
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pass, LDW replaces each probabilist
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Figure 6-17. Dialog box for definin
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Figure 6-18. Measure Category Dialo
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S E C T I O N Using LDW 2: Assessin
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measure utility functions for the g
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information as possible when you ch
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measures with categories require mu
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The "Reset" button deletes any asse
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You can change the shape of the cur
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Figure 7-4. Utility Assessment Scre
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very different from the average of
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Figure 7-6. Assessment matrix for A
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You can, however, leave the assessm
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properties dialog box can be select
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the same level. LDW provides a grap
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options in the Hierarchy menu to ad
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The check box labeled "Allow Repres
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Next you will see a tradeoff assess
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The Tradeoff::Use Alternatives to S
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Figure 7-13. Example of Direct Entr
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You can think of the importance num
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Figure 7-15. Assessment Screen for
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When you have selected two members
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("importance strength") that best d
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clicking on the "Initialize" button
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Set a Small k. The Enter Small k op
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select the tradeoff you would like
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Figure 7-18. Effects of consistency
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Using LDW 3: Reviewing Results Intr
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The curve shows how the utility fun
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The tradeoff graph has one measure
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When you select the option, you are
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the relative weights of the "Price"
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epresents a computer alternative wi
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Figure 8-11. Example of Review::Ass
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e true even if the measure has a ve
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an analysis are included in exactly
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Graph Weights The Graph Weights dis
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Figure 8-16. Results::Rank Alternat
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Figure 8-18. Dialog box for Results
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You can use the measure equivalents
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simulation for each alternative usi
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Sensitivity Graphs Sensitivity grap
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You can view a sensitivity table by
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Figure 8-28. Example of Results::Sc
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Figure 8-30. Example of Results::Sc
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In the dialog box, you are asked to
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Figure 8-34. Dialog box for Results
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Graph an Alternative The graph an a
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Figure 8-38. Example of Results::Gr
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Finally, the two radio buttons on t
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Figure 8-43. Example of Results::Co
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Printing and Saving Windows You can
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The dialog box will show you the fi
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Figure 8-45. Dialog box for Edit::C
Page 223 and 224: Changing the range for utility. You
Page 225 and 226: Figure 8-50. Dialog box for Prefere
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Page 229 and 230: copies the selected objects to the
Page 231 and 232: analysis with the skeleton analysis
Page 233 and 234: Figure 8-55. Dialog box for File::I
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Page 237 and 238: The idea of the Import Structure op
Page 239 and 240: Next, LDW asks you if it should app
Page 241 and 242: Other Options utility function for
Page 243: In addition, the Window menu contai
Page 247 and 248: In Depth Introduction This section
Page 249 and 250: A third example is a portfolio deci
Page 251 and 252: Each alternative has a raw score (c
Page 253 and 254: into more specific goals continues
Page 255 and 256: Measures in LDW You define measures
Page 257 and 258: computed measure levels to common u
Page 259 and 260: Converting the Measures to Common U
Page 261 and 262: Figure 9-2. Example of linear (stra
Page 263 and 264: For an example of the mid-level spl
Page 265 and 266: Since U(L0) = U(80) = 0 and U(L1) =
Page 267 and 268: Figure 9-5. Summary of SUF assessme
Page 269 and 270: describe two alternatives: A, which
Page 271 and 272: with equal chances of 40 and 70 per
Page 273: In the original formulation of the
Page 277 and 278: You begin the process by selecting
Page 279 and 280: Figure 9-7. Effects of goals with a
Page 281 and 282: 0.5. Then the weight assigned to "P
Page 283 and 284: ! You can use the "Smarter Method"
Page 285 and 286: allocates this weight before comput
Page 287 and 288: nth root of the product of the rati
Page 289 and 290: Figure 9-8. Summary of estimating t
Page 291 and 292: on the decision maker's response, L
Page 293 and 294: Figure 9-10. MUF assessment figure
Page 295 and 296: Now think of adjusting P so that th
Page 297 and 298: Another approach is to use the rang
Page 299 and 300: Figure 9-12. Quantitative range vs.
Page 301 and 302: If a measure’s range changes, LDW
Page 303 and 304: Figure 9-14 is an example of the ov
Page 305 and 306: Similarly, a single member can have
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Page 309 and 310: A probability of less than 0.5 for
Page 311 and 312: Interpreting the Ranking Results LD
Page 313: S E C T I O N Examples 10
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Page 318 and 319: The completed goals hierarchy is sh
Page 320 and 321: Buying a House The ranking results
Page 322 and 323: Figure 10-5. Goals hierarchy for bu
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Overall goal Quality goal Costs goa
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The preference assessments were don
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Figure 10-9. Goals hierarchy for re
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! Noise, ! Agricultural Impacts, an
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S E C T I O N Commands Summary 11
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Assess Menu Edit Menu The Assess me
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File Menu Edit::Insert Lets you add
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utility function” if the active g
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Matrix Menu ! Hierarchy -- options
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Results::Dynamic Sensitivity See th
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Review::Compute Utilities Compute t
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Tradeoff Menu View Menu LDW display
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S E C T I O N Glossary 12
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Common Units Certainty Equivalent C
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LDW File Level Lottery Measure assi
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MUF MUF Formula See also: Alternati
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Preference Set Probabilistic Level
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Tradeoff Trial program decides whic
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Bibliography B
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The classic reference on multiple m
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Appendix This appendix describes th
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= .125 Thus the weight for cost is
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Index adjusted AHP ................
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computing ................8 - 3 int
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