1. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-1 Multicriteria Decision Making u Decision problem often involve two or more conflicting criterion or objectives: –Investing: risk vs. return –Choosing Among Job Offers: salary, location, career potential, etc. –Selecting a Camcorder: price, warranty, zoom, weight, lighting, etc. –Choosing Among Job Applicants: education, experience, personality, etc. u We’ll consider two techniques for these types of problems: –The Multicriteria Scoring Model –The Analytic Hierarchy Process (AHP)

2. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-2 The Multicriteria Scoring Model u Score (or rate) each alternative on each criterion. u Assign weights the criterion reflecting their relative importance.  For each alternative j, compute a weighted average score as: w i = weight for criterion i s ij = score for alternative i on criterion j u See file Fig15-41.xls

3. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-3 The Analytic Hierarchy Process (AHP) u Provides a structured approach for determining the scores and weights in a multicriteria scoring model. u We’ll illustrate AHP using the following example: –A company wants to purchase a new payroll and personnel records information system. –Three systems are being considered (X, Y and Z). –Three criteria are relevant: v Price v User support v Ease of use

4. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-4 Pairwise Comparisons u The first step in AHP is to create a pairwise comparison matrix for each alternative on each criterion using the following values: Value Preference 1Equally Preferred 2Equally to Moderately Preferred 3Moderately Preferred 4Moderately to Strongly Preferred 5Strongly Preferred 6Strongly to Very Strongly Preferred 7Very Strongly Preferred 8 Very Strongly to Extremely Preferred 9Extremely Preferred  P ij = extent to which we prefer alternative i to j on a given criterion.  We assume P ji = 1/P ij u See price comparisons in file Fig15-43.xls

5. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-5 Price u X is Strongly Preferred to Y u X is Very Strongly Preferred to Z u Y is Moderately Preferred to Z

6. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-6 Support u X is Equally to Moderately Preferred to Z u Y is Moderately Preferred to X u Y is Strongly Preferred to Z

7. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-7 Ease of Use u Y is Equally to Moderately Preferred to X u Z is Moderately Preferred to X u Z is Equally to Moderately Preferred to Y

8. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-8 Criteria u Support is Moderately Preferred to Price u Ease of Use is Moderately to Strongly Preferred to Price u Ease of Use is Equally to Moderately Preferred to Support

9. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-9 Normalization & Scoring u To normalize a pairwise comparison matrix, 1) Compute the sum of each column, 2) Divide each entry in the matrix by its column sum.  The score (s j ) for each alternative is given by the average of each row in the normalized comparison matrix. u See file Fig15-43.xls

10. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-10 Consistency u We can check to make sure the decision maker was consistent in making the comparisons.  The consistency measure for alternative i is: where P ij = pairwise comparison of alternative i to j s j = score for alternative j  If the decision maker was perfectly consistent, each C i should equal to the number of alternatives in the problem.

11. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-11 Consistency (cont’d) u Typically, some inconsistency exists. u The inconsistency is not deemed a problem provided the Consistency Ratio (CR) is no more than 10% where, RI =0.000.580.901.121.241.321.41 for n =2345678

12. Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-12 Obtaining Remaining Scores & Weights u This process is repeated to obtain scores for the other criterion as well as the criterion weights. u The scores and weights are then used as inputs to a multicriteria scoring model in the usual way. u See file Fig15-43.xls