1 1 slide chapter 10 multicriteria decision making n a scoring model for job selection n spreadsheet...

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Chapter 10Chapter 10Multicriteria Decision MakingMulticriteria Decision Making

A Scoring Model for Job SelectionA Scoring Model for Job Selection Spreadsheet Solution of the Job Selection Spreadsheet Solution of the Job Selection

Scoring ModelScoring Model The Analytic Hierarchy ProcessThe Analytic Hierarchy Process Establishing Priorities Using AHPEstablishing Priorities Using AHP Using AHP to Develop an Overall Priority Using AHP to Develop an Overall Priority

RankingRanking

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Multicriteria Decision ProblemsMulticriteria Decision Problems

In this chapter we consider decision problems In this chapter we consider decision problems involving two or more criteria.involving two or more criteria.

These criteria are often in conflict as the decision These criteria are often in conflict as the decision maker attempts to identify the best decision maker attempts to identify the best decision alternative.alternative.

A trade-off among the multiple criteria is often A trade-off among the multiple criteria is often necessary.necessary.

Management science techniques can be used to:Management science techniques can be used to:• quantify the importance of each criterion, quantify the importance of each criterion, • evaluate how each decision alternative evaluate how each decision alternative

contributes to each criterion, andcontributes to each criterion, and• identify the decision alternative that comes identify the decision alternative that comes

closest to meeting the multiple criteria.closest to meeting the multiple criteria.

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A Scoring Model for Job SelectionA Scoring Model for Job Selection

A graduating college student with a double A graduating college student with a double major in Finance and Accounting has received major in Finance and Accounting has received the following three job offers:the following three job offers:• financial analyst for an investment firm in financial analyst for an investment firm in

ChicagoChicago• accountant for a manufacturing firm in accountant for a manufacturing firm in

DenverDenver• auditor for a CPA firm in Houstonauditor for a CPA firm in Houston

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The student made the following comments:The student made the following comments:• ““The financial analyst position provides the The financial analyst position provides the

best opportunity for my long-run career best opportunity for my long-run career advancement.”advancement.”

• ““I would prefer living in Denver rather than in I would prefer living in Denver rather than in Chicago or Houston.”Chicago or Houston.”

• ““I like the management style and philosophy I like the management style and philosophy at the Houston CPA firm the best.”at the Houston CPA firm the best.”

Clearly, this is a multicriteria decision problem.Clearly, this is a multicriteria decision problem.

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Considering only the Considering only the long-run career long-run career advancementadvancement criterion, the criterion, the financial analyst financial analyst position in Chicagoposition in Chicago is the best decision is the best decision alternative.alternative.

Considering only the Considering only the locationlocation criterion, the criterion, the accountant position in Denveraccountant position in Denver is the best is the best decision alternative.decision alternative.

Considering only the Considering only the stylestyle criterion, the criterion, the auditor auditor position in Houstonposition in Houston is the best alternative. is the best alternative.

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Steps Required to Develop a Scoring ModelSteps Required to Develop a Scoring Model• Step 1:Step 1: List the decision-making criteria. List the decision-making criteria.• Step 2:Step 2: Assign a weight to each criterion. Assign a weight to each criterion.• Step 3:Step 3: Rate how well each decision Rate how well each decision

alternative alternative satisfies each criterion.satisfies each criterion.• Step 4:Step 4: Compute the score for each decision Compute the score for each decision

alternative.alternative.• Step 5:Step 5: Order the decision alternatives from Order the decision alternatives from

highest highest score to lowest score. The score to lowest score. The alternative with alternative with the highest score is the the highest score is the recommended recommended alternative.alternative.

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Mathematical ModelMathematical Model

SSjj = = wwii r rijij

ii

where:where:

rrijij = rating for criterion = rating for criterion ii and decision and decision alternative alternative jj

SSjj = = score for decision alternativescore for decision alternative j j

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Step 1: List the criteria (important factors).Step 1: List the criteria (important factors).• Career advancement Career advancement • LocationLocation• ManagementManagement• SalarySalary• PrestigePrestige• Job SecurityJob Security• Enjoyable workEnjoyable work

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Five-Point Scale Chosen for Step 2Five-Point Scale Chosen for Step 2

ImportanceImportance WeightWeight

Very unimportantVery unimportant 11

Somewhat unimportantSomewhat unimportant 22

Average importanceAverage importance 33

Somewhat importantSomewhat important 44

Very importantVery important 55

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Step 2: Assign a weight to each criterion.Step 2: Assign a weight to each criterion.

CriterionCriterion ImportanceImportance WeightWeight

Career advancementCareer advancement Very importantVery important 55

LocationLocation Average importanceAverage importance 33

ManagementManagement Somewhat importantSomewhat important 44

SalarySalary Average importanceAverage importance 33

PrestigePrestige Somewhat unimportantSomewhat unimportant 22

Job securityJob security Somewhat importantSomewhat important 44

Enjoyable workEnjoyable work Very importantVery important 55

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Nine-Point Scale Chosen for Step 3Nine-Point Scale Chosen for Step 3

Level of SatisfactionLevel of Satisfaction RatingRating

Extremely lowExtremely low 11

Very lowVery low 22

LowLow 33

Slightly lowSlightly low 44

AverageAverage 55

Slightly highSlightly high 66

HighHigh 77

Very highVery high 88

Extremely highExtremely high 99

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Step 3:Step 3: RateRate how well each decision alternative how well each decision alternative satisfies each criterion.satisfies each criterion.

Decision AlternativeDecision Alternative

Analyst AccountantAnalyst Accountant Auditor Auditor

CriterionCriterion ChicagoChicago DenverDenver HoustonHouston

Career advancementCareer advancement 88 66 44

LocationLocation 33 88 77

ManagementManagement 55 66 99

SalarySalary 66 77 55

PrestigePrestige77 55 44

Job securityJob security 44 77 66

Enjoyable workEnjoyable work 88 66 55

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Step 4: Compute the score for each decision alternative.Step 4: Compute the score for each decision alternative.

Decision Alternative 1Decision Alternative 1 - - Analyst in ChicagoAnalyst in Chicago

CriterionCriterion Weight ( Weight (wwii) Rating () Rating (rrii11) ) wwiirrii11

Career advancementCareer advancement 5 5 x x 8 8 = = 4040

LocationLocation 3 3 3 3 9 9

ManagementManagement 4 4 5 5 2020

SalarySalary 3 3 6 6 1818

PrestigePrestige 2 2 7 7 1414

Job securityJob security 4 4 4 4 1616

Enjoyable workEnjoyable work 5 5 8 8 4040

ScoreScore 157 157

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Step 4: Compute the score for each decision Step 4: Compute the score for each decision alternative.alternative.

SSjj = = wwii r rijij

II

SS11 = 5(8)+3(3)+4(5)+3(6)+2(7)+4(4)+5(8) = 157 = 5(8)+3(3)+4(5)+3(6)+2(7)+4(4)+5(8) = 157

SS22 = 5(6)+3(8)+4(6)+3(7)+2(5)+4(7)+5(6) = 167 = 5(6)+3(8)+4(6)+3(7)+2(5)+4(7)+5(6) = 167

SS33 = 5(4)+3(7)+4(9)+3(5)+2(4)+4(6)+5(5) = 149 = 5(4)+3(7)+4(9)+3(5)+2(4)+4(6)+5(5) = 149

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Step 4: Compute the Step 4: Compute the scorescore for each decision for each decision alternative.alternative.

Decision AlternativeDecision Alternative

Analyst AccountantAnalyst Accountant Auditor Auditor

CriterionCriterion ChicagoChicago DenverDenver HoustonHouston

Career advancementCareer advancement 4040 3030 2020

LocationLocation 9 9 2424 2121

ManagementManagement 2020 2424 3636

SalarySalary 1818 2121 1515

PrestigePrestige1414 1010 8 8

Job securityJob security 1616 2828 2424

Enjoyable workEnjoyable work 4040 3030 2525

ScoreScore 157 157 167 167 149 149

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Step 5:Step 5: Order the decision alternatives from Order the decision alternatives from highest highest score to lowest score. The score to lowest score. The alternative with the alternative with the highest score is the highest score is the recommended alternative.recommended alternative.

• The The accountant position in Denveraccountant position in Denver has the has the highest score and is the highest score and is the recommended decision recommended decision alternativealternative..

• Note that the analyst position in Chicago ranks Note that the analyst position in Chicago ranks first in 4 of 7 criteria compared to only 2 of 7 for first in 4 of 7 criteria compared to only 2 of 7 for the accountant position in Denver.the accountant position in Denver.

• But when the weights of the criteria are But when the weights of the criteria are considered, the Denver position is superior to the considered, the Denver position is superior to the Chicago job.Chicago job.

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Partial Spreadsheet Showing Steps 1 - 3Partial Spreadsheet Showing Steps 1 - 3

A B C D E1 RATINGS2 Analyst Accountant Auditor3 Criteria Weight Chicago Denver Houston4 Career Advancement 5 8 6 45 Location 3 3 8 76 Management 4 5 6 97 Salary 3 6 7 58 Prestige 2 7 5 49 Job Security 4 4 7 610 Enjoyable Work 5 8 6 5

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Partial Spreadsheet Showing Formulas for Step 4Partial Spreadsheet Showing Formulas for Step 4

11 A B C D E F12 SCORING CALCULATIONS1314 Analyst Accountant Auditor15 Criteria Chicago Denver Houston16 Career Advancement =B4*C4 =B4*D4 =B4*E417 Location =B5*C5 =B5*D5 =B5*E518 Management =B6*C6 =B6*D6 =B6*E619 Salary =B7*C7 =B7*D7 =B7*E720 Prestige =B8*C8 =B8*D8 =B8*E821 Job Security =B9*C9 =B9*D9 =B9*E922 Enjoyable Work =B10*C10 =B10*D10 =B10*E1023 Score =sum(C16:C22)24 =sum(D16:D22)25 =sum(E16:E22)

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Partial Spreadsheet Showing Results of Step 4Partial Spreadsheet Showing Results of Step 4

11 A B C D E12 SCORING CALCULATIONS1314 Analyst Accountant Auditor15 Criteria Chicago Denver Houston16 Career Advancement 40 30 2017 Location 9 24 2118 Management 20 24 3619 Salary 18 21 1520 Prestige 14 10 821 Job Security 16 28 2422 Enjoyable Work 40 30 2523 Score 157 167 149

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Analytic Hierarchy ProcessAnalytic Hierarchy Process

The The Analytic Hierarchy Process (AHP)Analytic Hierarchy Process (AHP), is a , is a procedure designed to quantify managerial procedure designed to quantify managerial judgments of the relative importance of each of judgments of the relative importance of each of several conflicting criteria used in the decision several conflicting criteria used in the decision making process.making process.

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Step 1: List the Overall Goal, Criteria, and Step 1: List the Overall Goal, Criteria, and Decision Decision Alternatives Alternatives

Step 2: Develop a Pairwise Comparison MatrixStep 2: Develop a Pairwise Comparison Matrix

Rate the relative importance between each Rate the relative importance between each pair of decision alternatives. The matrix lists the pair of decision alternatives. The matrix lists the alternatives horizontally and vertically and has the alternatives horizontally and vertically and has the numerical ratings comparing the horizontal (first) numerical ratings comparing the horizontal (first) alternative with the vertical (second) alternative.alternative with the vertical (second) alternative.

Ratings are given as follows:Ratings are given as follows:

. . . continued. . . continued

For each criterion, perform steps 2 through 5For each criterion, perform steps 2 through 5For each criterion, perform steps 2 through 5For each criterion, perform steps 2 through 5

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Step 2: Pairwise Comparison Matrix (continued)Step 2: Pairwise Comparison Matrix (continued)

Compared to the secondCompared to the second

alternative, the first alternative isalternative, the first alternative is: : Numerical Numerical ratingrating

extremely preferred extremely preferred 99

very strongly preferred very strongly preferred 77

strongly preferred strongly preferred 55

moderately preferred moderately preferred 33

equally preferred equally preferred 11

Intermediate numeric ratings of 8, 6, 4, 2 can be Intermediate numeric ratings of 8, 6, 4, 2 can be assigned. A reciprocal rating (i.e. 1/9, 1/8, etc.) is assigned. A reciprocal rating (i.e. 1/9, 1/8, etc.) is assigned when the second alternative is preferred to assigned when the second alternative is preferred to the first. The value of 1 is always assigned when the first. The value of 1 is always assigned when comparing an alternative with itself. comparing an alternative with itself.

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Step 3: Develop a Normalized Matrix Step 3: Develop a Normalized Matrix

Divide each number in a column of the Divide each number in a column of the pairwise comparison matrix by its column sum.pairwise comparison matrix by its column sum.

Step 4: Develop the Priority Vector Step 4: Develop the Priority Vector

Average each row of the normalized Average each row of the normalized matrix. These row averages form the priority matrix. These row averages form the priority vector of alternative preferences with respect vector of alternative preferences with respect to the particular criterion. The values in this to the particular criterion. The values in this vector sum to 1.vector sum to 1.

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Step 5: Calculate a Consistency RatioStep 5: Calculate a Consistency Ratio

The consistency of the subjective input in the The consistency of the subjective input in the pairwise comparison matrix can be measured by pairwise comparison matrix can be measured by calculating a consistency ratio. A consistency ratio of calculating a consistency ratio. A consistency ratio of less than .1 is good. For ratios which are greater less than .1 is good. For ratios which are greater than .1, the subjective input should be re-evaluated.than .1, the subjective input should be re-evaluated.

Step 6: Develop a Priority MatrixStep 6: Develop a Priority Matrix

After steps 2 through 5 has been performed for After steps 2 through 5 has been performed for all criteria, the results of step 4 are summarized in a all criteria, the results of step 4 are summarized in a priority matrix by listing the decision alternatives priority matrix by listing the decision alternatives horizontally and the criteria vertically. The column horizontally and the criteria vertically. The column entries are the priority vectors for each criterion. entries are the priority vectors for each criterion.

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Step 7: Develop a Criteria Pairwise Development Step 7: Develop a Criteria Pairwise Development Matrix Matrix

This is done in the same manner as that This is done in the same manner as that used to construct alternative pairwise used to construct alternative pairwise comparison matrices by using subjective ratings comparison matrices by using subjective ratings (step 2). Similarly, normalize the matrix (step 3) (step 2). Similarly, normalize the matrix (step 3) and develop a criteria priority vector (step 4). and develop a criteria priority vector (step 4).

Step 8: Develop an Overall Priority VectorStep 8: Develop an Overall Priority Vector

Multiply the criteria priority vector (from Multiply the criteria priority vector (from step 7) by the priority matrix (from step 6).step 7) by the priority matrix (from step 6).

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Determining the Consistency RatioDetermining the Consistency Ratio

Step 1: Step 1:

For each row of the pairwise comparison For each row of the pairwise comparison matrix, determine a weighted sum by summing matrix, determine a weighted sum by summing the multiples of the entries by the priority of its the multiples of the entries by the priority of its corresponding (column) alternative.corresponding (column) alternative.

Step 2:Step 2:

For each row, divide its weighted sum by For each row, divide its weighted sum by the priority of its corresponding (row) alternative.the priority of its corresponding (row) alternative.

Step 3:Step 3:

Determine the average, Determine the average, maxmax, of the results , of the results of step 2.of step 2.

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Determining the Consistency RatioDetermining the Consistency Ratio

Step 4: Step 4:

Compute the consistency index, CI, of the Compute the consistency index, CI, of the nn alternatives by: CI = (alternatives by: CI = (maxmax - - nn)/()/(nn - 1). - 1).

Step 5:Step 5:

Determine the random index, RI, as follows:Determine the random index, RI, as follows:

Number of RandomNumber of Random Number of RandomNumber of Random

Alternative (Alternative (nn)) Index (RI)Index (RI) Alternative (Alternative (nn)) Index (RI)Index (RI)

3 0.583 0.58 6 6 1.24 1.24

4 0.904 0.90 7 7 1.32 1.32

5 1.125 1.12 8 8 1.41 1.41 Step 6:Step 6:

Determine the consistency ratio, CR, as follows:Determine the consistency ratio, CR, as follows:

CR = CR/RI.CR = CR/RI.

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Example: Gill GlassExample: Gill Glass

Designer Gill Glass must decide which of Designer Gill Glass must decide which of three manufacturers will develop his "signature" three manufacturers will develop his "signature" toothbrushes. Three factors seem important to toothbrushes. Three factors seem important to Gill: (1) his costs; (2) reliability of the product; and, Gill: (1) his costs; (2) reliability of the product; and, (3) delivery time of the orders.(3) delivery time of the orders.

The three manufacturers are Cornell The three manufacturers are Cornell Industries, Brush Pik, and Picobuy. Cornell Industries, Brush Pik, and Picobuy. Cornell Industries will sell toothbrushes to Gill Glass for Industries will sell toothbrushes to Gill Glass for $100 per gross, Brush Pik for $80 per gross, and $100 per gross, Brush Pik for $80 per gross, and Picobuy for $144 per gross. Gill has decided that in Picobuy for $144 per gross. Gill has decided that in terms of terms of priceprice, Brush Pik is moderately preferred to , Brush Pik is moderately preferred to Cornell and very strongly preferred to Picobuy. In Cornell and very strongly preferred to Picobuy. In turn Cornell is strongly to very strongly preferred to turn Cornell is strongly to very strongly preferred to Picobuy.Picobuy.

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Hierarchy for the Manufacturer Selection ProblemHierarchy for the Manufacturer Selection Problem

Select the Best Toothbrush Manufacturer

Cost Reliability Delivery Time

CornellBrush PikPicobuy



Overall Goal

Criteria

DecisionAlternatives

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Forming the Pairwise Comparison Matrix For CostForming the Pairwise Comparison Matrix For Cost• Since Brush Pik is moderately preferred to Since Brush Pik is moderately preferred to

Cornell, Cornell's entry in the Brush Pik row is Cornell, Cornell's entry in the Brush Pik row is 3 and Brush Pik's entry in the Cornell row is 3 and Brush Pik's entry in the Cornell row is 1/3.1/3.

• Since Brush Pik is very strongly preferred to Since Brush Pik is very strongly preferred to Picobuy, Picobuy's entry in the Brush Pik row Picobuy, Picobuy's entry in the Brush Pik row is 7 and Brush Pik's entry in the Picobuy row is is 7 and Brush Pik's entry in the Picobuy row is 1/7.1/7.

• Since Cornell is strongly to very strongly Since Cornell is strongly to very strongly preferred to Picobuy, Picobuy's entry in the preferred to Picobuy, Picobuy's entry in the Cornell row is 6 and Cornell's entry in the Cornell row is 6 and Cornell's entry in the Picobuy row is 1/6.Picobuy row is 1/6.

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Pairwise Comparison Matrix for CostPairwise Comparison Matrix for Cost

Cornell Brush Pik PicobuyCornell Brush Pik Picobuy

CornellCornell 1 1/3 1 1/3 6 6

Brush PikBrush Pik 3 3 1 1 7 7

PicobuyPicobuy 1/6 1/6 1/7 1/7 1 1

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Normalized Matrix for CostNormalized Matrix for Cost

Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum. For example, for Cornell the column sum = sum. For example, for Cornell the column sum = 1 + 3 + 1/6 = 25/6. This gives:1 + 3 + 1/6 = 25/6. This gives:


CornellCornell 6/25 7/31 6/25 7/31 6/14 6/14

Brush PikBrush Pik 18/25 21/31 18/25 21/31 7/14 7/14

PicobuyPicobuy 1/25 3/31 1/25 3/31 1/14 1/14

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Priority Vector For CostPriority Vector For Cost

The priority vector is determined by The priority vector is determined by averaging the row entries in the normalized averaging the row entries in the normalized matrix. Converting to decimals we get:matrix. Converting to decimals we get:

Cornell: ( 6/25 + 7/31 + 6/14)/3 Cornell: ( 6/25 + 7/31 + 6/14)/3 = .298 = .298

Brush Pik: (18/25 + 21/31 + 7/14)/3 Brush Pik: (18/25 + 21/31 + 7/14)/3 = .632 = .632

Picobuy: ( 1/25 + 3/31 + 1/14)/3 Picobuy: ( 1/25 + 3/31 + 1/14)/3 = .069 = .069

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Checking ConsistencyChecking Consistency• Multiply each column of the pairwise comparison Multiply each column of the pairwise comparison

matrix by its priority:matrix by its priority:

1 1/3 6 .923 1 1/3 6 .923

.298 3 + .632 1 + .069 7 = .298 3 + .632 1 + .069 7 = 2.009 2.009

1/6 1/7 1 .209 1/6 1/7 1 .209 • Divide these number by their priorities to get:Divide these number by their priorities to get:

.923/.298 = 3.097.923/.298 = 3.097

2.009/.632 = 3.1792.009/.632 = 3.179

.209/.069 = 3.029.209/.069 = 3.029

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Checking ConsistencyChecking Consistency

• Average the above results to get Average the above results to get maxmax..

maxmax = (3.097 + 3.179 + 3.029)/3 = 3.102 = (3.097 + 3.179 + 3.029)/3 = 3.102

• Compute the consistence index, CI, for two terms Compute the consistence index, CI, for two terms by:by:

CI = (CI = (maxmax - - nn)/()/(nn - 1) = (3.102 - 3)/2 = .051 - 1) = (3.102 - 3)/2 = .051

• Compute the consistency ratio, CR, by CI/RI, Compute the consistency ratio, CR, by CI/RI, where RI = .58 for 3 factors:where RI = .58 for 3 factors:

CR = CI/RI = .051/.58 = .088CR = CI/RI = .051/.58 = .088

Since the consistency ratio, CR, is less than .10, this Since the consistency ratio, CR, is less than .10, this is well within the acceptable range for consistency. is well within the acceptable range for consistency.

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Gill Glass has determined that for Gill Glass has determined that for reliabilityreliability, Cornell is very strongly preferable to , Cornell is very strongly preferable to Brush Pik and equally preferable to Picobuy. Brush Pik and equally preferable to Picobuy. Also, Picobuy is strongly preferable to Brush Pik.Also, Picobuy is strongly preferable to Brush Pik.

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Pairwise Comparison Matrix for ReliabilityPairwise Comparison Matrix for Reliability


CornellCornell 1 7 1 7 2 2

Brush PikBrush Pik 1/7 1/7 1 1 5 5

PicobuyPicobuy 1/2 1/2 1/5 1/5 1 1

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Normalized Matrix for ReliabilityNormalized Matrix for Reliability

Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum. For example, for Cornell the column sum = sum. For example, for Cornell the column sum = 1 + 1/7 + 1/2 = 23/14. This gives:1 + 1/7 + 1/2 = 23/14. This gives:


CornellCornell 14/23 35/41 14/23 35/41 2/8 2/8


PicobuyPicobuy 7/23 1/41 7/23 1/41 1/8 1/8

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Priority Vector For ReliabilityPriority Vector For Reliability

The priority vector is determined by averaging The priority vector is determined by averaging the row entries in the normalized matrix. Converting the row entries in the normalized matrix. Converting to decimals we get:to decimals we get:

Cornell: (14/23 + 35/41 + 2/8)/3 = .571 Cornell: (14/23 + 35/41 + 2/8)/3 = .571

Brush Pik: ( 2/23 + 5/41 + 5/8)/3 = .278 Brush Pik: ( 2/23 + 5/41 + 5/8)/3 = .278

Picobuy: ( 7/23 + 1/41 + 1/8)/3 = .151 Picobuy: ( 7/23 + 1/41 + 1/8)/3 = .151


Gill Glass’ responses to reliability could be Gill Glass’ responses to reliability could be checked for consistency in the same manner as was checked for consistency in the same manner as was cost.cost.

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Gill Glass has determined that for Gill Glass has determined that for delivery delivery timetime, Cornell is equally preferable to Picobuy. , Cornell is equally preferable to Picobuy. Both Cornell and Picobuy are very strongly to Both Cornell and Picobuy are very strongly to extremely preferable to Brush Pik.extremely preferable to Brush Pik.

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Pairwise Comparison Matrix for Delivery TimePairwise Comparison Matrix for Delivery Time


CornellCornell 1 8 1 8 1 1

Brush PikBrush Pik 1/8 1/8 1 1 1/8 1/8

PicobuyPicobuy 1 1 8 8 1 1

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Normalized Matrix for Delivery TimeNormalized Matrix for Delivery Time

Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum. sum.


CornellCornell 8/17 8/17 8/17 8/17 8/17 8/17


PicobuyPicobuy 8/17 8/17 8/17 8/17 8/17 8/17

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Priority Vector For Delivery TimePriority Vector For Delivery Time

The priority vector is determined by averaging The priority vector is determined by averaging the row entries in the normalized matrix. the row entries in the normalized matrix. Converting to decimals we get:Converting to decimals we get:

Cornell: (8/17 + 8/17 + 8/17)/3 = .471 Cornell: (8/17 + 8/17 + 8/17)/3 = .471

Brush Pik: (1/17 + 1/17 + 1/17)/3 = .059 Brush Pik: (1/17 + 1/17 + 1/17)/3 = .059

Picobuy: (8/17 + 8/17 + 8/17)/3 = .471 Picobuy: (8/17 + 8/17 + 8/17)/3 = .471


Gill Glass’ responses to delivery time could be Gill Glass’ responses to delivery time could be checked for consistency in the same manner as was checked for consistency in the same manner as was cost.cost.

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The accounting department has The accounting department has determined that in terms of determined that in terms of criteriacriteria, cost is , cost is extremely preferable to delivery time and very extremely preferable to delivery time and very strongly preferable to reliability, and that strongly preferable to reliability, and that reliability is very strongly preferable to delivery reliability is very strongly preferable to delivery time.time.

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Pairwise Comparison Matrix for CriteriaPairwise Comparison Matrix for Criteria

Cost Reliability DeliveryCost Reliability Delivery

CostCost 1 7 1 7 9 9

ReliabilityReliability 1/7 1/7 1 1 7 7

DeliveryDelivery 1/9 1/9 1/7 1/7 1 1

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Normalized Matrix for CriteriaNormalized Matrix for Criteria

Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum. sum.


CostCost 63/79 49/57 63/79 49/57 9/17 9/17

ReliabilityReliability 9/79 7/57 9/79 7/57 7/17 7/17

DeliveryDelivery 7/79 1/57 7/79 1/57 1/17 1/17

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Priority Vector For CriteriaPriority Vector For Criteria

The priority vector is determined by The priority vector is determined by averaging the row entries in the normalized averaging the row entries in the normalized matrix. Converting to decimals we get:matrix. Converting to decimals we get:

Cost: Cost: (63/79 + 49/57 + 9/17)/3 (63/79 + 49/57 + 9/17)/3 = .729 = .729

Reliability: Reliability: ( 9/79 + 7/57 + 7/17)/3 ( 9/79 + 7/57 + 7/17)/3 = .216 = .216

Delivery: Delivery: ( 7/79 + 1/57 + 1/17)/3 ( 7/79 + 1/57 + 1/17)/3 = .055= .055

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Overall Priority VectorOverall Priority Vector

The overall priorities are determined by The overall priorities are determined by multiplying the priority vector of the criteria by multiplying the priority vector of the criteria by the priorities for each decision alternative for the priorities for each decision alternative for each objective.each objective.

Priority VectorPriority Vector

for Criteriafor Criteria [ .729 .216 [ .729 .216 .055 ] .055 ]


Cornell Cornell .298 .571 .298 .571 .471 .471

Brush PikBrush Pik .632 .278 .632 .278 .059 .059

PicobuyPicobuy .069 .151 .069 .151 .471 .471

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Overall Priority Vector (continued)Overall Priority Vector (continued)

Thus, the overall priority vector is:Thus, the overall priority vector is:

Cornell:Cornell: (.729)(.298) + (.216)(.571) + (.055)(.729)(.298) + (.216)(.571) + (.055)(.471) = .366(.471) = .366

Brush Pik: (.729)(.632) + (.216)(.278) + (.055)Brush Pik: (.729)(.632) + (.216)(.278) + (.055)(.059) = .524(.059) = .524

Picobuy: (.729)(.069) + (.216)(.151) + (.055)Picobuy: (.729)(.069) + (.216)(.151) + (.055)(.471) = .109(.471) = .109

Brush Pik appears to be the overall Brush Pik appears to be the overall recommendation.recommendation.

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Spreadsheet LayoutSpreadsheet Layout

Pairwise Compar. Normalized Pairwise Compar. Normalized Wgt. Wgt. Consist.Consist.

MatricesMatrices MatricesMatrices PriorityPriority SumSum Meas.Meas.

Prior. SummaryPrior. Summary Overall Prior. Overall Prior.

Criteria (3x3)

Cost (3x3)

Reliability (3x3)

Deliv. Time (3x3)

Criteria (3x3)

(3x3)

Cost (3x3)

Reliability (3x3)

Deliv. Time (3x3)

(3x1)

(3x1)

(3x1)

(3x1)

(3x1)

Consist. Ratio

Consist. Ratio

Consist. Ratio

Consist. Ratio

(3x1) (3x1)

(3x1)

(3x1)

(3x1)

(3x1)

(3x1)

(3x1)

1 1 slide chapter 10 multicriteria decision making n a scoring model for job selection n spreadsheet...

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