1 1 Slide © 2005 Thomson/South-Western EMGT 501 HW Solutions Problem Problem

2 2 Slide © 2005 Thomson/South-Western a.b $1000 $700 $300 $800 $400 $200 $1600 $800 $400 Payoffs ( in thousands of $ ) High 0.2 Medium 0.5 Low 0.3 Without Com 0.4 With Com 0.6 High 0.3 Medium 0.4 Low 0.3 High 0.5 Medium 0.3 Low 0.2 Battle Pacific Space Pirates $640 $460 $1120 $724

3 3 Slide © 2005 Thomson/South-Western b. cont. Node 2: EV =.2(1,000K) +.5(700K) +.3(300K) = $640,000 Node 4: EV =.3(800K) +.4(400K) +.3(200K) = $460,000 Node 5: EV =.5(1,600K) +.3(800K) +.2(400K) = $1,120,000 Node 3: EV =.6(460K) +.4(1,120K) = $724,000 Recommendation: Space Pirates ($724K) is better than Battle Pacific ($640K).

4 4 Slide © 2005 Thomson/South-Western c. n Outcome and Probability n $1600K : (0.4)(0.5)=0.2 n $800K : (0.6)(0.3)+(0.4)(0.3)=0.3 n $400K : (0.6)(0.4)+(0.4)(0.2)=0.32 n $200K : (0.6)(0.3)=0.18

5 5 Slide © 2005 Thomson/South-Western c $ Probability Profit

6 6 Slide © 2005 Thomson/South-Western d. EV(Node 1) = 640K EV(Node 2) = P(Node 4)460K + P(Node 5)1120K Let P(Node 4) = p EV(Node 2) = 460p (1 – p) = -660p If 640 > -660p , then recommendation is changed. So, p >

7 7 Slide © 2005 Thomson/South-Western a. d1 : Purchase land d2 : Do not purchase land EV(d1)=(600K)(0.5)+(-200K)(0.5)=200K EV(d2)=0 Recommendation : d1(purchase) Expected Value = $200,000

8 8 Slide © 2005 Thomson/South-Western 13.21b EV(d 1 |H) = V s1 P(s 1 |H) + V s2 P(s 2 |H) = (600K)(0.18) + (-200K)(0.82) = -56K EV(d 2 |H) = 0 EV(d 1 |L) = V s1 P(s 1 |L) + V s2 P(s 2 |L) = (600K)(0.89) + (-200k)(0.11) = 512K EV(d 2 |L) = 0 If the investor predicts H, then d 2 is selected with EV(d 2 |H) = 0. Meanwhile, he predicts L, then d 1 is selected with EV(d 1 |L) = 512K

9 9 Slide © 2005 Thomson/South-Western 13.21b EV with SI = EV(d 1 |L)P(L) + EV(d 2 |H)P(H) = (512K)(0.45) + 0(0.55) = 230.4k

10 Slide © 2005 Thomson/South-Western c. EVSI =$230,400-$200,000=$30,400. Since the cost is $10,000. The investor should purchase the option.

11 Slide © 2005 Thomson/South-Western Home Work Due Day: Nov 18 (noon) 08

12 Slide © 2005 Thomson/South-Western Chapter 14 Multicriteria Decisions n Goal Programming n Goal Programming: Formulation n Scoring Models n Analytic Hierarchy Process (AHP) n Establishing Priorities Using AHP n Using AHP to Develop an Overall Priority Ranking

13 Slide © 2005 Thomson/South-Western Goal Programming n Goal programming may be used to solve linear programs with multiple objectives, with each objective viewed as a "goal". n In goal programming, d i + and d i -, deviation variables, are the amounts a targeted goal i is overachieved or underachieved, respectively. n The goals themselves are added to the constraint set with d i + and d i - acting as the surplus and slack variables.

14 Slide © 2005 Thomson/South-Western Goal Programming n One approach to goal programming is to satisfy goals in a priority sequence. Second-priority goals are pursued without reducing the first- priority goals, etc. n For each priority level, the objective function is to minimize the (weighted) sum of the goal deviations. n Previous "optimal" achievements of goals are added to the constraint set so that they are not degraded while trying to achieve lesser priority goals.

15 Slide © 2005 Thomson/South-Western Goal Programming Formulation Step 1: Decide the priority level of each goal. Step 2: Decide the weight on each goal. If a priority level has more than one goal, for each goal i decide the weight, w i, to be placed on the deviation(s), d i + and/or d i -, from the goal. If a priority level has more than one goal, for each goal i decide the weight, w i, to be placed on the deviation(s), d i + and/or d i -, from the goal.

16 Slide © 2005 Thomson/South-Western Goal Programming Formulation Step 3: Set up the initial linear program. Min w 1 d w 2 d 2 - s.t. Functional Constraints, s.t. Functional Constraints, and Goal Constraints and Goal Constraints Step 4: Solve the current linear program. If there is a lower priority level, go to step 5. Otherwise, a final solution has been reached.

17 Slide © 2005 Thomson/South-Western Goal Programming Formulation Step 5: Set up the new linear program. Consider the next-lower priority level goals and formulate a new objective function based on these goals. Add a constraint requiring the achievement of the next-higher priority level goals to be maintained. The new linear program might be: Min w 3 d w 4 d 4 - Min w 3 d w 4 d 4 - s.t. Functional Constraints, s.t. Functional Constraints, Goal Constraints, and Goal Constraints, and w 1 d w 2 d 2 - = k w 1 d w 2 d 2 - = k Go to step 4. (Repeat steps 4 and 5 until all priority levels have been examined.)

18 Slide © 2005 Thomson/South-Western Example: Conceptual Products Conceptual Products is a computer company that produces the CP400 and CP500 computers. The computers use different computers use different mother boards produced mother boards produced in abundant supply by the company, but use the same cases and disk drives. The CP400 models use two floppy disk drives and no zip disk drives whereas the CP500 models use one floppy disk drive and one zip disk drive.

19 Slide © 2005 Thomson/South-Western Example: Conceptual Products The disk drives and cases are bought from vendors. There are 1000 floppy disk drives, 500 zip disk drives, and 600 cases available to Conceptual Products on a weekly basis. It takes one hour to manufacture a CP400 and its profit is $200 and it takes one and one-half hours to manufacture a CP500 and its profit is $500.

20 Slide © 2005 Thomson/South-Western Example: Conceptual Products The company has four goals: The company has four goals: Priority 1: Meet a state contract of 200 CP400 machines weekly. (Goal 1) Priority 1: Meet a state contract of 200 CP400 machines weekly. (Goal 1) Priority 2: Make at least 500 total computers weekly. (Goal 2) Priority 2: Make at least 500 total computers weekly. (Goal 2) Priority 3: Make at least $250,000 weekly. (Goal 3) Priority 3: Make at least $250,000 weekly. (Goal 3) Priority 4: Use no more than 400 man-hours per week. (Goal 4) Priority 4: Use no more than 400 man-hours per week. (Goal 4)

21 Slide © 2005 Thomson/South-Western n Variables x 1 = number of CP400 computers produced weekly x 1 = number of CP400 computers produced weekly x 2 = number of CP500 computers produced weekly x 2 = number of CP500 computers produced weekly d i - = amount the right hand side of goal i is deficient d i - = amount the right hand side of goal i is deficient d i + = amount the right hand side of goal i is exceeded d i + = amount the right hand side of goal i is exceeded n Functional Constraints Availability of floppy disk drives: 2 x 1 + x 2 < 1000 Availability of zip disk drives: x 2 < 500 Availability of cases: x 1 + x 2 < 600 Goal Programming: Formulation

22 Slide © 2005 Thomson/South-Western n Goals (1) 200 CP400 computers weekly: x 1 + d d 1 + = 200 (2) 500 total computers weekly: (2) 500 total computers weekly: x 1 + x 2 + d d 2 + = 500 x 1 + x 2 + d d 2 + = 500 (3) $250(in thousands) profit: (3) $250(in thousands) profit:.2 x x 2 + d d 3 + = x x 2 + d d 3 + = 250 (4) 400 total man-hours weekly: (4) 400 total man-hours weekly: x x 2 + d d 4 + = 400 x x 2 + d d 4 + = 400 Non-negativity: Non-negativity: x 1, x 2, d i -, d i + > 0 for all i x 1, x 2, d i -, d i + > 0 for all i Goal Programming: Formulation

23 Slide © 2005 Thomson/South-Western n Objective Functions Priority 1: Minimize the amount the state contract is not met: Min d 1 - Priority 1: Minimize the amount the state contract is not met: Min d 1 - Priority 2: Minimize the number under 500 computers produced weekly: Min d 2 - Priority 2: Minimize the number under 500 computers produced weekly: Min d 2 - Priority 3: Minimize the amount under $250,000 earned weekly: Min d 3 - Priority 3: Minimize the amount under $250,000 earned weekly: Min d 3 - Priority 4: Minimize the man-hours over 400 used weekly: Min d 4 + Priority 4: Minimize the man-hours over 400 used weekly: Min d 4 + Goal Programming: Formulation

24 Slide © 2005 Thomson/South-Western n Formulation Summary Min P 1 ( d 1 - ) + P 2 ( d 2 - ) + P 3 ( d 3 - ) + P 4 ( d 4 + ) s.t. 2 x 1 + x 2 < 1000 s.t. 2 x 1 + x 2 < x 2 < x 2 < 500 x 1 + x 2 < 600 x 1 + x 2 < 600 x 1 + d d 1 + = 200 x 1 + d d 1 + = 200 x 1 + x 2 + d d 2 + = 500 x 1 + x 2 + d d 2 + = x x 2 + d d 3 + = x x 2 + d d 3 + = 250 x x 2 + d d 4 + = 400 x x 2 + d d 4 + = 400 x 1, x 2, d 1 -, d 1 +, d 2 -, d 2 +, d 3 -, d 3 +, d 4 -, d 4 + > 0 x 1, x 2, d 1 -, d 1 +, d 2 -, d 2 +, d 3 -, d 3 +, d 4 -, d 4 + > 0 Goal Programming: Formulation

25 Slide © 2005 Thomson/South-Western Scoring Model for Job Selection A graduating college student with a double major in Finance and Accounting has received the following three job offers: financial analyst for an investment financial analyst for an investment firm in Chicago firm in Chicago accountant for a manufacturing accountant for a manufacturing firm in Denver firm in Denver auditor for a CPA firm in Houston auditor for a CPA firm in Houston

26 Slide © 2005 Thomson/South-Western Scoring Model for Job Selection n The student made the following comments: “The financial analyst position “The financial analyst position provides the best opportunity for my long-run career advancement.” “I would prefer living in Denver “I would prefer living in Denver rather than in Chicago or Houston.” “I like the management style and “I like the management style and philosophy at the Houston CPA firm the best.” n Clearly, this is a multicriteria decision.

27 Slide © 2005 Thomson/South-Western Scoring Model for Job Selection n Considering only the long-run career advancement criterion: advancement criterion: The financial analyst position in The financial analyst position in Chicago is the best decision alternative. n Considering only the location criterion: The accountant position in Denver The accountant position in Denver is the best decision alternative. n Considering only the style criterion: The auditor position in Houston is the best alternative. The auditor position in Houston is the best alternative.

28 Slide © 2005 Thomson/South-Western Steps Required to Develop a Scoring Model n Step 1: List the decision-making criteria. n Step 2: Assign a weight to each criterion. n Step 3: Rate how well each decision alternative satisfies each criterion. n Step 4: Compute the score for each decision alternative. n Step 5: Order the decision alternatives from highest score to lowest score. The alternative with the highest score is the recommended alternative.

29 Slide © 2005 Thomson/South-Western n Mathematical Model S j =  w i r ij S j =  w i r ij iwhere: r ij = rating for criterion i and decision alternative j S j = score for decision alternative j Scoring Model for Job Selection

30 Slide © 2005 Thomson/South-Western Scoring Model: Step 1 n List of Criteria Career advancement Career advancement Location Location Management Management Salary Salary Prestige Prestige Job Security Job Security Enjoyable work Enjoyable work

31 Slide © 2005 Thomson/South-Western Scoring Model: Step 2 n Five-Point Scale Chosen Importance Weight Importance Weight Very unimportant1 Very unimportant1 Somewhat unimportant2 Somewhat unimportant2 Average importance3 Average importance3 Somewhat important4 Somewhat important4 Very important5 Very important5

32 Slide © 2005 Thomson/South-Western Scoring Model: Step 2 n Assigning a Weight to Each Criterion Criterion Importance Weight Career advancementVery important5 Career advancementVery important5 LocationAverage importance3 LocationAverage importance3 ManagementSomewhat important4 ManagementSomewhat important4 SalaryAverage importance3 SalaryAverage importance3 PrestigeSomewhat unimportant2 PrestigeSomewhat unimportant2 Job securitySomewhat important4 Job securitySomewhat important4 Enjoyable workVery important5 Enjoyable workVery important5

33 Slide © 2005 Thomson/South-Western n Nine-Point Scale Chosen Level of Satisfaction Rating Level of Satisfaction Rating Extremely low1 Extremely low1 Very low2 Very low2 Low3 Low3 Slightly low4 Slightly low4 Average5 Average5 Slightly high6 Slightly high6 High7 High7 Very high8 Very high8 Extremely high9 Extremely high9 Scoring Model: Step 3

34 Slide © 2005 Thomson/South-Western n Rate how well each decision alternative satisfies each criterion. Decision Alternative Decision Alternative Analyst Accountant Auditor Analyst Accountant Auditor Criterion Chicago Denver Houston Criterion Chicago Denver Houston Career advancement8 6 4 Location3 8 7 Management5 6 9 Salary6 7 5 Prestige7 5 4 Job security4 7 6 Enjoyable work8 6 5 Scoring Model: Step 3

35 Slide © 2005 Thomson/South-Western n Compute the score for each decision alternative. Decision Alternative 1 - Analyst in Chicago Decision Alternative 1 - Analyst in Chicago Criterion Weight ( w i ) Rating ( r i 1 ) w i r i 1 Criterion Weight ( w i ) Rating ( r i 1 ) w i r i 1 Career advancement 5 x 8 =40 Location Management Salary Prestige Job security Enjoyable work Score 157 Scoring Model: Step 4

36 Slide © 2005 Thomson/South-Western n Compute the score for each decision alternative. S 1 = 5(8)+3(3)+4(5)+3(6)+2(7)+4(4)+5(8) = 157 S 2 = 5(6)+3(8)+4(6)+3(7)+2(5)+4(7)+5(6) = 167 S 3 = 5(4)+3(7)+4(9)+3(5)+2(4)+4(6)+5(5) = 149 Scoring Model: Step 4

37 Slide © 2005 Thomson/South-Western n Compute the score for each decision alternative. Decision Alternative Decision Alternative Analyst Accountant Auditor Analyst Accountant Auditor Criterion Chicago Denver Houston Criterion Chicago Denver Houston Career advancement Location Management Salary Prestige Job security Enjoyable work Score Score Scoring Model: Step 4

38 Slide © 2005 Thomson/South-Western n Order the decision alternatives from highest score to lowest score. The alternative with the highest score is the recommended alternative. The accountant position in Denver has the highest score and is the recommended decision alternative. The accountant position in Denver has the highest score and is the recommended decision alternative. Note that the analyst position in Chicago ranks first in 4 of 7 criteria compared to only 2 of 7 for the accountant position in Denver. Note that the analyst position in Chicago ranks first in 4 of 7 criteria compared to only 2 of 7 for the accountant position in Denver. But when the weights of the criteria are considered, the Denver position is superior to the Chicago job. But when the weights of the criteria are considered, the Denver position is superior to the Chicago job. Scoring Model: Step 5

39 Slide © 2005 Thomson/South-Western Scoring Model for Job Selection n Partial Spreadsheet Showing Steps 1 - 3

40 Slide © 2005 Thomson/South-Western Scoring Model for Job Selection n Partial Spreadsheet Showing Formulas of Step 4

41 Slide © 2005 Thomson/South-Western Scoring Model for Job Selection n Partial Spreadsheet Showing Results of Step 4

42 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process The Analytic Hierarchy Process (AHP), is a procedure designed to quantify managerial judgments of the relative importance of each of several conflicting criteria used in the decision making process. The Analytic Hierarchy Process (AHP), is a procedure designed to quantify managerial judgments of the relative importance of each of several conflicting criteria used in the decision making process.

43 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process n Step 1: List the Overall Goal, Criteria, and Decision Alternatives n Step 2: Develop a Pairwise Comparison Matrix Rate the relative importance between each pair of decision alternatives. The matrix lists the alternatives horizontally and vertically and has the numerical ratings comparing the horizontal (first) alternative with the vertical (second) alternative. Ratings are given as follows:... continued... continued For each criterion, perform steps 2 through

44 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process n Step 2: Pairwise Comparison Matrix (continued) Compared to the second alternative, the first alternative is: Numerical rating extremely preferred 9 extremely preferred 9 very strongly preferred 7 very strongly preferred 7 strongly preferred 5 strongly preferred 5 moderately preferred 3 moderately preferred 3 equally preferred 1 equally preferred 1

45 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process n Step 2: Pairwise Comparison Matrix (continued) Intermediate numeric ratings of 8, 6, 4, 2 can be assigned. A reciprocal rating (i.e. 1/9, 1/8, etc.) is assigned when the second alternative is preferred to the first. The value of 1 is always assigned when comparing an alternative with itself.

46 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process n Step 3: Develop a Normalized Matrix Divide each number in a column of the pairwise comparison matrix by its column sum. n Step 4: Develop the Priority Vector Average each row of the normalized matrix. These row averages form the priority vector of alternative preferences with respect to the particular criterion. The values in this vector sum to 1.

47 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process n Step 5: Calculate a Consistency Ratio The consistency of the subjective input in the pairwise comparison matrix can be measured by calculating a consistency ratio. A consistency ratio of less than.1 is good. For ratios which are greater than.1, the subjective input should be re-evaluated For each criterion, perform steps 2 through

48 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process Step 6: Develop a Priority Matrix After steps 2 through 5 has been performed for all criteria, the results of step 4 are summarized in a priority matrix by listing the decision alternatives horizontally and the criteria vertically. The column entries are the priority vectors for each criterion.

49 Slide © 2005 Thomson/South-Western Analytic Hierarchy Process n Step 7: Develop a Criteria Pairwise Development Matrix This is done in the same manner as that used to construct alternative pairwise comparison matrices by using subjective ratings (step 2). Similarly, normalize the matrix (step 3) and develop a criteria priority vector (step 4). n Step 8: Develop an Overall Priority Vector Multiply the criteria priority vector (from step 7) by the priority matrix (from step 6).

50 Slide © 2005 Thomson/South-Western Determining the Consistency Ratio n Step 1: For each row of the pairwise comparison matrix, determine a weighted sum by summing the multiples of the entries by the priority of its corresponding (column) alternative. n Step 2: For each row, divide its weighted sum by the priority of its corresponding (row) alternative. n Step 3: Determine the average, max, of the results of step 2.

51 Slide © 2005 Thomson/South-Western n Step 4: Compute the consistency index, CI, of the n alternatives by: CI = ( max - n )/( n - 1). n Step 5: Determine the random index, RI, as follows: Number of Random Number of Random Number of Random Number of Random Alternative ( n ) Index (RI) Alternative ( n ) Index (RI) Alternative ( n ) Index (RI) Alternative ( n ) Index (RI) n Step 6: Compute the consistency ratio: CR = CR/RI. Determining the Consistency Ratio

52 Slide © 2005 Thomson/South-Western Example: Gill Glass Designer Gill Glass must decide which of three manufacturers will develop his "signature“ toothbrushes. Three factors are important to Gill: (1) his costs; (2) reliability of the product; and, (3) delivery time of the orders. The three manufacturers are Cornell Industries, Brush Pik, and Picobuy. Cornell Industries will sell Brush Pik, and Picobuy. Cornell Industries will sell toothbrushes to Gill Glass for $100 per gross, Brush Pik for $80 per gross, and Picobuy for $144 per gross.

53 Slide © 2005 Thomson/South-Western Example: Gill Glass n Hierarchy for the Manufacturer Selection Problem Select the Best Toothbrush Manufacturer Cost Cost ReliabilityReliability Delivery Time Cornell Brush Pik PicobuyCornell PicobuyCornell PicobuyCornell PicobuyCornell PicobuyCornell Picobuy Overall Goal Criteria DecisionAlternatives

54 Slide © 2005 Thomson/South-Western Pairwise Comparison Matrix: Cost Gill has decided that in terms of price, Brush Pik is moderately preferred to Cornell and very strongly preferred to Picobuy. In turn Cornell is strongly to very strongly preferred to Picobuy.

55 Slide © 2005 Thomson/South-Western n Since Brush Pik is moderately preferred to Cornell, Cornell's entry in the Brush Pik row is 3 and Brush Pik's entry in the Cornell row is 1/3. n Since Brush Pik is very strongly preferred to Picobuy, Picobuy's entry in the Brush Pik row is 7 and Brush Pik's entry in the Picobuy row is 1/7. n Since Cornell is strongly to very strongly preferred to Picobuy, Picobuy's entry in the Cornell row is 6 and Cornell's entry in the Picobuy row is 1/6. Pairwise Comparison Matrix: Cost

56 Slide © 2005 Thomson/South-Western Cornell Brush Pik Picobuy Cornell Brush Pik Picobuy Cornell 1 1/3 6 Cornell 1 1/3 6 Brush Pik Picobuy 1/6 1/7 1 Pairwise Comparison Matrix: Cost

57 Slide © 2005 Thomson/South-Western Divide each entry in the pairwise comparison matrix by its corresponding column sum. For example, for Cornell the column sum = /6 = 25/6. This gives: Cornell Brush Pik Picobuy Cornell Brush Pik Picobuy Cornell 6/25 7/31 6/14 Cornell 6/25 7/31 6/14 Brush Pik 18/25 21/31 7/14 Picobuy 1/25 3/31 1/14 Normalized Matrix: Cost

58 Slide © 2005 Thomson/South-Western The priority vector is determined by averaging the row entries in the normalized matrix. Converting to decimals we get: Cornell: ( 6/25 + 7/31 + 6/14)/3 =.298 Cornell: ( 6/25 + 7/31 + 6/14)/3 =.298 Brush Pik: (18/ /31 + 7/14)/3 =.632 Brush Pik: (18/ /31 + 7/14)/3 =.632 Picobuy: ( 1/25 + 3/31 + 1/14)/3 =.069 Picobuy: ( 1/25 + 3/31 + 1/14)/3 =.069 Priority Vector: Cost

59 Slide © 2005 Thomson/South-Western n Multiply each column of the pairwise comparison matrix by its priority: 1 1/ / = = /6 1/ /6 1/ n Divide these number by their priorities to get:.923/.298 = /.298 = /.632 = /.632 = /.069 = /.069 = Checking Consistency

60 Slide © 2005 Thomson/South-Western Average the above results to get max. Average the above results to get max. max = ( )/3 = max = ( )/3 = n Compute the consistence index, CI, for two terms. CI = ( max - n )/( n - 1) = ( )/2 =.051 CI = ( max - n )/( n - 1) = ( )/2 =.051 n Compute the consistency ratio, CR, by CI/RI, where RI =.58 for 3 factors: CR = CI/RI =.051/.58 =.088 CR = CI/RI =.051/.58 =.088 Since the consistency ratio, CR, is less than.10, this is well within the acceptable range for consistency. Checking Consistency

61 Slide © 2005 Thomson/South-Western Gill Glass has determined that for reliability, Cornell is very strongly preferable to Brush Pik and equally preferable to Picobuy. Also, Picobuy is strongly preferable to Brush Pik. Pairwise Comparison Matrix: Reliability

62 Slide © 2005 Thomson/South-Western Cornell Brush Pik Picobuy Cornell Cornell Brush Pik 1/7 1 5 Picobuy 1/2 1/5 1 Pairwise Comparison Matrix: Reliability

63 Slide © 2005 Thomson/South-Western Divide each entry in the pairwise comparison matrix by its corresponding column sum. For example, for Cornell the column sum = 1 + 1/7 + 1/2 = 23/14. This gives: Cornell Brush Pik Picobuy Cornell Brush Pik Picobuy Cornell 14/23 35/41 2/8 Cornell 14/23 35/41 2/8 Brush Pik 2/23 5/41 5/8 Picobuy 7/23 1/41 1/8 Normalized Matrix: Reliability

64 Slide © 2005 Thomson/South-Western The priority vector is determined by averaging the row entries in the normalized matrix. Converting to decimals we get: Cornell: (14/ /41 + 2/8)/3 =.571 Cornell: (14/ /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 n Checking Consistency Gill Glass’ responses to reliability could be checked for consistency in the same manner as was cost. Priority Vector: Reliability

65 Slide © 2005 Thomson/South-Western Gill Glass has determined that for delivery time, Cornell is equally preferable to Picobuy. Both Cornell and Picobuy are very strongly to extremely preferable to Brush Pik. Pairwise Comparison Matrix: Delivery Time

66 Slide © 2005 Thomson/South-Western Cornell Brush Pik Picobuy Cornell Brush Pik Picobuy Cornell Cornell Brush Pik 1/8 1 1/8 Picobuy Pairwise Comparison Matrix: Delivery Time

67 Slide © 2005 Thomson/South-Western Divide each entry in the pairwise comparison matrix by its corresponding column sum. Cornell Brush Pik Picobuy Cornell Brush Pik Picobuy Cornell 8/17 8/17 8/17 Cornell 8/17 8/17 8/17 Brush Pik 1/17 1/17 1/17 Picobuy 8/17 8/17 8/17 Normalized Matrix: Delivery Time

68 Slide © 2005 Thomson/South-Western The priority vector is determined by averaging the row entries in the normalized matrix. 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 n Checking Consistency Gill Glass’ responses to delivery time could be checked for consistency in the same manner as was cost. Priority Vector: Delivery Time

69 Slide © 2005 Thomson/South-Western The accounting department has determined that in terms of criteria, cost is extremely preferable to delivery time and very strongly preferable to reliability, and that reliability is very strongly preferable to delivery time. Pairwise Comparison Matrix: Criteria

70 Slide © 2005 Thomson/South-Western Cost Reliability Delivery Cost Reliability Delivery Cost Cost Reliability 1/7 1 7 Delivery 1/9 1/7 1 Pairwise Comparison Matrix: Criteria

71 Slide © 2005 Thomson/South-Western Divide each entry in the pairwise comparison matrix by its corresponding column sum. Cost Reliability Delivery Cost Reliability Delivery Cost 63/79 49/57 9/17 Reliability 9/79 7/57 7/17 Delivery 7/79 1/57 1/17 Normalized Matrix: Criteria

72 Slide © 2005 Thomson/South-Western The priority vector is determined by averaging the row entries in the normalized matrix. Converting to decimals we get: Cost: (63/ /57 + 9/17)/3 =.729 Cost: (63/ /57 + 9/17)/3 =.729 Reliability: ( 9/79 + 7/57 + 7/17)/3 =.216 Reliability: ( 9/79 + 7/57 + 7/17)/3 =.216 Delivery: ( 7/79 + 1/57 + 1/17)/3 =.055 Delivery: ( 7/79 + 1/57 + 1/17)/3 =.055 Priority Vector: Criteria

73 Slide © 2005 Thomson/South-Western The overall priorities are determined by multiplying the priority vector of the criteria by the priorities for each decision alternative for each objective. Priority Vector Priority Vector for Criteria [ ] for Criteria [ ] Cost Reliability Delivery Cost Reliability Delivery Cornell Brush Pik Picobuy Overall Priority Vector

74 Slide © 2005 Thomson/South-Western Thus, the overall priority vector is: Cornell: (.729)(.298) + (.216)(.571) + (.055)(.471) =.366 Cornell: (.729)(.298) + (.216)(.571) + (.055)(.471) =.366 Brush Pik: (.729)(.632) + (.216)(.278) + (.055)(.059) =.524 Brush Pik: (.729)(.632) + (.216)(.278) + (.055)(.059) =.524 Picobuy: (.729)(.069) + (.216)(.151) + (.055)(.471) =.109 Picobuy: (.729)(.069) + (.216)(.151) + (.055)(.471) =.109 Brush Pik appears to be the overall recommendation. Overall Priority Vector