What is AHP? According to Operations Management 4th Edition by Russell and Taylor III it is a quantitative method for ranking decision alternatives and selection the one given multiple criteria. AHP is a process for developing a numerical score to rank each decision alternative based on how well each alternative meets the decision maker s criteria.
What does it answer? The question Which one do we choose? or Which one is best? by selecting the best alternative that matches all of the decision maker s criteria.
What does it use? Simple mathematics criteria < set by the decision maker > preferences of that criteria < also set by the decision maker> the standard preference table
Standard Preference Table PREFERENCE LEVEL Equally preferred Equally to moderately preferred Moderately preferred Moderately to strongly preferred Strongly preferred Strongly to very strongly preferred Very strongly preferred Very strongly to extremely preferred Extremely preferred NUMERICAL VALUE 1 2 3 4 5 6 7 8 9
Why not make up your own preference table? Because the standard preference table has been determined by experienced researchers in AHP to be a reasonable basis for comparing two alternatives.
How is it used? Say you have two criteria. Cost and quality for product A & B. The cost for A= $60 and the quality is above average. The cost for B=$15 and the quality is right at average. Which do you choose? By making a matrix the price of B is very strongly preferred to A and A is only moderately preferred to B. The matrices of these preferences would look like....
Matrices of A and B COST A B A 1 1/7 B 7 1 Since price B is very strongly preferred to the price of A. The score of B to A is 7 and A to B is the reciprocal or inverse of 1/7 QUALITY A B A 1 3 B 1/3 1
Our sample problem Jilley Bean Co. is selecting a new location to expand its operations. The company want to use AHP to help it decide which location to build its new plant. Jilley Bean Co. has four criteria they will base their decision on these are the following: property price, distance from suppliers, the quality of the labor pool, and the cost of labor. They have three locations to decide from.
Matrices given criteria and preferences PRICE A B C A 1 3 2 B 1/3 1 1/5 C 1/2 5 1 DISTANCE A B C A 1 6 1/3 B 1/6 1 1/9 C 3 9 1 LABOR A B C A 1 1/3 1 B 3 1 7 C 1 1/7 1 WAGES A B C A 1 1/3 1/2 B 3 1 4 C 2 1/4 1 Showing that in preference in price A and C are the equally preferred but are preferred over B.
How it is done ~ STEP ONE PRICE A B C A 1 3 2 + + + B 1/3 1 1/5 + + + C 1/2 5 1 = 11/6 9 16/5 First sum (add up) all the values in each column.
How it is done ~ STEP TWO PRICE A B C A 1/11/6 = 6/11 3/9 = 3/9 2/16/5 = 5/8 + + + B 1/3/11/6 = 2/11 1/9 = 9 1/5/16/5 1/16 + + + C 1/2/11/6 = 3/11 5/9 = 5/9 1/16/5 = 5/16 = 1 1 1 Next the values in each column are divided by the corresponding column sums. NOTICE: the values in each column sum to 1.
How it is done ~ STEP THREE PRICE A B C Row Average A 6/11 ~.5455 + 3/9~.3333 + 5/8~.6250 = 1.5038 /3 =.512 B 2/11~.1818 + 1/9~.1111 + 1/16~.0625 =.3544 /3 =.1185 C 3/11~.2727 + 5/9~.5556 + 5/16~.3803 = 1.2086 /3 =.3803 1.000 Next convert fractions to decimals and find the average of each row.
How it is done ~ STEP FOUR Find the average for all the criterion by doing steps 1-3 on all the criteria. Arriving at the following Location Price Distance Labor Wages A.5012.2819.1790.1561 B.1185.0598.6850.6196 C.3803.6583.1360.2243
How it is done ~ STEP FIVE Rank the criteria in order of importance ~use the same method used in ranking each criterion. Criteria Price Distance Labor Wages Price 1 1/5 3 4 Distance 5 1 9 7 Labor 1/3 1/9 1 2 Wages 1/4 1/7 1/2 1
How it is done ~ STEP 6-9 Repeat steps 1-4 with the new matrices. You should arrive at the following : Criteria Price Distance Labor Wage Row Average Price.1519.1375.2222.2857.1933 Distance.7595.6878.6667.5000.6535 Labor.0506.0764.0741.1429.0860 Wage.0380.0983.0370.0714.0612 1.000
Row average= preference vector for the criteria CRITERIA Price.1993 Distance.6535 Labor.0860 Wage.0612 Clearly the price of the land is #2, follows distance to suppliers, labor pool quality, and last cost of wages.
FINAL CALCULATIONS Take the criteria matrix and multiple it by the preference vector Location Price Distance Labor Wages A.5012.2819.1790.1561 B.1185.0598.6850.6196 C.3803.6583.1360.2243 X CRITERIA Price.1993 Distance.6535 Labor.0860 Wage.0612 Location A score =.1993(.0512) +.6535(.2819) +.0860(.1790) +.0621(.1561) =.3091 Location B score =.1993(.1185) +.6535(.0598) +.0860(.6850) +.0612(.6196) =.1595 Location C score =.1993(.3803) +.6535(.6583) +.0860(.1360) +.0612(.2243) =.5314
And the results are... LOCATION Score A.3091 B.1595 C.5314 1.0000 Based on the scored Location C should be chosen for Jilley Bean Co. to built a plant.
How is AHP is used in real life? Expert Choice a company that specializes in AHP design software and performs services with it. Some of their clientele are: Ford Motor Company Sprint PCS Department of Agriculture (USDA) Navy National Health Service of the United Kingdom Ferrari SpA in Italy
How is AHP is used in real life? The USDA used it for the selection of bridge materials across the nation in several states.
Is there anything AHP cannot be used for? Not really as long as the decision maker has set criteria and set preferences of that criteria AHP can be used.
Analytic Hierarchy Process
The Analytic Hierarchy Process (AHP) Founded by Saaty in 1980. It is a popular and widely used method for multicriteria decision making. Allows the use of qualitative, as well as quantitative criteria in evaluation. Wide range of applications exists: Selecting a car for purchasing Deciding upon a place to visit for vacation Deciding upon an MBA program after graduation. 25
AHP-General Idea Develop an hierarchy of decision criteria and define the alternative courses of actions. AHP algorithm is basically composed of two steps: 1. Determine the relative weights of the decision criteria 2. Determine the relative rankings (priorities) of alternatives! Both qualitative and quantitative information can be compared by using informed judgments to derive weights and priorities. 26
Example: Car Selection Objective Selecting a car Criteria Style, Reliability, Fuel-economy Cost? Alternatives Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata 27
Hierarchy tree Selecting a New Car Style Reliability Fuel Economy Civic Saturn Escort Miata Alternative courses of action 28
Ranking of Criteria and Alternatives Pairwise comparisons are made with the grades ranging from 1-9. A basic, but very reasonable assumption for comparing alternatives: If attribute A is absolutely more important than attribute B and is rated at 9, then B must be absolutely less important than A and is graded as 1/9. These pairwise comparisons are carried out for all factors to be considered, usually not more than 7, and the matrix is completed. 29
Ranking Scale for Criteria and Alternatives 30
Ranking of criteria Style Reliability Fuel Economy Style Reliability Fuel Economy 1 1/2 3 2 1 4 1/3 1/4 1 31
Ranking of priorities Consider [Ax = max x] where A is the comparison matrix of size n n, for n criteria, also called the priority matrix. x is the Eigenvector of size n 1, also called the priority vector. max is the Eigenvalue, max > n. To find the ranking of priorities, namely the Eigen Vector X: 1) Normalize the column entries by dividing each entry by the sum of the column. 2) Take the overall row averages. A= 1 0.5 3 2 1 4 0.33 0.25 1.0 Normalized Column Sums 0.30 0.29 0.38 0.60 0.57 0.50 0.10 0.14 0.13 Column sums 3.33 1.75 8.00 1.00 1.00 1.00 Row averages 0.30 X= 0.60 0.10 Priority vector 32
Criteria weights Style.30 Reliability.60 Fuel Economy.10 Selecting a New Car 1.00 Style 0.30 Reliability 0.60 Fuel Economy 0.10 33
Checking for Consistency The next stage is to calculate a Consistency Ratio (CR) to measure how consistent the judgments have been relative to large samples of purely random judgments. AHP evaluations are based on the aasumption that the decision maker is rational, i.e., if A is preferred to B and B is preferred to C, then A is preferred to C. If the CR is greater than 0.1 the judgments are untrustworthy because they are too close for comfort to randomness and the exercise is valueless or must be repeated. 34
Calculation of Consistency Ratio The next stage is to calculate max so as to lead to the Consistency Index and the Consistency Ratio. Consider [Ax = max x] where x is the Eigenvector. 1 0.5 3 2 1 4 0.333 0.25 1.0 A x Ax x 0.30 0.60 0.10 0.90 = 1.60 0.35 = max 0.30 0.60 0.10 λmax=average{0.90/0.30, 1.60/0.6, 0.35/0.10}=3.06 Consistency index, CI is found by CI=(λmax-n)/(n-1)=(3.06-3)/(3-1)= 0.03 35
Consistency Ratio The final step is to calculate the Consistency Ratio, CR by using the table below, derived from Saaty s book. The upper row is the order of the random matrix, and the lower row is the corresponding index of consistency for random judgments. Each of the numbers in this table is the average of CI s derived from a sample of randomly selected reciprocal matrices of AHP method. An inconsistency of 10% or less implies that the adjustment is small as compared to the actual values of the eigenvector entries. A CR as high as, say, 90% would mean that the pairwise judgments are just about random and are completely untrustworthy! In this case, comparisons should be repeated. In the above example: CR=CI/0.58=0.03/0.58=0.05 0.05<0.1, so the evaluations are consistent! 36
Ranking alternatives Style Civic Saturn Escort Miata Civic 1 1/4 4 1/6 Saturn 4 1 4 1/4 Escort 1/4 1/4 1 1/5 Miata 6 4 5 1 Reliability Civic Saturn Escort Miata Civic 1 2 5 1 Saturn 1/2 1 3 2 Escort 1/5 1/3 1 1/4 Miata 1 1/2 4 1 Priority vector 0.13 0.24 0.07 0.56 0.38 0.29 0.07 0.26 37
Ranking alternatives Miles/gallon Normalized Fuel Economy Civic 34.30 Saturn 27.24 Escort 24.21 Miata 28 113.25 1.0! Since fuel economy is a quantitative measure, fuel consumption ratios can be used to determine the relative ranking of alternatives; however this is not obligatory. Pairwise comparisons may still be used in some cases. 38
Selecting a New Car 1.00 Style 0.30 Reliability 0.60 Fuel Economy 0.10 Civic 0.13 Saturn 0.24 Escort 0.07 Miata 0.56 Civic 0.38 Saturn 0.29 Escort 0.07 Miata 0.26 Civic 0.30 Saturn 0.24 Escort 0.21 Miata 0.25 39
Style Reliability Fuel Economy Ranking of alternatives Civic Saturn Escort Miata.13.38.30.24.29.24.07.07.21.56.26.25 x.30.60.10 =.30.27.08.35 Priority matrix Criteria Weights 40
Including Cost as a Decision Criteria Adding cost as a a new criterion is very difficult in AHP. A new column and a new row will be added in the evaluation matrix. However, whole evaluation should be repeated since addition of a new criterion might affect the relative importance of other criteria as well! Instead one may think of normalizing the costs directly and calculate the cost/benefit ratio for comparing alternatives! Cost Normalized Cost Benefits Cost/Benefits Ratio CIVIC $12K.22.30 0.73 SATURN $15K.28.27 1.03 ESCORT $9K.17.08 2.13 MIATA $18K.33.35 0.92 41
Benefit Methods for including cost criterion Use graphical representations to make trade-offs. Calculate cost/benefit ratios Use linear programming Use seperate benefit and cost trees and then combine the results 40 35 30 25 20 15 10 5 0 Miata Civic Saturn Escort 0 5 10 15 20 25 30 35 Cost 42
Complex decisions Many levels of criteria and sub-criteria exists for complex problems. 43
AHP Software: Professional commercial software Expert Choice developed by Expert Choice Inc. is available which simplifies the implementation of the AHP s steps and automates many of its computations computations sensitivity analysis graphs, tables 44
Ex 2: Evaluation of Job Offers Ex: Peter is offered 4 jobs from Acme Manufacturing (A), Bankers Bank (B), Creative Consulting (C), and Dynamic Decision Making (D). He bases his evaluation on the criteria such as location, salary, job content, and long-term prospects. Step 1: Decide upon the relative importance of the selection criteria: Location Salary Content Long-term Location Salary Content Long-term 1 1/5 1/3 1/2 5 1 2 4 3 1/2 1 3 2 1/2 1/3 1 45
Priority Vectors: 1) Normalize the column entries by dividing each entry by the sum of the column. 2) Take the overall row averages Location Salary Content Long-term Average Location Salary Content Long-term 0.091 0.102 0.091 0.059 0.455 0.513 0.545 0.471 0.273 0.256 0.273 0.353 0.182 0.128 0.091 0.118 0.086 0.496 0.289 0.130 + + 1 1 1 1 1 46
Example 2: Evaluation of Job Offers Step 2: Evaluate alternatives w.r.t. each criteria Location Scores Relative Location Scores A B C D A B C D Avg. A B C D 1 1/2 1/3 5 2 1 1/2 7 3 2 1 9 1/5 1/7 1/9 1 A B C D 0.161 0.137 0.171 0.227 0.322 0.275 0.257 0.312 0.484 0.549 0.514 0.409 0.032 0.040 0.057 0.045 0.174 0.293 0.489 0.044 47
Example 2: Calculation of Relative Scores Relative Scores for Each Criteria Location Salary Content Long-Term Relative weights for each criteria Relative scores for each alternative A B C D 0.174 0.050 0.210 0.510 0.293 0.444 0.038 0.012 0.489 0.312 0.354 0.290 0.044 0.194 0.398 0.188 0.086 x 0.496 0.289 = 0.130 0.164 0.256 0.335 0.238 48
Cons Pros More about AHP: Pros and Cons It allows multi criteria decision making. It is applicable when it is difficult to formulate criteria evaluations, i.e., it allows qualitative evaluation as well as quantitative evaluation. It is applicable for group decision making environments There are hidden assumptions like consistency. Repeating evaluations is cumbersome. Difficult to use when the number of criteria or alternatives is high, i.e., more than 7. Difficult to add a new criterion or alternative Difficult to take out an existing criterion or alternative, since the best alternative might differ if the worst one is excluded. Users should be trained to use AHP methodology. Use GDSS Use constraints to eliminate some alternatives Use cost/benefit ratio if applicable 49
Group Decision Making The AHP allows group decision making, where group members can use their experience, values and knowledge to break down a problem into a hierarchy and solve. Doing so provides: Understand the conflicting ideas in the organization and try to reach a consensus. Minimize dominance by a strong member of the group. Members of the group may vote for the criteria to form the AHP tree. (Overall priorities are determined by the weighted averages of the priorities obtained from members of the group.) However; The GDSS does not replace all the requirements for group decision making. Open meetings with the involvement of all members are still an asset. 50
Example 3: AHP in project management Prequalification of contractors aims at the elimination of incompetent contractors from the bidding process. It is the choice of the decision maker to eliminate contractor E from the AHP evalution since it is not feasible at all!! Experience Financial stability Quality performance Manpower resources Contractor A Contractor B Contractor C Contractor D Contractor E 5 years experience 7 years experience 8 years experience 10 years experience 15 years experience Two similar projects One similar project No similar project Two similar projects No similar project Special procurement experience 1 international project $7 M assets $10 M assets $14 M assets $11 M assets $6 M assets High growth rate $5.5 M liabilities $6 M liabilities $4 M liabilities $1.5 M liabilities Part of a group of Good relation with No liability companies banks Good organization Average organization Good organization Good organization Bad organization C.M. personnel C.M. personnel C.M. team Good reputation Unethical techniques Good reputation Two delayed projects Government award Many certi cates One project terminated Many certi cates Safety program Good reputation Cost raised in some projects Average quality Safety program QA/QC program 150 labourers 100 labourers 120 labourers 90 labourers 40 labourers 10 special skilled labourers 200 by subcontract Good skilled labors 130 by subcontract 260 by subcontract Availability in peaks 25 special skilled labourers 51
Example 3 (cont. d) Equipment resources Current works load Contractor A Contractor B Contractor C Contractor D Contractor E 4 mixer machines 6 mixer machines 1 batching plant 4 mixer machines 2 mixer machines 1 excavator 1 excavator 2 concrete transferring trucks 1 excavator 10 others 15 others 1 bulldozer 2 mixer machines 9 others 1 big project ending 2 projects in mid (1 medium +1 small) 20 others 1 excavator 15,000 sf steel formwork 2 projects ending (1 big+ 1 medium) 1 bulldozer 16 others 17,000 sf steel formwork 1 medium project started 2 big projects ending 2 projects ending 1 medium (1 big + 1 medium) project in mid 2000 sf steel formwork 6000 sf wooden formwork 2 small projects started 3 projects ending (2 small + 1 medium) 52
Hierarchy Tree Selecting the most suitable contractor Experience Financial Stability Quality Performence Manpower Resources Equipment Resources Current workload Contractor A Contractor B Contractor C Contractor D Contractor E 53
Example 3: AHP in project management Step 1: Evaluation of the weights of the criteria Step 2: a) Pairwise comparison matrix for experience 54
Example 3: AHP in project management Calculation of priority vector: x = Probably Contractor-E should have been eliminated. It appears to be the worst. Note that a DSS supports the decision maker, it can not replace him/her. Thus, an AHP Based DSS should allow the decision maker to make sensitivity analysis of his judgements on the overall priorities! 55
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An Example with AHP
Choosing the most satisfied school Goal: To select the most satisfied school. Criteria: learning, friends, school life, vocational training, college prep. and music classes. Alternatives: School A, school B, and school C.
Hierarchy: Goal Satisfaction with School Learning Friends School Vocational College Music Life Training Prep. Classes School A School B School C
Pairwise comparisons: School Selection L F SL VT CP MC Weights Learning 1 4 3 1 3 4.32 Friends 1/4 1 7 3 1/5 1.14 School Life 1/3 1/7 1 1/5 1/5 1/6.03 Vocational Trng. 1 1/3 5 1 1 1/3.13 College Prep. 1/3 5 5 1 1 3.24 Music Classes 1/4 1 6 3 1/3 1.14
Comparison of Schools with Respect to the Six Characteristics Learning A B C Priorities A 1 1/3 1/2.16 B 3 1 3.59 C 2 1/3 1.25 Friends A B C Priorities A 1 1 1.33 B 1 1 1.33 C 1 1 1.33 School Life A B C Priorities A 1 5 1.45 B 1/5 1 1/5.09 C 1 5 1.46 Vocational Trng. A B C Priorities A 1 9 7.77 B 1/9 1 1/5.05 C 1/7 5 1.17 College Prep. A B C Priorities A 1 1/2 1.25 B 2 1 2.50 C 1 1/2 1.25 Music Classes A B C Priorities A 1 6 4.69 B 1/6 1 1/3.09 C 1/4 3 1.22
Composition and Synthesis Impacts of School on Criteria.32.14.03.13.24.14 L F SL VT CP MC Composite Impact of Schools A B C.16.33.45.77.25.69.37.59.33.09.05.50.09.38.25.33.46.17.25.22.25 School A:.16*.32+.33*.14+.45*.03+.77*.13+.25*.24+.69*.14=.37
Overall final outcome School B is the best school with an overall priority of 0.38, followed by school A.
BWT PROBLEM -19.Bernard Mee, the head of the department of management science at Tech, is evaluating faculty for raises at the end of the academic year. He is considering three faculty members for raises: John Abbott, Megan Bates, and Debbie Cook. Faculty evaluations are based on three criteria-teaching research, and service. Professor Mee's pairwise comparisons for each of the three faculty members for each criterion and his pairwise comparison matrix for the three criteria are as follows: Determine an overall ranking of the three faculty members by using AHP. Faculty Member Teaching A B C A 1 2 1/3 B 1/2 1 1/5 C 3 5 1 Faculty Member Research A B C A 1 3 1/2 B 1/3 1 1 C 2 1 1 Faculty Member Service A B C A 1 3 6 B 1/3 1 2 C 1/6 1/2 1 Criterion Teaching Research Service Teaching 1 3 5 Research 1/3 1 2 Service 1/5 1/2 1 64
BWT ANSWER 19: Teaching Faculty Member A B C A 1,00 2,00 0,33 B 0,50 1,00 0,20 C 3,00 5,00 1,00 Column Sum 4,50 8,00 1,53 Faculty Member Teaching A B C ROW- AVG A 0,22 0,25 0,22 0,23 B 0,11 0,13 0,13 0,12 C 0,67 0,63 0,65 0,65 Research Faculty Member A B C A 1,00 3,00 0,50 B 0,33 1,00 1,00 C 2,00 1,00 1,00 Column Sum 3,33 5,00 2,50 Faculty Member Research A B C ROW- AVG A 0,30 0,60 0,20 0,37 B 0,10 0,20 0,40 0,23 C 0,60 0,20 0,40 0,40 65
Service Faculty Member A B C A 1,00 3,00 6,00 B 0,33 1,00 2,00 C 0,17 0,50 1,00 Column Sum 1,50 4,50 9,00 Service Faculty Member A B C ROW- AVG A 0,67 0,67 0,67 0,67 B 0,22 0,22 0,22 0,22 C 0,11 0,11 0,11 0,11 Criterion Teaching Research Service Teaching 1,00 3,00 5,00 Research 0,33 1,00 2,00 Service 0,20 0,50 1,00 Column Sum 1,53 4,50 8,00 Criterion Teaching Research Service ROW- AVG Teaching 0,65 0,67 0,63 0,65 Research 0,22 0,22 0,25 0,23 Service 0,13 0,11 0,13 0,12 66
Teaching Research Service PR- VEC SCORE 0,23 0,37 0,67 0,65 0,31 0,12 0,23 0,22 0,23 0,16 0,65 0,40 0,11 0,12 0,53 C>A>B 67
BWT PROBLEM - 21. Megan Moppett is a sales representative for Technical Software Systems (TSS), and she receives a commission for every new system installation she sells to a client. Her earnings during the Past few years have been very high, and she wants to invest in a mutual fund. She is considering three funds: the Temple Global Fund, the Alliance Blue Chip Fund, and the Madison Bond Fund. She has three criteria for selection-potential return (based on historical trends and forecasts), risk, and the fund's load factor. Megan's pairwise comparisons for the funds for each of their criteria and her pairwise comparison of the three criteria are as follows: Determine the fund in which Megan should invest. Potential Return Fon Global Blue Chip Bond Global 1,00 0,25 2,00 Blue Chip 4,00 1,00 6,00 Bond 0,50 0,17 1,00 Column Sum 5,50 1,42 9,00 Fon Potential Return Global Blue Chip Bond ROW- AVG Global 0,18 0,18 0,22 0,19 Blue Chip 0,73 0,70 0,67 0,70 Bond 0,09 0,12 0,11 0,11 Risk Fon Global Blue Chip Bond Global 1,00 2,00 0,33 Blue Chip 0,50 1,00 0,20 Bond 3,00 5,00 1,00 Column Sum 4,50 8,00 1,53 Fon Risk Global Blue Chip Bond ROW- AVG Global 0,22 0,25 0,22 0,23 Blue Chip 0,11 0,13 0,13 0,12 Bond 0,67 0,63 0,65 68 0,65
BWT ANSWER 21: Fund s Load Fon Global Blue Chip Bond Global 1,00 1,00 0,33 Blue Chip 1,00 1,00 0,33 Bond 3,00 3,00 1,00 Column Sum 5,00 5,00 1,67 Fon Global Fund s Load Blue Chip Bond ROW- AVG Global 0,20 0,20 0,20 0,20 Blue Chip 0,20 0,20 0,20 0,20 Bond 0,60 0,60 0,60 0,60 Kriter Potential Return Risk Fund s Load Getiri 1,00 3,00 5,00 Kriter Potential Return Risk Fund s Load ROW- AVG Risk 0,33 1,00 2,00 Yük 0,20 0,50 1,00 Getiri 0,65 0,67 0,63 0,65 Risk 0,22 0,22 0,25 0,23 Column Sum 1,53 4,50 8,00 Service 0,13 0,11 0,13 0,12 69
Return Risk Fund s Priority Load Vector SCORE 0,19 0,23 0,20 0,65 0,20 0,70 0,12 0,20 0,23 0,51 0,11 0,65 0,60 0,12 0,29 B>C>A 70
BWT PROBLEM - 23. Alex Wall is shopping for a new four-wheel-drive utility vehicle and has dentified three models from which she will choose-an Explorer, a Tiooper, and a Passport. She will make her selection based on Consumer Digest ratings, price, and each vehicle s appearance. Following are Alex s pairwise comparisons for the vehicles for each ofher criteria and her criteria preferences: Using AHP, determine which vehicle Alex should purchase.. Consumer Digest Rating Price Vehicle Explorer Trooper Passport Vehicle Explorer Trooper Passport Explorer 1 4 3 Trooper 1/4 1 1/2 Passport 1/3 2 1 Explorer 1 1/4 1/6 Trooper 4 1 2 Passport 6 1/2 1 Appearance Vehicle Explorer Trooper Passport Criterion Consumer Digest Rating Price Appearance Explorer 1 4 3 Trooper 1/4 1 1/2 Passport 1/3 2 1 Consumer Digest Rating 1 2 4 Price 1/2 1 3 Appearance 1/4 1/3 1 71
BWT ANSWER 23 Consumer Digest Rating Vehicle Explorer Trooper Passport Explorer 1,00 4,00 3,00 Trooper 0,25 1,00 0,50 Passport 0,33 2,00 1,00 Column Sum 1,58 7,00 4,50 Consumer Digest Rating Vehicle Explorer Trooper Passport ROW- AVG Explorer 0,63 0,57 0,67 0,62 Trooper 0,16 0,14 0,11 0,14 Passport 0,21 0,29 0,22 0,24 Fiyat Vehicle Explorer Trooper Passport Explorer 1,00 0,25 0,17 Fiyat Vehicle Explorer Trooper Passport ROW- AVG Trooper 4,00 1,00 2,00 Passport 6,00 0,50 1,00 Explorer 0,09 0,14 0,05 0,10 Trooper 0,36 0,57 0,63 0,52 Column Sum 11,00 1,75 3,17 Passport 0,55 0,29 0,32 0,38 72
Appearance Vehicle Explorer Trooper Passport Explorer 1,00 4,00 3,00 Vehicle Appearance Explorer Trooper Passport ROW- AVG Trooper 0,25 1,00 0,50 Passport 0,33 2,00 1,00 Explorer 0,63 0,57 0,67 0,62 Trooper 0,16 0,14 0,11 0,14 Column Sum 1,58 7,00 4,50 Passport 0,21 0,29 0,22 0,24 Criteria CDR Price Appearance CDR 1,00 2,00 4,00 Price 0,50 1,00 3,00 Appearance 0,25 0,33 1,00 Criteria CDR Price Appearance ROW- AVG CDR 0,57 0,60 0,50 0,56 Fiyat 0,29 0,30 0,38 0,32 Column Sum 1,75 3,33 8,00 Appearance 0,14 0,10 0,13 0,12 73
CDR Price Appearance Priority Vector SCORE 0,62 0,10 0,62 0,56 0,45 0,14 0,52 0,14 0,32 0,26 0,24 0,38 0,24 0,12 0,29 A>C>B 74
BWT PROBLEM - 25. Carol Latta is visiting hotels in Los Angeles to decide where to hold a convention for a national organization of college business school teachers she represents. There are three hotels from which to choose-the Cheraton, the Milton, and the Harriott. The criteria she is to use to make her selection are ambiance, location (based on safety and walking distance to attractions and restaurants), and cost to the organization. Following are the pairwise comparisons she has developed that indicate her preference for each hotel for each criterion and her pairwise comparisons for the criteria: Develop an overall ranking of the three hotels, using AHP, to help Carol Latta decide where to hold the meeting. Ambiance Location Hotel Cheraton Milton Harriott Hotel Cheraton Milton Harriott Cheraton 1 1/2 1/5 Milton 2 1 1/3 Harriott 5 3 1 Cheraton 1 5 3 Milton 1/5 1 1/4 Harriott 1/3 4 1 Cost Hotel Cheraton Milton Harriott Cheraton 2 2 5 Milton 1/2 1 2 Harriott 1/5 1/2 1 Criterion Ambiance Location Cost Ambiance 1 2 4 Location 1/2 1 3 Cost 1/4 1/3 751
BWT ANSWER 25 Ambiance Hotel Cheraton Milton Harriot Cheraton 1,00 0,50 0,20 Milton 2,00 1,00 0,33 Harriot 5,00 3,00 1,00 Column Sum 8,00 4,50 1,53 Ambiance Hotel Cheraton Milton Harriot ROW- AVG Cheraton 0,13 0,11 0,13 0,12 Milton 0,25 0,22 0,22 0,23 Harriot 0,63 0,67 0,65 0,65 Location Hotel Cheraton Milton Harriot Cheraton 1,00 5,00 3,00 Location Hotel Cheraton Milton Harriot ROW- AVG Milton 0,20 1,00 0,25 Harriot 0,33 4,00 1,00 Cheraton 0,65 0,50 0,71 0,62 Milton 0,13 0,10 0,06 0,10 Column Sum 1,53 10,00 4,25 Harriot 0,22 0,40 0,24 0,28 76
Cost Hotel Cheraton Milton Harriot Cheraton 1,00 2,00 5,00 Milton 0,50 1,00 2,00 Harriot 0,20 0,50 1,00 Cost Hotel Cheraton Milton Harriot ROW- AVG Cheraton 0,59 0,57 0,63 0,59 Milton 0,29 0,29 0,25 0,28 Column Sum 1,70 3,50 8,00 Harriot 0,12 0,14 0,13 0,13 Criteria Ambiance Location Cost Ambiance 1,00 2,00 4,00 Criteria Ambiance Location Cost ROW- AVG Location 0,50 1,00 3,00 Cost 0,25 0,33 1,00 Ambiance 0,57 0,60 0,50 0,56 Location 0,29 0,30 0,38 0,32 Column Sum 1,75 3,33 8,00 Cost 0,14 0,10 0,13 0,12 77
Ambiance Location Cost Priority Vector SCORE 0,12 0,62 0,59 0,56 0,34 0,23 0,10 0,28 0,32 0,19 0,65 0,28 0,13 0,12 0,47 C>A>B 78
BWT PROBLEM - 31. Students at a university in Nottingham, England, are planning a summer holiday to one of three European locations: Greece (G), Mallorca (M), or Ibiza (I). They are to base their decision on three criteria-weather, cost, and potential fun (based on an Internet survey of friends and acquaintances at other colleges). The students have developed the following pairwise comparisons for each criterion and for the three criteria: If the students use AHP to help make a decision, which location will they select for their summer holiday? Weather Location G M I G 1 1/3 1/3 M 3 1 1 I 3 1 1 Cost Location G M I G 1 3 5 M 1/3 1 2 I 1/5 1/2 1 Fun Criterion Weather Cost Fun Location G M I Weather 1 4 1/4 G 1 1/2 5 M 2 1 3 Cost 1/4 1 1/5 I 1/5 1/3 1 Fun 4 5 1 79
BWT ANSWER 31 Weather Yer G M I G 1,00 0,33 0,33 M 3,00 1,00 1,00 I 3,00 1,00 1,00 Column Sum 7,00 2,33 2,33 Weather Yer G M I ROW- AVG G 0,14 0,14 0,14 0,14 M 0,43 0,43 0,43 0,43 I 0,43 0,43 0,43 0,43 Cost Yer G M I G 1,00 3,00 5,00 M 0,33 1,00 2,00 I 0,20 0,50 1,00 Cost Yer G M I ROW- AVG G 0,65 0,67 0,63 0,65 M 0,22 0,22 0,25 0,23 I 0,13 0,11 0,13 0,12 80
Fun Yer G M I G 1,00 0,50 5,00 M 2,00 1,00 3,00 I 0,20 0,33 1,00 Fun Yer G M I ROW- AVG G 0,31 0,27 0,56 0,38 M 0,63 0,55 0,33 0,50 Column Sum 3,20 1,83 9,00 I 0,06 0,18 0,11 0,12 Criteria Weather Cost Fun Weather 1,00 4,00 0,25 Cost 0,25 1,00 0,20 Fun 4,00 5,00 1,00 Criteria Weather Cost Fun ROW- AVG Weather 0,19 0,40 0,17 0,25 Cost 0,05 0,10 0,14 0,10 Column Sum 5,25 10,00 1,45 Fun 0,76 0,50 0,69 0,65 81
Weather Cost Fun Priority Vector SCORE 0,14 0,65 0,38 0,25 0,35 0,43 0,23 0,50 0,10 0,46 0,43 0,12 0,12 0,65 0,20 B>A>C 82
BWT PROBLEM - 33. The management science and information technology majors at Tech select one of two available options within the major-decision support systems (DSS) or operations management (OM). Student advisers use AHP with the students to determine which option they should select. The criteria used by the advisers are student aptitude and interests, faculty who teach in the options, and potential job availability. An adviser has helped one major develop the following pairwise comparisons: Which option should the student select? Aptitude Option DSS OM DSS 1 3 OM 1/3 1 Faculty Option DSS OM DSS 1 1/5 OM 5 1 Jobs Criterion Aptitude Faculty Jobs Option DSS OM DSS 1 4 OM 1/4 1 Aptitude 1 1/2 1/4 Faculty 2 1 1/3 Jobs 4 3 1 83
BWT ANSWER 33 Aptitude Option DSS OM DSS 1,00 3,00 OM 0,33 1,00 Aptitude Option DSS OM ROW- AVG DSS 0,75 0,75 0,75 Column Sum 1,33 4,00 OM 0,25 0,25 0,25 Faculty Option DSS OM DSS 1,00 0,20 OM 5,00 1,00 Faculty Option DSS OM ROW- AVG DSS 0,17 0,17 0,17 Column Sum 6,00 1,20 OM 0,83 0,83 0,83 84
Jobs Seçenek DSS OM DSS 1,00 4,00 Jobs Seçenek DSS OM ROW- AVG OM 0,25 1,00 DSS 0,80 0,80 0,80 Column Sum 1,25 5,00 OM 0,20 0,20 0,20 Criteria Aptitude Faculty Jobs Aptitude 1,00 0,50 0,25 Faculty 2,00 1,00 0,33 Jobs 4,00 3,00 1,00 Criteria Aptitude Faculty Jobs ROW- AVG Aptitude 0,14 0,11 0,16 0,14 Faculty 0,29 0,22 0,21 0,24 Column Sum 7,00 4,50 1,58 Jobs 0,57 0,67 0,63 0,62 85
Aptitude Faculty Jobs Priority Vector SCORE 0,75 0,17 0,80 0,14 0,64 0,25 0,83 0,20 0,24 0,36 0,62 A>B 86
BWT PROBLEM - 35. The town of Blacksburg needs a larger modern middle school. The current middle school is in the center of town and is over 40 years old. There are two proposals for a new school-renovate and expand the current facility and keep it in town or build a new school on the outskirts of town. Different groups in town have strong feelings about the proposals. Some citizens want to retain the sense of tradition of the old school and like it in town, where it helps engender a sense of community. Others view the old school as antiquated and beyond saving and believe keeping the school in town near bars, traffic, and college students to be negative. The county school board will make the final decision. The school board has asked several management science professors from the local college to use AHP to help evaluate the proposals. The school board has identified four groups from which it wants to solicit input regarding their preferences: the middle school PTA, the middle school teachers, current and former middle school students, and the town council. The management science professors have developed the following pairwise comparison matrices for each of these groups: The school board's pairwise comparison of the four groups from which it is soliciting preferences is as follows: a) Based on the AHp analysis conducted by the management science professors, proposal should the school board select? b) Check the school board's pairwise comparison of the criteria for consistency. 87
PTA Teachers Proposal Renovate New Renovate 1 1/3 New 3 1 Proposal Renovate New Renovate 1 1/9 New 9 1 Students Proposal Renovate New Renovate 1 2 New 1/2 1 Town council Proposal Renovate New Renovate 1 5 New 1/5 1 Group PTA Teachers Students Town council PTA 1 5 2 1/4 Teachers 1/5 1 1/4 1/7 Students 1/2 4 1 1/5 Town council 4 7 5 1 88
BWT ANSWER 35 PTA Proposal Genişlet Yeni Genişlet 1,00 0,33 Yeni 3,00 1,00 Column Sum 4,00 1,33 PTA Proposal Genişlet Yeni ROW- AVG Genişlet 0,25 0,25 0,25 Yeni 0,75 0,75 0,75 Teachers Proposal Genişlet Yeni Genişlet 1,00 0,11 Teachers Proposal Genişlet Yeni ROW- AVG Yeni 9,00 1,00 Genişlet 0,10 0,10 0,10 Column Sum 10,00 1,11 Yeni 0,90 0,90 0,90 89
Students Proposal Genişlet Yeni Genişlet 1,00 2,00 Yeni 0,50 1,00 Column Sum 1,50 3,00 Students Proposal Genişlet Yeni ROW- AVG Genişlet 0,67 0,67 0,67 Yeni 0,33 0,33 0,33 Town council Proposal Genişlet Yeni Genişlet 1,00 5,00 Town council Proposal Genişlet Yeni ROW- AVG Yeni 0,20 1,00 Genişlet 0,83 0,83 0,83 Column Sum 1,20 6,00 Yeni 0,17 0,17 0,17 90
Criteria PTA Teachers Students Town council PTA 1,00 5,00 2,00 0,25 Teachers 0,20 1,00 0,25 0,14 Students 0,50 4,00 1,00 0,20 Town council 4,00 7,00 5,00 1,00 Column Sum 5,70 17,00 8,25 1,59 Criteria PTA Teachers Students Town council ROW- AVG PTA 0,18 0,29 0,24 0,16 0,22 Teachers 0,04 0,06 0,03 0,09 0,05 Students 0,09 0,24 0,12 0,13 0,14 Town council 0,70 0,41 0,61 0,63 0,59 PTA Teachers Students Town council Priority Vector SCORE 0,25 0,10 0,67 0,83 0,22 0,65 0,75 0,90 0,33 0,17 0,05 0,36 0,14 0,59 A>B 91
BWT PROBLEM 37.Federated Health Care has contracted to be Tech's primary health care provider for faculty and staff. There are three major hospitals in the area (within 35 miles)-county, Memorial, and General-that have full-service emergency rooms. Federated wants to designate one of the hospitals as its primary care emergency room for İts members. The company's criteria for selection are quality of medical care, as determined by a patient survey; distance to the emergency room by the majority of is members; speed of medical attention at the emergency room; and cost. Following are thee pairwise comparisons of the emergency rooms for each of the four criteria and the pairwise comparisons for the criteria: Using AHP, determine which hospital emergency room Federated Health Care should designate as İts primary care provider. Medical care Distance Hospital County Memorial General Hospital County Memorial General County 1 1/6 1/3 Memorial 6 1 3 County 1 7 4 Memorial 1/7 1 2 General 3 1/3 1 General 1/4 1/2 1 92
Speed of Attention Cost Hospital County Memorial General County 1 1/2 3 Memorial 2 1 4 General 1/3 1/4 1 Hospital County Memorial General County 1 6 4 Memorial 1/6 1 1/2 General 1/4 2 1 Criterion Medical care Distance Speed of Attention Cost Medical 1 8 6 3 care Distance 1/8 1 1/2 1/6 Speed of Attention 1/6 2 1 1/4 Cost 1/3 6 4 1 93
BWT ANSWER 37 Medical care Hospital County Memorial General County 1,00 0,17 0,33 Memorial 6,00 1,00 3,00 General 3,00 0,33 1,00 Column Sum 10,00 1,50 4,33 Medical care Hospital County Memorial General ROW- AVG County 0,10 0,11 0,08 0,10 Memorial 0,60 0,67 0,69 0,65 General 0,30 0,22 0,23 0,25 Distance Hospital County Memorial General County 1,00 7,00 4,00 Memorial 0,14 1,00 2,00 General 0,25 0,50 1,00 Distance Hospital County Memorial General ROW- AVG County 0,72 0,82 0,57 0,70 Memorial 0,10 0,12 0,29 0,17 Column Sum 1,39 8,50 7,00 General 0,18 0,06 0,14 0,13 94
Speed of Attention Hospital County Memorial General County 1,00 0,50 3,00 Speed of Attention Hospital County Memorial General ROW- AVG Memorial 2,00 1,00 4,00 General 0,33 0,25 1,00 County 0,30 0,29 0,38 0,32 Memorial 0,60 0,57 0,50 0,56 Column Sum 3,33 1,75 8,00 General 0,10 0,14 0,13 0,12 Cost Hospital County Memorial General County 1,00 6,00 4,00 Cost Hospital County Memorial General ROW- AVG Memorial 0,17 1,00 0,50 General 0,25 2,00 1,00 County 0,70 0,67 0,73 0,70 Memorial 0,12 0,11 0,09 0,11 Column Sum 1,42 9,00 5,50 General 0,18 0,22 0,18 0,19 95
Criteria Medical care Medical care Distance Speed of Attention Cost 1,00 8,00 6,00 3,00 Distance 0,13 1,00 0,50 0,17 Speed of Attention 0,17 2,00 1,00 0,25 Cost 0,33 6,00 4,00 1,00 Column Sum 1,63 17,00 11,50 4,42 Criteria Medical care Medical care Distance Speed of Attention Cost ROW- AVG 0,61 0,47 0,52 0,68 0,57 Distance 0,08 0,06 0,04 0,04 0,05 Speed of Attention 0,10 0,12 0,09 0,06 0,09 Maliyet 0,20 0,35 0,35 0,23 0,28 Medical Speed of Distance care Attention Cost Priority Vector SCORE 0,10 0,70 0,32 0,70 0,57 0,31 0,65 0,17 0,56 0,11 0,05 0,46 0,25 0,13 0,12 0,19 0,09 0,21 0,28 B>A>C 96
BWT PROBLEM 39. A faculty committee in the department of management science at Tech is evaluating three new text-books for its introductory management science course, which all business students are required to take. The texts, identified by the authors, are Adams/Jones, Barnes, and Cook/Smith. The committee's selection criteria are topical coverage, readability, cost, and the available supplements. Following are the committee's pairwise comparisons of the three textbooks for each of the four criteria and the committee's pairwise comparisons for the criteria: Using AHP, determine which textbook the committee should select. Check the consistency of the pairwise comparison matrix fort he criteria. Coverage Readability Textbook A B C A 1 1/5 1/4 B 5 1 3 C 4 1/3 1 Textbook A B C A 1 2 3 B 1/2 1 3 C 1/3 1/3 1 97
Cost Supplements Textbook A B C A 1 1/2 1/5 B 2 1 1/3 C 5 3 1 Textbook A B C A 1 4 7 B 1/4 1 3 C 1/7 1/3 1 Criterion Coverage Readability Cost Supplements Coverage 1 1/2 1/4 2 Readability 2 1 1/3 5 Cost 4 3 1 3 Supplements 1/2 1/5 1/3 1 98
BWT ANSWER 39 99