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DIT 1141: OPERATIONS MANAGEMENTDIT 1141: OPERATIONS MANAGEMENT
DEPARTMENT OF DECISION AND DEPARTMENT OF DECISION AND INFORMATION TECHNOLOGIESINFORMATION TECHNOLOGIES
COLLEGE OF COMMERCE AND FINANCECOLLEGE OF COMMERCE AND FINANCE
VILLANOVA UNIVERSITYVILLANOVA UNIVERSITY
INTRODUCTIONINTRODUCTION
INTRODUCTIONINTRODUCTION
Operations management is the process of obtaining Operations management is the process of obtaining and utilizing resources to produce useful goods and utilizing resources to produce useful goods and services so as to meet the goals of the and services so as to meet the goals of the organization.organization.
INTRODUCTIONINTRODUCTION
Production management is concerned with the Production management is concerned with the manufacturing of goods:manufacturing of goods:
Examples of goods:Examples of goods:
carscars
booksbooks
chairschairs
computerscomputers
houseshouses
etc.etc.
INTRODUCTIONINTRODUCTION
Operations management is also concerned with the Operations management is also concerned with the management of service industries as well as the management of service industries as well as the manufacturing of goods.manufacturing of goods.
INTRODUCTIONINTRODUCTION
Examples of services:Examples of services:
retailing/foodretailing/food
bankingbanking
educationeducation
health carehealth care
utilitiesutilities
insuranceinsurance
government agenciesgovernment agencies
etc.etc.
OVERVIEW OF OPERATIONS OVERVIEW OF OPERATIONS MANAGEMENT MODELMANAGEMENT MODEL
TransformationTransformation ProcessProcess
OutputOutput
Goods orGoods orServicesServices
ControlControl
Input: resourcesInput: resources raw materialsraw materials machinesmachines personnelpersonnel capitalcapital land/buildingsland/buildings utilitiesutilities informationinformation etc.etc.
OVERVIEW OF OPERATIONS OVERVIEW OF OPERATIONS MANAGEMENT MODELMANAGEMENT MODEL
Operations management considers Operations management considers howhow the input are the input are transformed into goods or services.transformed into goods or services.
Control is when something is learned about the Control is when something is learned about the goods or services that is used to more effectively goods or services that is used to more effectively transform future goods or services.transform future goods or services.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
Automobile factoryAutomobile factory
Input
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
Automobile factoryAutomobile factory
Input
steel, plastic
glass, paint
tools
equipment
machines
personnel, buildings
utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
Automobile factoryAutomobile factory
Input
steel, plastic
glass, paint
tools Transformation
equipment process
machines
personnel, buildings
utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
Automobile factoryAutomobile factory
InputOutput
steel, plastic
glass, paint
tools Transformation
equipment process
machines
personnel, buildings
utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
Automobile factoryAutomobile factory
InputOutput
steel, plastic Car
glass, paint
tools Transformation
equipment process
machines
personnel, buildings
utilities, etc.
OPERATIONS MANAGEMENT OPERATIONS MANAGEMENT QUESTIONSQUESTIONS
1. How many items will be demanded next month?1. How many items will be demanded next month?
2. How many items should be produced next month?2. How many items should be produced next month?
3. How many workers are needed to satisfy the 3. How many workers are needed to satisfy the proposed production level?proposed production level?
OPERATIONS MANAGEMENT OPERATIONS MANAGEMENT QUESTIONSQUESTIONS
4. If a plant is built, how should the activities be 4. If a plant is built, how should the activities be scheduled so that the project is completed on time, scheduled so that the project is completed on time, within budget, and with acceptable quality?within budget, and with acceptable quality?
5. How is the quality of our output measured and 5. How is the quality of our output measured and how is it improved?how is it improved?
6. If tires are needed, how many should be ordered?6. If tires are needed, how many should be ordered?
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
HospitalHospital
InputInput
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
HospitalHospital
InputInput
patients, doctorspatients, doctors
nurses, drugsnurses, drugs
bedsbeds
building building
medical equipment medical equipment
support staff, computerssupport staff, computers
utilities, etc.utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
HospitalHospital
InputInput
patients, doctorspatients, doctors
nurses, drugsnurses, drugs Transformation Transformation
bedsbeds Process Process
building building
medical equipment medical equipment
support staff, computerssupport staff, computers
utilities, etc.utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
HospitalHospital
InputInput OutputOutput
patients, doctorspatients, doctors
nurses, drugsnurses, drugs Transformation Transformation
bedsbeds Process Process
building building
medical equipment medical equipment
support staff, computerssupport staff, computers
utilities, etc.utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
HospitalHospital
InputInput OutputOutput
patients, doctorspatients, doctors A treated A treated patientpatient
nurses, drugsnurses, drugs Transformation Transformation
bedsbeds Process Process
building building
medical equipment medical equipment
support staff, computerssupport staff, computers
utilities, etc.utilities, etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput
students, professorsstudents, professors
secretariessecretaries
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput
students, professorsstudents, professors
secretaries, drugssecretaries, drugs
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput
students, professorsstudents, professors
secretaries, drugssecretaries, drugs
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput
students, professorsstudents, professors
secretaries, lab equipmentsecretaries, lab equipment
dormitoriesdormitories
staff, computers staff, computers
buildingsbuildings
etc.etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput
students, professorsstudents, professors
secretaries, lab equipmentsecretaries, lab equipment
dormitoriesdormitories
staff, computers Transformationstaff, computers Transformation
buildings buildings processprocess
etc.etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput OutputOutput
students, professorsstudents, professors
secretaries, lab equipment secretaries, lab equipment
dormitoriesdormitories
staff, computers Transformationstaff, computers Transformation
buildings buildings processprocess
etc.etc.
EXAMPLE OF OPERATIONS EXAMPLE OF OPERATIONS MANAGEMENT PROCESSMANAGEMENT PROCESS
UniversityUniversity
InputInput OutputOutput
students, professorsstudents, professors A more highly A more highly
secretaries, lab equipment secretaries, lab equipment educated educated
dormitoriesdormitories student student
staff, computers Transformationstaff, computers Transformation
buildings buildings processprocess
etc.etc.
DECISION MAKING IN DECISION MAKING IN OPERATIONS: OPERATIONS:
THE ANALYTIC THE ANALYTIC HIERARCHY PROCESSHIERARCHY PROCESS
What is the Analytic Hierarchy Process (AHP)?What is the Analytic Hierarchy Process (AHP)?
The AHP, developed by Tom Saaty, is a decision-The AHP, developed by Tom Saaty, is a decision-making method for prioritizing alternatives when making method for prioritizing alternatives when multi-criteria must be considered.multi-criteria must be considered.
An approach for structuring a problem as a hierarchy An approach for structuring a problem as a hierarchy or set of integrated levels.or set of integrated levels.
INTRODUCTIONINTRODUCTION
AHP problems are structured in at least three levels:AHP problems are structured in at least three levels:
The goalThe goal, such as selecting the best car to purchase,, such as selecting the best car to purchase,
The criteriaThe criteria, such as cost, safety, and appearance,, such as cost, safety, and appearance,
The alternativesThe alternatives, namely the cars themselves., namely the cars themselves.
INTRODUCTIONINTRODUCTION
The decision-maker:The decision-maker:
measures the extent to which each measures the extent to which each alternative achieves each criterion, and alternative achieves each criterion, and
determines the relative importance of the determines the relative importance of the criteria in meeting the goal, and criteria in meeting the goal, and
synthesizes the results to determine the synthesizes the results to determine the relative importance of the alternatives in relative importance of the alternatives in meeting the goal.meeting the goal.
INTRODUCTIONINTRODUCTION
APPROACHAPPROACH
How does AHP capture human judgments?How does AHP capture human judgments?
AHP AHP nevernever requires you to make an absolute requires you to make an absolute judgment or assessment. You would never be judgment or assessment. You would never be asked to directly estimate the weight of a stone in asked to directly estimate the weight of a stone in kilograms.kilograms.
AHP AHP doesdoes require you to make a relative assessment require you to make a relative assessment between between twotwo items at a time. AHP uses a ratio items at a time. AHP uses a ratio scale of measurement. scale of measurement.
APPROACHAPPROACHSuppose the weights of two stones are being Suppose the weights of two stones are being
assessed. AHP would ask: How much heavier (or assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B?lighter) is stone A compared to stone B?
AHP might tell us that, of the total weight of stones AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total weight, A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight.whereas, stone B has 35% of the total weight.
APPROACHAPPROACHIndividual AHP judgments are called Individual AHP judgments are called pairwise pairwise
comparisonscomparisons..
These judgments can be based on objective or These judgments can be based on objective or subjective information.subjective information.
For example, smoothness might be a subjective For example, smoothness might be a subjective criterion used to compare two stones. Pairwise criterion used to compare two stones. Pairwise comparisons could be based on touch. comparisons could be based on touch.
APPROACHAPPROACHHowever, suppose stone A is a diamond worth However, suppose stone A is a diamond worth
$1,000.00 and stone B is a ruby worth $300.00.$1,000.00 and stone B is a ruby worth $300.00.
This objective information could be used as a basis This objective information could be used as a basis for a pairwise comparison based on the value of for a pairwise comparison based on the value of the stones.the stones.
APPROACHAPPROACHConsistency of judgments can also be measured. Consistency of judgments can also be measured.
Consistency is important when three or more Consistency is important when three or more items are being compared. items are being compared.
Suppose we judge a basketball to be twice as large as Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to be three times as a soccer ball and a soccer ball to be three times as large as a softball. large as a softball.
To be perfectly consistent, a basketball must be six To be perfectly consistent, a basketball must be six times as large as a softball.times as large as a softball.
APPROACHAPPROACH
AHP does not require perfect consistency, however, AHP does not require perfect consistency, however, it does provide a measure of consistency. it does provide a measure of consistency.
We will discuss consistency in more detail later.We will discuss consistency in more detail later.
AHP APPLICATIONSAHP APPLICATIONS
AHP has been successfully applied to a variety of AHP has been successfully applied to a variety of problems.problems.
1.1. R&D projects and research papers;R&D projects and research papers;
2.2. vendors, transport carriers, and site locations;vendors, transport carriers, and site locations;
3.3. employee appraisal and salary increases;employee appraisal and salary increases;
4.4. product formulation and pharmaceutical licensing;product formulation and pharmaceutical licensing;
5.5. capital budgeting and strategic planning;capital budgeting and strategic planning;
6.6. surgical residents, medical treatment, and surgical residents, medical treatment, and diagnostic testing.diagnostic testing.
AHP APPLICATIONSAHP APPLICATIONS
The product and service evaluations prepared by The product and service evaluations prepared by consumer testing services is another potential consumer testing services is another potential application.application.
Products and services, such as self propelled lawn Products and services, such as self propelled lawn mowers are evaluated. mowers are evaluated.
Factors include: bagging, mulching, discharging, Factors include: bagging, mulching, discharging, handling, and ease of use.handling, and ease of use.
An overall score for each mower is determined.An overall score for each mower is determined.
AHP APPLICATIONSAHP APPLICATIONS
Would you make your purchasing decision based Would you make your purchasing decision based solely on this score?solely on this score?
Probably not! Some of the information will be Probably not! Some of the information will be helpful. helpful.
Some additional questions are:Some additional questions are:
How important is each criterion?How important is each criterion?
Would you weigh the criteria the same way?Would you weigh the criteria the same way?
Are all of the criteria considered important to you?Are all of the criteria considered important to you?
Are there other criteria that are important to you?Are there other criteria that are important to you?
Have you ever thought about these issues?Have you ever thought about these issues?
RANKING SPORTS RECORDSRANKING SPORTS RECORDS
The AHP has been used to rank outstanding season, The AHP has been used to rank outstanding season, career, and single event records across sports.career, and single event records across sports.
SeasonSeason
1.1. Babe Ruth, 1920: .847 slugging averageBabe Ruth, 1920: .847 slugging average
2.2. Joe DiMaggio, 1944: 56 game hitting streakJoe DiMaggio, 1944: 56 game hitting streak
3.3. Wilt Chamberlain, 1961-62: 50.4 points per game Wilt Chamberlain, 1961-62: 50.4 points per game scoring averagescoring average
RANKING SPORTS RECORDSRANKING SPORTS RECORDSCareerCareer
1.1. Johnny Unitas, 1956-70: touchdown passes in 47 Johnny Unitas, 1956-70: touchdown passes in 47 consecutive gamesconsecutive games
2.2. Babe Ruth, 1914-35: .690 slugging averageBabe Ruth, 1914-35: .690 slugging average
3.3. Walter Payton, 1975-86: 16,193 rushing yardageWalter Payton, 1975-86: 16,193 rushing yardage
Single eventSingle event
1.1. Wilt Chamberlain, 1962: 100 points scoredWilt Chamberlain, 1962: 100 points scored
2.2. Norm Van Brocklin, 1951: 554 passing yardsNorm Van Brocklin, 1951: 554 passing yards
3.3. Bob Beamon, 1968: 29' 2.5" long jumpBob Beamon, 1968: 29' 2.5" long jump
RANKING SPORTS RECORDSRANKING SPORTS RECORDSHow do we compare records from different sports?How do we compare records from different sports?
It all depends on the criteria that you select!It all depends on the criteria that you select!
Golden and Wasil (1987) used the following criteria:Golden and Wasil (1987) used the following criteria:
1.1. Duration of record - years record has stood, years Duration of record - years record has stood, years expected to standexpected to stand
2.2. Incremental improvement - % better than previous Incremental improvement - % better than previous recordrecord
3.3. Other record characteristics - glamour, purity Other record characteristics - glamour, purity (single person vs. team)(single person vs. team)
RANKING SPORTS RECORDSRANKING SPORTS RECORDSDid this article end all arguments about sports records?Did this article end all arguments about sports records?
Absolutely not! Absolutely not!
In bars and living rooms across the country, people still In bars and living rooms across the country, people still argue about sports. argue about sports.
AHP provides a methodology to structure the debate. AHP provides a methodology to structure the debate.
Different criteria and different judgments could Different criteria and different judgments could produce different results.produce different results.
A FINAL POINT ABOUT SPORTSA FINAL POINT ABOUT SPORTS
In reading the sports pages we often see discussion In reading the sports pages we often see discussion of how well teams match up across different of how well teams match up across different positions. positions.
These match-ups are often used to predict a winner. These match-ups are often used to predict a winner.
Match-ups is a pairwise comparison concept!Match-ups is a pairwise comparison concept!
AHP APPLICATIONSAHP APPLICATIONS
Our culture is obsessed with quantitative rankings of Our culture is obsessed with quantitative rankings of all sorts of things.all sorts of things.
There are many measurement problems associated There are many measurement problems associated with rankings of products, sports teams, with rankings of products, sports teams, universities, and the like.universities, and the like.
Many of these issues are discussed on a web site at:Many of these issues are discussed on a web site at:
http://www.expertchoice.com/annie.person.
The discussion of how to compare records from The discussion of how to compare records from different sports recalls a saying from childhood:different sports recalls a saying from childhood:
APPLES AND ORANGESAPPLES AND ORANGES
The discussion of how to compare records from The discussion of how to compare records from different sports recalls a saying from childhood:different sports recalls a saying from childhood:
You can’t compare apples and oranges. All you You can’t compare apples and oranges. All you get is mixed fruit!get is mixed fruit!
APPLES AND ORANGESAPPLES AND ORANGES
The discussion of how to compare records from The discussion of how to compare records from different sports recalls a saying from childhood:different sports recalls a saying from childhood:
You can’t compare apples and oranges. All you You can’t compare apples and oranges. All you get is mixed fruit!get is mixed fruit!
After the discussion about sports, do you still believe After the discussion about sports, do you still believe this statement?this statement?
APPLES AND ORANGESAPPLES AND ORANGES
APPLES AND ORANGESAPPLES AND ORANGESThe discussion of how to compare records from The discussion of how to compare records from
different sports recalls a saying from childhood:different sports recalls a saying from childhood:
You can’t compare apples and oranges. All you You can’t compare apples and oranges. All you get is mixed fruit!get is mixed fruit!
After the discussion about sports, do you still believe After the discussion about sports, do you still believe this statement?this statement?
We hope not!!!We hope not!!!
What criteria might What criteria might youyou use when comparing apples use when comparing apples and oranges?and oranges?
There are a vast set of criteria that may change There are a vast set of criteria that may change depending upon time of day or season of year:depending upon time of day or season of year:
taste,taste, texture,texture, smell,smell,
ripeness,ripeness, juiciness,juiciness, nutrition,nutrition,
shape,shape, weight,weight, color, andcolor, and
cost.cost.
Can you think of others?Can you think of others?
APPLES AND ORANGESAPPLES AND ORANGES
The point is that people are often confronted with the The point is that people are often confronted with the choice between apples and oranges. choice between apples and oranges.
Their choice is based on some psychological Their choice is based on some psychological assessment of: assessment of:
relevant criteria, relevant criteria,
their importance, and their importance, and
how well the alternatives achieve the how well the alternatives achieve the criteria.criteria.
APPLES AND ORANGESAPPLES AND ORANGES
CAR PURCHASE EXAMPLECAR PURCHASE EXAMPLE
We now consider a motivating example. We now consider a motivating example.
After completing this example, you will have an After completing this example, you will have an understanding of the basics of AHP and its understanding of the basics of AHP and its application through Expert Choice application through Expert Choice (www.expertchoice.com).(www.expertchoice.com).
We want to apply the AHP to help a couple decide We want to apply the AHP to help a couple decide which car they should purchase. which car they should purchase.
CAR PURCHASE EXAMPLECAR PURCHASE EXAMPLE
The couple is considering three criteria: cost, safety, The couple is considering three criteria: cost, safety, and appearance.and appearance.
They have narrowed their alternatives to three They have narrowed their alternatives to three specific cars: Honda, Mazda, and Volvo.specific cars: Honda, Mazda, and Volvo.
We demonstrate how to build the AHP hierarchy in We demonstrate how to build the AHP hierarchy in Expert Choice.Expert Choice.
Select the Select the FFile, ile, NNew ew option and enter a file name option and enter a file name such as CARS.EC1. (You must use the EC1 file such as CARS.EC1. (You must use the EC1 file extension.)extension.)
Choose the Choose the DDirectirect option to create the model. Next, option to create the model. Next, specify the description of the goal, such as, “Select specify the description of the goal, such as, “Select the best car.”the best car.”
EXPERT CHOICE: FILE SETUPEXPERT CHOICE: FILE SETUP
To enter the criteria, use the To enter the criteria, use the EEdit, dit, IInsert nsert command. command. Use the Esc key when finished entering the Use the Esc key when finished entering the criteria.criteria.
To add the alternative cars under the cost node, To add the alternative cars under the cost node, simply highlight the cost node and again use the simply highlight the cost node and again use the EEdit, dit, IInsert nsert command. Use the Esc key when command. Use the Esc key when finished.finished.
EXPERT CHOICE: FILE SETUPEXPERT CHOICE: FILE SETUP
To include the same alternatives under the other To include the same alternatives under the other criteria nodes, first highlight the cost node, then criteria nodes, first highlight the cost node, then select select EEdit, dit, RReplicate children of current node, To eplicate children of current node, To PPeers, eers, YYeses..
Double-click on the goal node to display the Double-click on the goal node to display the complete hierarchy.complete hierarchy.
Additional details can be found in the Expert Choice Additional details can be found in the Expert Choice tutorial provided with the software.tutorial provided with the software.
EXPERT CHOICE: FILE SETUPEXPERT CHOICE: FILE SETUP
ANALYZING THE HIERARCHYANALYZING THE HIERARCHY
1.1. Determine the weights of the alternatives for each Determine the weights of the alternatives for each criterion.criterion.
2.2. Determine the priorities or weights of the criteria Determine the priorities or weights of the criteria in achieving the goal.in achieving the goal.
3.3. Determine the overall weight of each alternative in Determine the overall weight of each alternative in achieving the goal. This is accomplished by achieving the goal. This is accomplished by combining the results of the first two stages and is combining the results of the first two stages and is called synthesis.called synthesis.
HYPOTHETICAL DATA FOR CAR HYPOTHETICAL DATA FOR CAR PURCHASE EXAMPLEPURCHASE EXAMPLE
CarCar CostCost Safety*Safety* AppearanceAppearance HondaHonda $22,000$22,000 2828 SportySporty Mazda Mazda 28,500 28,500 3939 SlickSlick Volvo Volvo 33,000 33,000 5252 DullDull
* Safety Rating from a consumer testing service - the * Safety Rating from a consumer testing service - the higher the number, the safer the car.higher the number, the safer the car.
DETERMINING PRIORITIESDETERMINING PRIORITIES
The couple begins by making The couple begins by making pairwise comparison pairwise comparison judgmentsjudgments between each pair of cars for the cost between each pair of cars for the cost criterion.criterion.
In our example, three judgments are needed: Honda In our example, three judgments are needed: Honda to Mazda, Mazda to Volvo, and Honda to Volvo. to Mazda, Mazda to Volvo, and Honda to Volvo.
STANDARD 1 - 9 MEASUREMENT SCALESTANDARD 1 - 9 MEASUREMENT SCALEIntensity of ImportanceIntensity of Importance DefinitionDefinition ExplanationExplanation
11 Equal importanceEqual importance Two activities contribute equallyTwo activities contribute equally
33 Moderate importanceModerate importance Experience and judgment slightly favor oneExperience and judgment slightly favor one
activity over anotheractivity over another
55 Strong importanceStrong importance Experience and judgment strongly favor oneExperience and judgment strongly favor one
activity over anotheractivity over another
77 Very strongVery strong An activity is favored very strongly overAn activity is favored very strongly over
anotheranother
99 Extreme importanceExtreme importance The evidence favoring one activity overThe evidence favoring one activity over
another is of the highest possible orderanother is of the highest possible order
of affirmationof affirmation
2, 4, 6, 82, 4, 6, 8 For compromiseFor compromise Sometimes one needs to interpolate aSometimes one needs to interpolate a
valuesvalues compromise between the above judgmentcompromise between the above judgment
numerically because there is no goodnumerically because there is no good
word to describe itword to describe it
1.1 - 1.91.1 - 1.9 For tied activitiesFor tied activities When elements are close and nearlyWhen elements are close and nearly
indistinguishable; moderate is 1.3 andindistinguishable; moderate is 1.3 and
extreme is 1.9extreme is 1.9
Reciprocals of aboveReciprocals of above If activity A hasIf activity A has For example, if the pairwise comparison ofFor example, if the pairwise comparison of
one of the above one of the above A to B is 3.0, then the pairwise comparisonA to B is 3.0, then the pairwise comparison
numbers assignednumbers assigned of B to A is 1/3of B to A is 1/3
to it when compared to it when compared
with activity B, with activity B,
then B has the then B has the
reciprocal value reciprocal value
when compared to A.when compared to A.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
The pairwise comparisons are represented in the The pairwise comparisons are represented in the form of pairwise comparison matrices. form of pairwise comparison matrices.
The computation of the weights are also shown.The computation of the weights are also shown.
Consider the pairwise comparison matrix to compare Consider the pairwise comparison matrix to compare the cars for the cost criterion. the cars for the cost criterion.
Remember that the costs of the three cars are: Remember that the costs of the three cars are: $22000, $28500, and $33000, respectively.$22000, $28500, and $33000, respectively.
If we compare the Honda to the Honda, obviously If we compare the Honda to the Honda, obviously they are equal. they are equal.
Therefore, a 1 (equal preferred) is placed in the first Therefore, a 1 (equal preferred) is placed in the first row, first column entry of the matrix.row, first column entry of the matrix.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda Honda 11
28.5K28.5K Mazda Mazda
33K33K VolvoVolvo
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
The other entries along the main diagonal of the The other entries along the main diagonal of the matrix are also 1. matrix are also 1.
This simply means that everything is equally This simply means that everything is equally preferred to itself.preferred to itself.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 Honda 1
28.5K28.5K Mazda Mazda 11
33K33K VolvoVolvo 11
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
Suppose we believe the Honda ($22000) is equally Suppose we believe the Honda ($22000) is equally to moderately preferred to the Mazda ($28500). to moderately preferred to the Mazda ($28500). Place a 2 in the row 1, column 2 entry.Place a 2 in the row 1, column 2 entry.
Some might argue that the Honda should be 1.295 Some might argue that the Honda should be 1.295 times better than the Mazda (28,500/22,000). times better than the Mazda (28,500/22,000).
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
Do you agree?Do you agree?
It depends! It depends!
For some, $28,500 is significantly greater than For some, $28,500 is significantly greater than $22,000, implying a judgments greater than 1.295. $22,000, implying a judgments greater than 1.295.
Others with a lot of money may perceive virtually no Others with a lot of money may perceive virtually no difference between the two costs, implying a difference between the two costs, implying a judgment somewhere between 1 and 1.295. judgment somewhere between 1 and 1.295.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 Honda 1 2 2
28.5K28.5K Mazda 1Mazda 1
33K33K VolvoVolvo 1 1
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
If the Honda is 2 times better than the Mazda, this If the Honda is 2 times better than the Mazda, this implies that the Mazda ($28500) is one half as implies that the Mazda ($28500) is one half as good as the Honda ($22000). good as the Honda ($22000).
The reciprocal judgment, (1/2), should be placed in The reciprocal judgment, (1/2), should be placed in the row 2, column 1 entry of the matrix.the row 2, column 1 entry of the matrix.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2Honda 1 2
28.5K28.5K Mazda Mazda 1/21/2 1 1
33K33K VolvoVolvo 1 1
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
Suppose that we judge the Mazda ($28500) to be Suppose that we judge the Mazda ($28500) to be equally to moderately preferred to the Volvo equally to moderately preferred to the Volvo ($33000). ($33000).
The following judgments would be entered in the The following judgments would be entered in the matrix.matrix.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2Honda 1 2
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 22
33K33K VolvoVolvo 1/2 1/2 1 1
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
Assuming perfect consistency of judgments, we Assuming perfect consistency of judgments, we would expect that the Honda ($22000) is 4 times would expect that the Honda ($22000) is 4 times (that is, moderately to strongly) preferred to the (that is, moderately to strongly) preferred to the Volvo ($33000). Volvo ($33000).
We will relax this assumption later.We will relax this assumption later.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2Honda 1 2 4 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K VolvoVolvo 1/4 1/4 1/2 11/2 1
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
The matrix is now complete and the weights for each The matrix is now complete and the weights for each car (for the cost criterion) can be computed.car (for the cost criterion) can be computed.
The exact computational procedure is implemented The exact computational procedure is implemented in Expert Choice. For details see Expert Choice in Expert Choice. For details see Expert Choice homepage and download AHPDEMO.EXE.homepage and download AHPDEMO.EXE.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
A simple three step procedure can be used to A simple three step procedure can be used to approximate the weights for each alternative.approximate the weights for each alternative.
Essentially, this procedure normalizes the ratios of Essentially, this procedure normalizes the ratios of the judgments between any pair of alternatives.the judgments between any pair of alternatives.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K Volvo 1/4 1/2 1Volvo 1/4 1/2 1
------- ------- -------------- ------- -------
COLUMN TOTALSCOLUMN TOTALS
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K Volvo 1/4 1/2 1Volvo 1/4 1/2 1
------- ------- -------------- ------- -------
COLUMN TOTALSCOLUMN TOTALS 7/4 7/2 7 7/4 7/2 7
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K Volvo 1/4 1/2 1Volvo 1/4 1/2 1
------- ------- -------------- ------- -------
COLUMN TOTALS 7/4 7/2 7 COLUMN TOTALS 7/4 7/2 7
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
22.. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K Volvo 1/4 1/2 1Volvo 1/4 1/2 1
------- ------- -------------- ------- -------
COLUMN TOTALS 7/4 7/2 7COLUMN TOTALS 7/4 7/2 7
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda Mazda VolvoHonda Mazda Volvo
HondaHonda 4/7* 4/7 4/7 4/7* 4/7 4/7
MazdaMazda 2/7 2/7 2/7 2/7 2/7 2/7
VolvoVolvo 1/7 1/7 1/7 1/7 1/7 1/7
* This entry is obtained by dividing the Honda entry in the original matrix (1) by * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).the Honda column total (7/4).
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
Notice that no variation is seen across the rows because Notice that no variation is seen across the rows because the judgments are perfectly consistent.the judgments are perfectly consistent.
For the third column, judgments totaling 7 were For the third column, judgments totaling 7 were awarded. The Honda received 4 of 7 (57.1%), the awarded. The Honda received 4 of 7 (57.1%), the Mazda 2 of 7 (28.6%), and the Volvo 1 of 7 (14.3%) Mazda 2 of 7 (28.6%), and the Volvo 1 of 7 (14.3%) of the weight. of the weight.
Similar comparisons can be made for the other two Similar comparisons can be made for the other two columns.columns.
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K Volvo 1/4 1/2 1Volvo 1/4 1/2 1
------- ------- -------------- ------- -------
COLUMN TOTALS 7/4 7/2 7COLUMN TOTALS 7/4 7/2 7
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda Mazda VolvoHonda Mazda Volvo
HondaHonda 4/7* 4/7 4/7 4/7* 4/7 4/7
MazdaMazda 2/7 2/7 2/7 2/7 2/7 2/7
VolvoVolvo 1/7 1/7 1/7 1/7 1/7 1/7
* This entry is obtained by dividing the Honda entry in the original matrix (1) by * This entry is obtained by dividing the Honda entry in the original matrix (1) by
the Honda column total (7/4).the Honda column total (7/4).
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 2 2
33K33K Volvo 1/4 1/2 1Volvo 1/4 1/2 1
------- ------- -------------- ------- -------
COLUMN TOTALS 7/4 7/2 7COLUMN TOTALS 7/4 7/2 7
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS
Honda Mazda Volvo (ROW AVG.)Honda Mazda Volvo (ROW AVG.)
Honda Honda 4/7* 4/7 4/7 0.571 4/7* 4/7 4/7 0.571
MazdaMazda 2/7 2/7 2/7 0.286 2/7 2/7 2/7 0.286
VolvoVolvo 1/7 1/7 1/7 0.143 1/7 1/7 1/7 0.143
--------- ---------
TOTALTOTAL 1.000 1.000
* This entry is obtained by dividing the Honda entry in the original matrix (1) by * This entry is obtained by dividing the Honda entry in the original matrix (1) by
the Honda column total (7/4).the Honda column total (7/4).
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
Expert Choice offers a variety of modes for entering Expert Choice offers a variety of modes for entering the judgments. the judgments.
Highlight the cost node, select Highlight the cost node, select AAssessment. ssessment.
There are three options: There are three options: PPairwise, airwise, DDataata, and , and RRatingsatings. .
Ratings will be discussed later.Ratings will be discussed later.
EXPERT CHOICE: Entering JudgmentsEXPERT CHOICE: Entering Judgments
The The DDataata option allows the user to enter data items option allows the user to enter data items for each alternative, for example, costs, miles per for each alternative, for example, costs, miles per gallon, and number of defects. gallon, and number of defects.
Expert Choice takes the ratio of these data items and Expert Choice takes the ratio of these data items and converts them into pairwise comparisons.converts them into pairwise comparisons.
What assumption are you making if you use the Data What assumption are you making if you use the Data option?option?
The data items have a linear preference scale, that The data items have a linear preference scale, that is, a $20,000 car is twice as good as a $40,000 car. is, a $20,000 car is twice as good as a $40,000 car.
EXPERT CHOICE: Entering JudgmentsEXPERT CHOICE: Entering Judgments
To enter our cost judgments choose To enter our cost judgments choose PPairwise.airwise.
When comparing alternatives select When comparing alternatives select PPreferencereference for for TTypeype; for criteria select ; for criteria select IImportancemportance..
ModesModes options are: options are: VVerbal, erbal, MMatrix atrix (numerical), (numerical), QQuestionnaire, uestionnaire, and and GGraphicraphic. .
AAssessment, ssessment, PPairwise, airwise, MMatrix atrix is demonstrated. is demonstrated.
Enter judgments, Enter judgments, CCalculatealculate and and RRecordecord. .
EXPERT CHOICE: Entering JudgmentsEXPERT CHOICE: Entering Judgments
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTSSince our pairwise comparisons were perfectly Since our pairwise comparisons were perfectly
consistent, Expert Choice reports consistent, Expert Choice reports INCONSISTENCY RATIO = 0.0.INCONSISTENCY RATIO = 0.0.
If this ratio is greater than 0.1 some revision of If this ratio is greater than 0.1 some revision of judgments is required.judgments is required.
Select Select InconsisInconsisttencyency (within (within AAssessmentssessment, , PPairwiseairwise) ) to identify the most inconsistent judgments.to identify the most inconsistent judgments.
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTSInconsistency of judgments may result from:Inconsistency of judgments may result from:
problems of estimation;problems of estimation;
errors between the comparisons;errors between the comparisons;
or, the comparisons may be naturally inconsistent. or, the comparisons may be naturally inconsistent.
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTSOne example of natural inconsistency is in a sporting One example of natural inconsistency is in a sporting
contest. contest.
If team A is twice as likely to beat team B, and if If team A is twice as likely to beat team B, and if team B is three times as likely to beat team C, this team B is three times as likely to beat team C, this does not necessarily imply that team A is six times does not necessarily imply that team A is six times as likely to beat team C. as likely to beat team C.
This inconsistency may result because of the way This inconsistency may result because of the way that the teams “match-up” overall.that the teams “match-up” overall.
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTS
The point is not to stop inconsistency from The point is not to stop inconsistency from occurring. occurring.
Make sure that the level of inconsistency remains Make sure that the level of inconsistency remains within some reasonable limit. within some reasonable limit.
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTS
How does a judgment change affect the car weights?How does a judgment change affect the car weights?
Suppose the Mazda to Volvo changes from 2 to 3. Suppose the Mazda to Volvo changes from 2 to 3.
This obviously changes the comparison for Volvo to This obviously changes the comparison for Volvo to Mazda from (1/2) to (1/3). Mazda from (1/2) to (1/3).
The judgments are now somewhat inconsistent. The judgments are now somewhat inconsistent.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 3 3
33K33K Volvo 1/4Volvo 1/4 1/3 1/3 11
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 3 3
33K33K Volvo 1/4 1/3 1Volvo 1/4 1/3 1
------- ------- -------------- ------- -------
COLUMN TOTALSCOLUMN TOTALS 7/4 10/3 8 7/4 10/3 8
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
22.. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 3 3
33K33K Volvo 1/4 1/3 1Volvo 1/4 1/3 1
------- ------- -------------- ------- -------
COLUMN TOTALS COLUMN TOTALS 7/4 10/3 87/4 10/3 8
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
Honda Mazda VolvoHonda Mazda Volvo
HondaHonda 4/7* 6/10 4/8 4/7* 6/10 4/8
MazdaMazda 2/7 3/10 3/8 2/7 3/10 3/8
VolvoVolvo 1/7 1/10 1/8 1/7 1/10 1/8
* This entry is obtained by dividing the Honda entry in the original matrix (1) by * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).the Honda column total (7/4).
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
1.1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
2.2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
THIS RESULTS IN THE ADJUSTED MATRIX.THIS RESULTS IN THE ADJUSTED MATRIX.
3.3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
A. ORIGINAL COST PAIRWISE COMPARISON MATRIX A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
Honda Mazda Volvo Honda Mazda Volvo
22K22K Honda 1 2 4 Honda 1 2 4
28.5K28.5K Mazda 1/2 1Mazda 1/2 1 3 3
33K33K Volvo 1/4 1/3 1Volvo 1/4 1/3 1
------- ------- -------------- ------- -------
COLUMN TOTALS 7/4 10/3 8COLUMN TOTALS 7/4 10/3 8
B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTSB. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS
Honda Mazda Volvo (ROW AVG.)Honda Mazda Volvo (ROW AVG.)
Honda 4/7* 6/10 4/8Honda 4/7* 6/10 4/8 0.557 0.557
Mazda 2/7 3/10 3/8Mazda 2/7 3/10 3/8 0.320 0.320
Volvo 1/7 1/10 1/8Volvo 1/7 1/10 1/8 0.123 0.123
----------------
TOTAL TOTAL 1.0001.000
* This entry is obtained by dividing the Honda entry in the original matrix (1) by * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).the Honda column total (7/4).
COST PAIRWISE COMPARISONSCOST PAIRWISE COMPARISONS
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTS
The new weights are: 0.557, 0.320, and 0.123. The The new weights are: 0.557, 0.320, and 0.123. The inconsistency resulted in some change in the inconsistency resulted in some change in the original weights of 0.571, 0.286, and 0.143. original weights of 0.571, 0.286, and 0.143.
As expected, the weight for the Mazda increased As expected, the weight for the Mazda increased while the weight for the Volvo decreased.while the weight for the Volvo decreased.
The weights now vary across each row. Essentially, The weights now vary across each row. Essentially, inconsistency measures the degree of variation inconsistency measures the degree of variation across the rows.across the rows.
Highlight cost node, select Highlight cost node, select AAssessment, ssessment, PPairwise.airwise.
Enter a 3 in the Mazda to Volvo cell then Enter a 3 in the Mazda to Volvo cell then CCalculatealculate..
The weights of 0.558, 0.320, and 0.122 are slightly The weights of 0.558, 0.320, and 0.122 are slightly different from the three-step procedure weights.different from the three-step procedure weights.
This is not due to rounding -- Expert Choice gives This is not due to rounding -- Expert Choice gives the exact results.the exact results.
The INCONSISTENCY RATIO is now 0.02.The INCONSISTENCY RATIO is now 0.02.
EXPERT CHOICE: Revising JudgmentsEXPERT CHOICE: Revising Judgments
INCONSISTENCY OF JUDGMENTSINCONSISTENCY OF JUDGMENTS
The weights can also be used to measure the The weights can also be used to measure the effectiveness of the alternatives. effectiveness of the alternatives.
For example, based on all pairwise comparisons, we For example, based on all pairwise comparisons, we determined that the Honda is 1.74 (0.558/0.320) determined that the Honda is 1.74 (0.558/0.320) times better than the Mazda.times better than the Mazda.
Why is this ratio 1.74 and not the pairwise Why is this ratio 1.74 and not the pairwise comparison of 2?comparison of 2?
Inconsistency in the judgments!Inconsistency in the judgments!
REMAINING COMPUTATIONSREMAINING COMPUTATIONSNext, the cars must be pairwise compared for the Next, the cars must be pairwise compared for the
safety criterion and then for the appearance safety criterion and then for the appearance criterion. criterion.
These judgments are shown on the next page.These judgments are shown on the next page.
Since the Mazda to Honda safety comparison is 2, Since the Mazda to Honda safety comparison is 2, highlight the Honda to Mazda cell, click highlight the Honda to Mazda cell, click IInvertnvert, , and enter 2.and enter 2.
This judgment now appears in red.This judgment now appears in red.
SAFETY & APPEARANCE JUDGMENTSSAFETY & APPEARANCE JUDGMENTS
Safety Pairwise Comparison Matrix Safety Pairwise Comparison Matrix
HondaHonda MazdaMazda Volvo Volvo
2828 Honda Honda 11 1/21/2 1/51/5
3939 Mazda Mazda 22 11 1/41/4
5252 Volvo Volvo 55 44 11
Appearance Pairwise Comparison Matrix Appearance Pairwise Comparison Matrix
HondaHonda MazdaMazda Volvo Volvo
SportySportyHondaHonda 11 55 99
SlickSlick MazdaMazda 1/51/5 11 22
DullDull VolvoVolvo 1/91/9 1/21/2 1 1
REMAINING COMPUTATIONSREMAINING COMPUTATIONS
Next, the criteria must be pairwise compared. Next, the criteria must be pairwise compared.
These judgments are shown on the next page. These judgments are shown on the next page.
There are no data to support these judgments since There are no data to support these judgments since they are purely a reflection of your preferences.they are purely a reflection of your preferences.
CRITERIA JUDGMENTSCRITERIA JUDGMENTS
Original Criteria Pairwise Comparison MatrixOriginal Criteria Pairwise Comparison Matrix
CostCost SafetySafety AppearanceAppearance
CostCost 11 1/21/2 33
SafetySafety 22 11 55
AppearanceAppearance 1/31/3 1/51/5 11
REMAINING COMPUTATIONSREMAINING COMPUTATIONS
The last stage computes the final weights for each car. The last stage computes the final weights for each car.
Multiply the criteria weight by the car weight for each Multiply the criteria weight by the car weight for each criterion and then sum over all criteria. criterion and then sum over all criteria.
This is nothing more than a weighted average.This is nothing more than a weighted average.
The computational results are shown next.The computational results are shown next.
FINAL CAR WEIGHTSFINAL CAR WEIGHTS CRITERIA WEIGHTSCRITERIA WEIGHTS
COST SAFETY APPEARANCECOST SAFETY APPEARANCE
0.309 0.582 0.1090.309 0.582 0.109
CARS CARS FINAL WEIGHTS FINAL WEIGHTS
Honda 0.558 0.117 0.761Honda 0.558 0.117 0.761
Mazda 0.320 0.200 0.158Mazda 0.320 0.200 0.158
Volvo 0.122 0.683 0.082Volvo 0.122 0.683 0.082
FINAL CAR WEIGHTSFINAL CAR WEIGHTS CRITERIA WEIGHTSCRITERIA WEIGHTS
COST SAFETY APPEARANCECOST SAFETY APPEARANCE
0.309 0.582 0.1090.309 0.582 0.109
CARS CARS FINAL WEIGHTS FINAL WEIGHTS
Honda 0.558 0.117 0.761 Honda 0.558 0.117 0.761 0.3240.324
Mazda 0.320 0.200 0.158Mazda 0.320 0.200 0.158
Volvo 0.122 0.683 0.082Volvo 0.122 0.683 0.082
Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
0.1730.173 0.068 0.068 0.083 0.083
FINAL CAR WEIGHTSFINAL CAR WEIGHTS CRITERIA WEIGHTSCRITERIA WEIGHTS
COST SAFETY APPEARANCECOST SAFETY APPEARANCE
0.309 0.582 0.1090.309 0.582 0.109
CARS CARS FINAL WEIGHTS FINAL WEIGHTS
Honda 0.558 0.117 0.761 0.324Honda 0.558 0.117 0.761 0.324
Mazda 0.320 0.200 0.158 Mazda 0.320 0.200 0.158 0.2320.232
Volvo 0.122 0.683 0.082Volvo 0.122 0.683 0.082
Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
0.1730.173 0.068 0.068 0.083 0.083
Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
0.0990.099 0.116 0.116 0.017 0.017
FINAL CAR WEIGHTSFINAL CAR WEIGHTS CRITERIA WEIGHTSCRITERIA WEIGHTS
COST SAFETY APPEARANCECOST SAFETY APPEARANCE
0.309 0.582 0.1090.309 0.582 0.109
CARS CARS FINAL WEIGHTS FINAL WEIGHTS
Honda 0.558 0.117 0.761 0.324Honda 0.558 0.117 0.761 0.324
Mazda 0.320 0.200 0.158 0.232Mazda 0.320 0.200 0.158 0.232
Volvo 0.122 0.683 0.082Volvo 0.122 0.683 0.082 0.444 0.444
Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
0.1730.173 0.068 0.068 0.083 0.083
Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
0.0990.099 0.116 0.116 0.017 0.017
Volvo: (0.122)(0.309) + (0.683)(0.582) + (0.082)(0.109) = 0.444Volvo: (0.122)(0.309) + (0.683)(0.582) + (0.082)(0.109) = 0.444
0.0380.038 0.397 0.397 0.009 0.009
LOCAL VS GLOBAL WEIGHTSLOCAL VS GLOBAL WEIGHTS
For cost, the local weights for the cars are 0.558, 0.320, For cost, the local weights for the cars are 0.558, 0.320, and 0.122 and sum to 1.000.and 0.122 and sum to 1.000.
The global weights are computed by multiplying the cost The global weights are computed by multiplying the cost criterion weight by the local car weights.criterion weight by the local car weights.
The global weights are 0.173, 0.099, and 0.038 and sum to The global weights are 0.173, 0.099, and 0.038 and sum to the cost criterion weight of 0.309.the cost criterion weight of 0.309.
To compute the final weights select To compute the final weights select SSynthesisynthesis ( (from from GGOALOAL).).
Choose Choose DisDisttributiveributive Mode and Display Mode and Display SSummaryummary..
DDetailsetails provides the global weights. provides the global weights.
The output can also be exported to a spreadsheet The output can also be exported to a spreadsheet using the using the UUtilitiestilities, , Export Model(s) to SpreadsheetExport Model(s) to Spreadsheet commands.commands.
EXPERT CHOICE: SynthesisEXPERT CHOICE: Synthesis
The Print icon can be used to select certain options. The Print icon can be used to select certain options.
The recommended print options are: The recommended print options are: EEntire Tree, ntire Tree, TTree Views, ree Views, JJudgments/Data, udgments/Data, andand S Syynthesisnthesis..
EXPERT CHOICE: PrintingEXPERT CHOICE: Printing
INTERPRETING THE RESULTSINTERPRETING THE RESULTS
The final weights provide a measure of the relative The final weights provide a measure of the relative performance of each alternative. performance of each alternative.
It is important to properly interpret the meaning of It is important to properly interpret the meaning of these numbers.these numbers.
The Volvo is ranked first, the Honda second, and The Volvo is ranked first, the Honda second, and Mazda third.Mazda third.
The Volvo is preferred 1.37 (0.444/0.324) times The Volvo is preferred 1.37 (0.444/0.324) times more than the Honda.more than the Honda.
INTERPRETING THE RESULTSINTERPRETING THE RESULTSShould we buy the Volvo?Should we buy the Volvo?
The output is a decision-making aid and cannot The output is a decision-making aid and cannot replace the decision-maker.replace the decision-maker.
The results can be used to support discussion and The results can be used to support discussion and possibly the judgments will be revised. possibly the judgments will be revised.
This iterative process is quite normal. This iterative process is quite normal.
AHP can help to facilitate communication and AHP can help to facilitate communication and generate consensus between different groups. generate consensus between different groups.
SENSITIVITY ANALYSISSENSITIVITY ANALYSIS
Sensitivity analysis is an important aspect of any Sensitivity analysis is an important aspect of any decision-making process.decision-making process.
Sensitivity analysis determines whether small changes Sensitivity analysis determines whether small changes in judgments affects the final weights and rankings in judgments affects the final weights and rankings of the alternatives. of the alternatives.
If so, the decision-maker may want to review the If so, the decision-maker may want to review the sensitive judgments.sensitive judgments.
EXPERT CHOICE: Sensitivity AnalysisEXPERT CHOICE: Sensitivity Analysis
In Expert Choice sensitivity analysis from the GOAL In Expert Choice sensitivity analysis from the GOAL shows how the weights and the rankings of the shows how the weights and the rankings of the alternatives change if some or all of the criteria alternatives change if some or all of the criteria weights change.weights change.
There are five graphical sensitivity analysis modes There are five graphical sensitivity analysis modes available: Performance, Dynamic, Gradient, Two-available: Performance, Dynamic, Gradient, Two-Dimensional, and Difference. Dimensional, and Difference.
The first three show how a change in a criterion The first three show how a change in a criterion weight affects the final weights of the alternatives.weight affects the final weights of the alternatives.
The last two show how the alternatives perform with The last two show how the alternatives perform with respect to any two criteria.respect to any two criteria.
PerformancePerformance: places all sensitivity information on a : places all sensitivity information on a single chart with horizontal line graphs for the single chart with horizontal line graphs for the alternatives linked to vertical bars for the criteria.alternatives linked to vertical bars for the criteria.
DynamicDynamic: two sets of dynamically linked horizontal : two sets of dynamically linked horizontal bar graphs: one for criteria and one for bar graphs: one for criteria and one for alternatives.alternatives.
EXPERT CHOICE: Sensitivity AnalysisEXPERT CHOICE: Sensitivity Analysis
GradientGradient: a line graph that shows how the weights of : a line graph that shows how the weights of the alternatives vary according to the weight the alternatives vary according to the weight assigned to a specific criterion. (Use the assigned to a specific criterion. (Use the XX-Axis-Axis to to change the selected criterion.)change the selected criterion.)
Two-DimensionalTwo-Dimensional: shows how well the alternatives : shows how well the alternatives perform with respect to any two criteria.perform with respect to any two criteria.
DifferenceDifference: a graph that shows the differences : a graph that shows the differences between any two alternatives for any criterion.between any two alternatives for any criterion.
EXPERT CHOICE: Sensitivity AnalysisEXPERT CHOICE: Sensitivity Analysis
An important use of sensitivity analysis is to An important use of sensitivity analysis is to determine how much a given criterion weight determine how much a given criterion weight must change before there is a change in the must change before there is a change in the rankings of the two highest alternatives. rankings of the two highest alternatives.
This type of breakeven analysis can be easily done in This type of breakeven analysis can be easily done in Expert Choice.Expert Choice.
EXPERT CHOICE: Sensitivity AnalysisEXPERT CHOICE: Sensitivity Analysis
Choose Choose DDynamicynamic from the from the Sensitivity-Sensitivity-GGraphsraphs option. option.
Drag the cost criterion bar 30.9% to approximately Drag the cost criterion bar 30.9% to approximately 45.9%, and see that the Volvo and Honda have the 45.9%, and see that the Volvo and Honda have the same highest final weight. same highest final weight.
The final rankings are relatively insensitive to a The final rankings are relatively insensitive to a change in the cost criterion weight because the change in the cost criterion weight because the cost weight had to be increased by almost 50% to cost weight had to be increased by almost 50% to get a change in the rankings.get a change in the rankings.
EXPERT CHOICE: Sensitivity AnalysisEXPERT CHOICE: Sensitivity Analysis
NEW PRODUCT INTRODUCTIONNEW PRODUCT INTRODUCTION
CHOCK-FUL-O-CHIPS developed the following CHOCK-FUL-O-CHIPS developed the following hierarchy and data that can be used to help decide hierarchy and data that can be used to help decide which chocolate chip recipe they should use.which chocolate chip recipe they should use.
Select the best recipeSelect the best recipe
Taste Cost Fat ContentTaste Cost Fat Content
Recipe 1Recipe 1
Recipe 2Recipe 2
Recipe 3Recipe 3
Recipe 4Recipe 4
Recipe 1Recipe 1
Recipe 2Recipe 2
Recipe 3Recipe 3
Recipe 4Recipe 4
Recipe 1Recipe 1
Recipe 2Recipe 2
Recipe 3Recipe 3
Recipe 4Recipe 4
RECIPE DATARECIPE DATA
Taste Fat ContentTaste Fat Content
Recipe Cost* Rating** (Grams)*Recipe Cost* Rating** (Grams)*
11 $0.166 $0.166 54%54% 8.08.0
22 0.099 0.099 24%24% 7.07.0
33 0.265 0.265 20%20% 3.53.5
44 0.224 0.224 43%43% 6.06.0* Per one ounce cookie* Per one ounce cookie
** Percentage of people who rated a cookie either an 8 or ** Percentage of people who rated a cookie either an 8 or 9 on a 9-point scale, where 9 means extremely liked, 8 9 on a 9-point scale, where 9 means extremely liked, 8 means liked very much, and down to one which means means liked very much, and down to one which means extremely disliked. extremely disliked.
TASTE PAIRWISE COMPARISON TASTE PAIRWISE COMPARISON MATRIXMATRIX
54% 24% 20% 43%54% 24% 20% 43%
Recipe 1 Recipe 2 Recipe 3 Recipe 4Recipe 1 Recipe 2 Recipe 3 Recipe 4
Recipe 1Recipe 1 1 1
Recipe 2Recipe 2 11
Recipe 3Recipe 3 1 1
Recipe 4Recipe 4 11
COST PAIRWISE COMPARISON COST PAIRWISE COMPARISON MATRIXMATRIX
0.166 0.099 0.265 0.2240.166 0.099 0.265 0.224
Recipe 1 Recipe 2 Recipe 3 Recipe 4Recipe 1 Recipe 2 Recipe 3 Recipe 4
Recipe 1Recipe 1 1 1
Recipe 2Recipe 2 11
Recipe 3Recipe 3 1 1
Recipe 4Recipe 4 11
FAT CONTENT PAIRWISE FAT CONTENT PAIRWISE COMPARISON MATRIXCOMPARISON MATRIX
8.0 7.0 3.5 6.08.0 7.0 3.5 6.0
Recipe 1 Recipe 2 Recipe 3 Recipe 4Recipe 1 Recipe 2 Recipe 3 Recipe 4
Recipe 1Recipe 1 1 1
Recipe 2Recipe 2 11
Recipe 3Recipe 3 1 1
Recipe 4Recipe 4 11
CRITERIA PAIRWISE CRITERIA PAIRWISE COMPARISON MATRIXCOMPARISON MATRIX
TasteTaste CostCost Fat ContentFat Content
TasteTaste 1 1
CostCost 1 1
Fat ContentFat Content 11
FINAL WEIGHTS FROM EXPERT FINAL WEIGHTS FROM EXPERT CHOICECHOICE
Criteria WeightsCriteria Weights
Taste Cost Fat ContentTaste Cost Fat Content
FinalFinal
Weights Weights
Recipe 1Recipe 1
Recipe 2Recipe 2
Recipe 3 Recipe 3
Recipe 4Recipe 4
SUMMARYSUMMARY
In this chapter:In this chapter:
we provided an overview of operations management; we provided an overview of operations management; andand
offered the AHP as a decision-making process with offered the AHP as a decision-making process with application in operations management.application in operations management.
SUMMARYSUMMARY
AHP benefits include:AHP benefits include:
natural way to elicit judgments;natural way to elicit judgments;
measure degree of inconsistency;measure degree of inconsistency;
easy to use;easy to use;
allows broad participation; andallows broad participation; and
fully supported by Expert Choice.fully supported by Expert Choice.