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DIT 1141: OPERATIONS MANAGEMENT DEPARTMENT OF DECISION AND INFORMATION TECHNOLOGIES COLLEGE OF COMMERCE AND FINANCE VILL

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DIT 1141: OPERATIONS MANAGEMENT

DEPARTMENT OF DECISION AND INFORMATION TECHNOLOGIES

COLLEGE OF COMMERCE AND FINANCE

VILLANOVA UNIVERSITY

INTRODUCTION

- Operations management is the process of obtaining and utilizing resources to produce useful goods and services so as to meet the goals of the organization.

INTRODUCTION

- Production management is concerned with the manufacturing of goods:
- Examples of goods:
- cars
- books
- chairs
- computers
- houses
- etc.

INTRODUCTION

- Operations management is also concerned with the management of service industries as well as the manufacturing of goods.

INTRODUCTION

- Examples of services:
- retailing/food
- banking
- education
- health care
- utilities
- insurance
- government agencies
- etc.

OVERVIEW OF OPERATIONS MANAGEMENT MODEL

Input: resources

raw materials

machines

personnel

capital

land/buildings

utilities

information

etc.

Output

Goods or

Services

Transformation

Process

Control

OVERVIEW OF OPERATIONS MANAGEMENT MODEL

- Operations management considers how the input are transformed into goods or services.
- Control is when something is learned about the goods or services that is used to more effectively transform future goods or services.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Automobile factory
- Input

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Automobile factory
- Input
- steel, plastic
- glass, paint
- tools
- equipment
- machines
- personnel, buildings
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Automobile factory
- Input
- steel, plastic
- glass, paint
- tools Transformation
- equipment process
- machines
- personnel, buildings
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Automobile factory
- Input Output
- steel, plastic
- glass, paint
- tools Transformation
- equipment process
- machines
- personnel, buildings
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Automobile factory
- Input Output
- steel, plastic Car
- glass, paint
- tools Transformation
- equipment process
- machines
- personnel, buildings
- utilities, etc.

OPERATIONS MANAGEMENT QUESTIONS

- 1. How many items will be demanded next month?
- 2. How many items should be produced next month?
- 3. How many workers are needed to satisfy the proposed production level?

OPERATIONS MANAGEMENT QUESTIONS

- 4. If a plant is built, how should the activities be scheduled so that the project is completed on time, within budget, and with acceptable quality?
- 5. How is the quality of our output measured and how is it improved?
- 6. If tires are needed, how many should be ordered?

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Hospital
- Input

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Hospital
- Input
- patients, doctors
- nurses, drugs
- beds
- building
- medical equipment
- support staff, computers
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Hospital
- Input
- patients, doctors
- nurses, drugs Transformation
- beds Process
- building
- medical equipment
- support staff, computers
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Hospital
- Input Output
- patients, doctors
- nurses, drugs Transformation
- beds Process
- building
- medical equipment
- support staff, computers
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- Hospital
- Input Output
- patients, doctors A treated patient
- nurses, drugs Transformation
- beds Process
- building
- medical equipment
- support staff, computers
- utilities, etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input
- students, professors
- secretaries

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input
- students, professors
- secretaries, drugs

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input
- students, professors
- secretaries, drugs

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input
- students, professors
- secretaries, lab equipment
- dormitories
- staff, computers
- buildings
- etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input
- students, professors
- secretaries, lab equipment
- dormitories
- staff, computers Transformation
- buildings process
- etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input Output
- students, professors
- secretaries, lab equipment
- dormitories
- staff, computers Transformation
- buildings process
- etc.

EXAMPLE OF OPERATIONS MANAGEMENT PROCESS

- University
- Input Output
- students, professors A more highly
- secretaries, lab equipment educated
- dormitories student
- staff, computers Transformation
- buildings process
- etc.

INTRODUCTION

- What is the Analytic Hierarchy Process (AHP)?
- The AHP, developed by Tom Saaty, is a decision-making method for prioritizing alternatives when multi-criteria must be considered.
- An approach for structuring a problem as a hierarchy or set of integrated levels.

INTRODUCTION

- AHP problems are structured in at least three levels:
- The goal, such as selecting the best car to purchase,
- The criteria, such as cost, safety, and appearance,
- The alternatives, namely the cars themselves.

INTRODUCTION

- The decision-maker:
- measures the extent to which each alternative achieves each criterion, and
- determines the relative importance of the criteria in meeting the goal, and
- synthesizes the results to determine the relative importance of the alternatives in meeting the goal.

APPROACH

- How does AHP capture human judgments?
- AHP never requires you to make an absolute judgment or assessment. You would never be asked to directly estimate the weight of a stone in kilograms.
- AHP does require you to make a relative assessment between two items at a time. AHP uses a ratio scale of measurement.

APPROACH

- Suppose the weights of two stones are being assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B?
- AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight.

APPROACH

- Individual AHP judgments are called pairwise comparisons.
- These judgments can be based on objective or subjective information.
- For example, smoothness might be a subjective criterion used to compare two stones. Pairwise comparisons could be based on touch.

APPROACH

- However, suppose stone A is a diamond worth $1,000.00 and stone B is a ruby worth $300.00.
- This objective information could be used as a basis for a pairwise comparison based on the value of the stones.

APPROACH

- Consistency of judgments can also be measured. Consistency is important when three or more items are being compared.
- Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to be three times as large as a softball.
- To be perfectly consistent, a basketball must be six times as large as a softball.

APPROACH

- AHP does not require perfect consistency, however, it does provide a measure of consistency.
- We will discuss consistency in more detail later.

AHP APPLICATIONS

- AHP has been successfully applied to a variety of problems.
- 1. R&D projects and research papers;
- 2. vendors, transport carriers, and site locations;
- 3. employee appraisal and salary increases;
- 4. product formulation and pharmaceutical licensing;
- 5. capital budgeting and strategic planning;
- 6. surgical residents, medical treatment, and diagnostic testing.

AHP APPLICATIONS

- The product and service evaluations prepared by consumer testing services is another potential application.
- Products and services, such as self propelled lawn mowers are evaluated.
- Factors include: bagging, mulching, discharging, handling, and ease of use.
- An overall score for each mower is determined.

AHP APPLICATIONS

- Would you make your purchasing decision based solely on this score?
- Probably not! Some of the information will be helpful.
- Some additional questions are:
- How important is each criterion?
- Would you weigh the criteria the same way?
- Are all of the criteria considered important to you?
- Are there other criteria that are important to you?
- Have you ever thought about these issues?

RANKING SPORTS RECORDS

- The AHP has been used to rank outstanding season, career, and single event records across sports.
- Season
- 1. Babe Ruth, 1920: .847 slugging average
- 2. Joe DiMaggio, 1944: 56 game hitting streak
- 3. Wilt Chamberlain, 1961-62: 50.4 points per game scoring average

RANKING SPORTS RECORDS

- Career
- 1. Johnny Unitas, 1956-70: touchdown passes in 47 consecutive games
- 2. Babe Ruth, 1914-35: .690 slugging average
- 3. Walter Payton, 1975-86: 16,193 rushing yardage
- Single event
- 1. Wilt Chamberlain, 1962: 100 points scored
- 2. Norm Van Brocklin, 1951: 554 passing yards
- 3. Bob Beamon, 1968: 29' 2.5" long jump

RANKING SPORTS RECORDS

- How do we compare records from different sports?
- It all depends on the criteria that you select!
- Golden and Wasil (1987) used the following criteria:
- 1. Duration of record - years record has stood, years expected to stand
- 2. Incremental improvement - % better than previous record
- 3. Other record characteristics - glamour, purity (single person vs. team)

RANKING SPORTS RECORDS

- Did this article end all arguments about sports records?
- Absolutely not!
- In bars and living rooms across the country, people still argue about sports.
- AHP provides a methodology to structure the debate.
- Different criteria and different judgments could produce different results.

A FINAL POINT ABOUT SPORTS

- In reading the sports pages we often see discussion of how well teams match up across different positions.
- These match-ups are often used to predict a winner.
- Match-ups is a pairwise comparison concept!

AHP APPLICATIONS

- Our culture is obsessed with quantitative rankings of all sorts of things.
- There are many measurement problems associated with rankings of products, sports teams, universities, and the like.
- Many of these issues are discussed on a web site at:
- http://www.expertchoice.com/annie.person.

APPLES AND ORANGES

- The discussion of how to compare records from different sports recalls a saying from childhood:

APPLES AND ORANGES

- The discussion of how to compare records from different sports recalls a saying from childhood:
- You can’t compare apples and oranges. All you get is mixed fruit!

APPLES AND ORANGES

- The discussion of how to compare records from different sports recalls a saying from childhood:
- You can’t compare apples and oranges. All you get is mixed fruit!
- After the discussion about sports, do you still believe this statement?

APPLES AND ORANGES

- The discussion of how to compare records from different sports recalls a saying from childhood:
- You can’t compare apples and oranges. All you get is mixed fruit!
- After the discussion about sports, do you still believe this statement?
- We hope not!!!

APPLES AND ORANGES

- What criteria might you use when comparing apples and oranges?
- There are a vast set of criteria that may change depending upon time of day or season of year:
- taste, texture, smell,
- ripeness, juiciness, nutrition,
- shape, weight, color, and
- cost.
- Can you think of others?

APPLES AND ORANGES

- The point is that people are often confronted with the choice between apples and oranges.
- Their choice is based on some psychological assessment of:
- relevant criteria,
- their importance, and
- how well the alternatives achieve the criteria.

CAR PURCHASE EXAMPLE

- We now consider a motivating example.
- After completing this example, you will have an understanding of the basics of AHP and its application through Expert Choice (www.expertchoice.com).
- We want to apply the AHP to help a couple decide which car they should purchase.

CAR PURCHASE EXAMPLE

- The couple is considering three criteria: cost, safety, and appearance.
- They have narrowed their alternatives to three specific cars: Honda, Mazda, and Volvo.
- We demonstrate how to build the AHP hierarchy in Expert Choice.

EXPERT CHOICE: FILE SETUP

- Select the File, New option and enter a file name such as CARS.EC1. (You must use the EC1 file extension.)
- Choose the Direct option to create the model. Next, specify the description of the goal, such as, “Select the best car.”

EXPERT CHOICE: FILE SETUP

- To enter the criteria, use the Edit, Insert command. Use the Esc key when finished entering the criteria.
- To add the alternative cars under the cost node, simply highlight the cost node and again use the Edit, Insert command. Use the Esc key when finished.

EXPERT CHOICE: FILE SETUP

- To include the same alternatives under the other criteria nodes, first highlight the cost node, then select Edit, Replicate children of current node, To Peers, Yes.
- Double-click on the goal node to display the complete hierarchy.
- Additional details can be found in the Expert Choice tutorial provided with the software.

ANALYZING THE HIERARCHY

- 1. Determine the weights of the alternatives for each criterion.
- 2. Determine the priorities or weights of the criteria in achieving the goal.
- 3. Determine the overall weight of each alternative in achieving the goal. This is accomplished by combining the results of the first two stages and is called synthesis.

HYPOTHETICAL DATA FOR CAR PURCHASE EXAMPLE

Car CostSafety*Appearance

Honda $22,000 28 Sporty

Mazda 28,500 39 Slick

Volvo 33,000 52 Dull

* Safety Rating from a consumer testing service - the higher the number, the safer the car.

DETERMINING PRIORITIES

- The couple begins by making pairwise comparison judgments between each pair of cars for the cost criterion.
- In our example, three judgments are needed: Honda to Mazda, Mazda to Volvo, and Honda to Volvo.

STANDARD 1 - 9 MEASUREMENT SCALE

- Intensity of ImportanceDefinitionExplanation
- 1 Equal importance Two activities contribute equally
- 3 Moderate importance Experience and judgment slightly favor one
- activity over another
- 5 Strong importance Experience and judgment strongly favor one
- activity over another
- 7 Very strong An activity is favored very strongly over
- another
- 9 Extreme importance The evidence favoring one activity over
- another is of the highest possible order
- of affirmation
- 2, 4, 6, 8 For compromise Sometimes one needs to interpolate a
- values compromise between the above judgment
- numerically because there is no good
- word to describe it
- 1.1 - 1.9 For tied activities When elements are close and nearly
- indistinguishable; moderate is 1.3 and
- extreme is 1.9
- Reciprocals of above If activity A has For example, if the pairwise comparison of
- one of the above A to B is 3.0, then the pairwise comparison
- numbers assigned of B to A is 1/3
- to it when compared
- with activity B,
- then B has the
- reciprocal value
- when compared to A.

COST PAIRWISE COMPARISONS

- The pairwise comparisons are represented in the form of pairwise comparison matrices.
- The computation of the weights are also shown.
- Consider the pairwise comparison matrix to compare the cars for the cost criterion.
- Remember that the costs of the three cars are: $22000, $28500, and $33000, respectively.

COST PAIRWISE COMPARISONS

- If we compare the Honda to the Honda, obviously they are equal.
- Therefore, a 1 (equal preferred) is placed in the first row, first column entry of the matrix.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1
- 28.5KMazda
- 33K Volvo

COST PAIRWISE COMPARISONS

- The other entries along the main diagonal of the matrix are also 1.
- This simply means that everything is equally preferred to itself.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1
- 28.5KMazda 1
- 33K Volvo1

COST PAIRWISE COMPARISONS

- Suppose we believe the Honda ($22000) is equally to moderately preferred to the Mazda ($28500). Place a 2 in the row 1, column 2 entry.
- Some might argue that the Honda should be 1.295 times better than the Mazda (28,500/22,000).

COST PAIRWISE COMPARISONS

- Do you agree?
- It depends!
- For some, $28,500 is significantly greater than $22,000, implying a judgments greater than 1.295.
- Others with a lot of money may perceive virtually no difference between the two costs, implying a judgment somewhere between 1 and 1.295.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2
- 28.5KMazda 1
- 33K Volvo 1

COST PAIRWISE COMPARISONS

- If the Honda is 2 times better than the Mazda, this implies that the Mazda ($28500) is one half as good as the Honda ($22000).
- The reciprocal judgment, (1/2), should be placed in the row 2, column 1 entry of the matrix.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2
- 28.5KMazda 1/2 1
- 33K Volvo 1

COST PAIRWISE COMPARISONS

- Suppose that we judge the Mazda ($28500) to be equally to moderately preferred to the Volvo ($33000).
- The following judgments would be entered in the matrix.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2
- 28.5KMazda 1/2 12
- 33K Volvo 1/2 1

COST PAIRWISE COMPARISONS

- Assuming perfect consistency of judgments, we would expect that the Honda ($22000) is 4 times (that is, moderately to strongly) preferred to the Volvo ($33000).
- We will relax this assumption later.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5KMazda 1/2 12
- 33K Volvo 1/4 1/2 1

COST PAIRWISE COMPARISONS

- The matrix is now complete and the weights for each car (for the cost criterion) can be computed.
- The exact computational procedure is implemented in Expert Choice. For details see Expert Choice homepage and download AHPDEMO.EXE.

COST PAIRWISE COMPARISONS

- A simple three step procedure can be used to approximate the weights for each alternative.
- Essentially, this procedure normalizes the ratios of the judgments between any pair of alternatives.

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5KMazda 1/2 12
- 33K Volvo 1/4 1/2 1
- ------- ------- -------
- COLUMN TOTALS

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5KMazda 1/2 12
- 33K Volvo 1/4 1/2 1
- ------- ------- -------
- COLUMN TOTALS 7/4 7/2 7

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5KMazda 1/2 12
- 33K Volvo 1/4 1/2 1
- ------- ------- -------
- COLUMN TOTALS 7/4 7/2 7

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5K Mazda 1/2 12
- 33K Volvo 1/4 1/2 1
- ------- ------- -------
- COLUMN TOTALS 7/4 7/2 7
- B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- Honda 4/7* 4/7 4/7
- Mazda 2/7 2/7 2/7
- Volvo 1/7 1/7 1/7
- * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).

COST PAIRWISE COMPARISONS

- Notice that no variation is seen across the rows because the judgments are perfectly consistent.
- For the third column, judgments totaling 7 were awarded. The Honda received 4 of 7 (57.1%), the Mazda 2 of 7 (28.6%), and the Volvo 1 of 7 (14.3%) of the weight.
- Similar comparisons can be made for the other two columns.

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5K Mazda 1/2 12
- 33K Volvo 1/4 1/2 1
- ------- ------- -------
- COLUMN TOTALS 7/4 7/2 7
- B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- Honda 4/7* 4/7 4/7
- Mazda 2/7 2/7 2/7
- Volvo 1/7 1/7 1/7
- * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5K Mazda 1/2 12
- 33K Volvo 1/4 1/2 1
- ------- ------- -------
- COLUMN TOTALS 7/4 7/2 7
- B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS
- Honda Mazda Volvo (ROW AVG.)
- Honda 4/7* 4/7 4/7 0.571
- Mazda 2/7 2/7 2/7 0.286
- Volvo 1/7 1/7 1/7 0.143
- ---------
- TOTAL 1.000
- * This entry is obtained by dividing the Honda entry in the original matrix (1) by the Honda column total (7/4).

EXPERT CHOICE: Entering Judgments

- Expert Choice offers a variety of modes for entering the judgments.
- Highlight the cost node, select Assessment.
- There are three options: Pairwise, Data, and Ratings.
- Ratings will be discussed later.

EXPERT CHOICE: Entering Judgments

- The Data option allows the user to enter data items for each alternative, for example, costs, miles per gallon, and number of defects.
- Expert Choice takes the ratio of these data items and converts them into pairwise comparisons.
- What assumption are you making if you use the Data option?
- The data items have a linear preference scale, that is, a $20,000 car is twice as good as a $40,000 car.

EXPERT CHOICE: Entering Judgments

- To enter our cost judgments choose Pairwise.
- When comparing alternatives select Preference for Type; for criteria select Importance.
- Modes options are: Verbal, Matrix (numerical), Questionnaire, and Graphic.
- Assessment, Pairwise, Matrix is demonstrated.
- Enter judgments, Calculate and Record.

INCONSISTENCY OF JUDGMENTS

- Since our pairwise comparisons were perfectly consistent, Expert Choice reports INCONSISTENCY RATIO = 0.0.
- If this ratio is greater than 0.1 some revision of judgments is required.
- Select Inconsistency (within Assessment, Pairwise) to identify the most inconsistent judgments.

INCONSISTENCY OF JUDGMENTS

- Inconsistency of judgments may result from:
- problems of estimation;
- errors between the comparisons;
- or, the comparisons may be naturally inconsistent.

INCONSISTENCY OF JUDGMENTS

- One example of natural inconsistency is in a sporting contest.
- 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 does not necessarily imply that team A is six times as likely to beat team C.
- This inconsistency may result because of the way that the teams “match-up” overall.

INCONSISTENCY OF JUDGMENTS

- The point is not to stop inconsistency from occurring.
- Make sure that the level of inconsistency remains within some reasonable limit.

INCONSISTENCY OF JUDGMENTS

- How does a judgment change affect the car weights?
- Suppose the Mazda to Volvo changes from 2 to 3.
- This obviously changes the comparison for Volvo to Mazda from (1/2) to (1/3).
- The judgments are now somewhat inconsistent.

COST PAIRWISE COMPARISONS

- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5KMazda 1/2 1 3
- 33K Volvo 1/4 1/3 1

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5K Mazda 1/2 13
- 33K Volvo 1/4 1/3 1
- ------- ------- -------
- COLUMN TOTALS 7/4 10/3 8

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5KMazda 1/2 13
- 33K Volvo 1/4 1/3 1
- ------- ------- -------
- COLUMN TOTALS 7/4 10/3 8
- B. ADJUSTED COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- Honda 4/7* 6/10 4/8
- Mazda 2/7 3/10 3/8
- Volvo 1/7 1/10 1/8

COST PAIRWISE COMPARISONS

- 1. SUM THE ELEMENTS IN EACH COLUMN OF THE ORIGINAL MATRIX.
- 2. DIVIDE EACH ELEMENT IN THE ORIGINAL MATRIX BY ITS COLUMN SUM.
- THIS RESULTS IN THE ADJUSTED MATRIX.
- 3. COMPUTE THE ROW AVERAGES - THESE ARE THE WEIGHTS.
- A. ORIGINAL COST PAIRWISE COMPARISON MATRIX
- Honda Mazda Volvo
- 22K Honda 1 2 4
- 28.5K Mazda 1/2 13
- 33K Volvo 1/4 1/3 1
- ------- ------- -------
- COLUMN TOTALS 7/4 10/3 8
- B. ADJUSTED COST PAIRWISE COMPARISON MATRIX WEIGHTS
- Honda Mazda Volvo (ROW AVG.)
- Honda 4/7* 6/10 4/8 0.557
- Mazda 2/7 3/10 3/8 0.320
- Volvo 1/7 1/10 1/8 0.123
- --------
- TOTAL 1.000

INCONSISTENCY OF JUDGMENTS

- The new weights are: 0.557, 0.320, and 0.123. The inconsistency resulted in some change in the original weights of 0.571, 0.286, and 0.143.
- As expected, the weight for the Mazda increased while the weight for the Volvo decreased.
- The weights now vary across each row. Essentially, inconsistency measures the degree of variation across the rows.

EXPERT CHOICE: Revising Judgments

- Highlight cost node, select Assessment, Pairwise.
- Enter a 3 in the Mazda to Volvo cell then Calculate.
- The weights of 0.558, 0.320, and 0.122 are slightly different from the three-step procedure weights.
- This is not due to rounding -- Expert Choice gives the exact results.
- The INCONSISTENCY RATIO is now 0.02.

INCONSISTENCY OF JUDGMENTS

- The weights can also be used to measure the effectiveness of the alternatives.
- For example, based on all pairwise comparisons, we determined that the Honda is 1.74 (0.558/0.320) times better than the Mazda.
- Why is this ratio 1.74 and not the pairwise comparison of 2?
- Inconsistency in the judgments!

REMAINING COMPUTATIONS

- Next, the cars must be pairwise compared for the safety criterion and then for the appearance criterion.
- These judgments are shown on the next page.
- Since the Mazda to Honda safety comparison is 2, highlight the Honda to Mazda cell, click Invert, and enter 2.
- This judgment now appears in red.

SAFETY & APPEARANCE JUDGMENTS

- Safety Pairwise Comparison Matrix
- Honda Mazda Volvo
- 28 Honda 1 1/2 1/5
- 39 Mazda 2 1 1/4
- 52 Volvo 5 4 1
- Appearance Pairwise Comparison Matrix
- Honda Mazda Volvo
- SportyHonda 1 5 9
- Slick Mazda 1/5 1 2
- Dull Volvo 1/9 1/2 1

REMAINING COMPUTATIONS

- Next, the criteria must be pairwise compared.
- These judgments are shown on the next page.
- There are no data to support these judgments since they are purely a reflection of your preferences.

CRITERIA JUDGMENTS

- Original Criteria Pairwise Comparison Matrix
- Cost Safety Appearance
- Cost 1 1/2 3
- Safety 2 1 5
- Appearance 1/3 1/5 1

REMAINING COMPUTATIONS

- The last stage computes the final weights for each car.
- Multiply the criteria weight by the car weight for each criterion and then sum over all criteria.
- This is nothing more than a weighted average.
- The computational results are shown next.

FINAL CAR WEIGHTS

- CRITERIA WEIGHTS
- COST SAFETY APPEARANCE
- 0.309 0.582 0.109
- CARS FINAL WEIGHTS
- Honda 0.558 0.117 0.761
- Mazda 0.320 0.200 0.158
- Volvo 0.122 0.683 0.082

FINAL CAR WEIGHTS

- CRITERIA WEIGHTS
- COST SAFETY APPEARANCE
- 0.309 0.582 0.109
- CARS FINAL WEIGHTS
- Honda 0.558 0.117 0.761 0.324
- Mazda 0.320 0.200 0.158
- Volvo 0.122 0.683 0.082
- Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
- 0.173 0.068 0.083

FINAL CAR WEIGHTS

- CRITERIA WEIGHTS
- COST SAFETY APPEARANCE
- 0.309 0.582 0.109
- CARS FINAL WEIGHTS
- Honda 0.558 0.117 0.761 0.324
- Mazda 0.320 0.200 0.158 0.232
- Volvo 0.122 0.683 0.082
- Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
- 0.173 0.068 0.083
- Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
- 0.099 0.116 0.017

FINAL CAR WEIGHTS

- CRITERIA WEIGHTS
- COST SAFETY APPEARANCE
- 0.309 0.582 0.109
- CARS FINAL WEIGHTS
- Honda 0.558 0.117 0.761 0.324
- Mazda 0.320 0.200 0.158 0.232
- Volvo 0.122 0.683 0.082 0.444
- Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324
- 0.173 0.068 0.083
- Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232
- 0.099 0.116 0.017
- Volvo: (0.122)(0.309) + (0.683)(0.582) + (0.082)(0.109) = 0.444
- 0.038 0.397 0.009

LOCAL VS GLOBAL WEIGHTS

- For cost, the local weights for the cars are 0.558, 0.320, and 0.122 and sum to 1.000.
- The global weights are computed by multiplying the cost criterion weight by the local car weights.
- The global weights are 0.173, 0.099, and 0.038 and sum to the cost criterion weight of 0.309.

EXPERT CHOICE: Synthesis

- To compute the final weights select Synthesis (from GOAL).
- Choose Distributive Mode and Display Summary.
- Details provides the global weights.
- The output can also be exported to a spreadsheet using the Utilities, Export Model(s) to Spreadsheet commands.

EXPERT CHOICE: Printing

- The Print icon can be used to select certain options.
- The recommended print options are: Entire Tree, Tree Views, Judgments/Data, and Synthesis.

INTERPRETING THE RESULTS

- The final weights provide a measure of the relative performance of each alternative.
- It is important to properly interpret the meaning of these numbers.
- The Volvo is ranked first, the Honda second, and Mazda third.
- The Volvo is preferred 1.37 (0.444/0.324) times more than the Honda.

INTERPRETING THE RESULTS

- Should we buy the Volvo?
- The output is a decision-making aid and cannot replace the decision-maker.
- The results can be used to support discussion and possibly the judgments will be revised.
- This iterative process is quite normal.
- AHP can help to facilitate communication and generate consensus between different groups.

SENSITIVITY ANALYSIS

- Sensitivity analysis is an important aspect of any decision-making process.
- Sensitivity analysis determines whether small changes in judgments affects the final weights and rankings of the alternatives.
- If so, the decision-maker may want to review the sensitive judgments.

EXPERT CHOICE: Sensitivity Analysis

- In Expert Choice sensitivity analysis from the GOAL shows how the weights and the rankings of the alternatives change if some or all of the criteria weights change.
- There are five graphical sensitivity analysis modes available: Performance, Dynamic, Gradient, Two-Dimensional, and Difference.
- The first three show how a change in a criterion weight affects the final weights of the alternatives.

EXPERT CHOICE: Sensitivity Analysis

- The last two show how the alternatives perform with respect to any two criteria.
- Performance: places all sensitivity information on a single chart with horizontal line graphs for the alternatives linked to vertical bars for the criteria.
- Dynamic: two sets of dynamically linked horizontal bar graphs: one for criteria and one for alternatives.

EXPERT CHOICE: Sensitivity Analysis

- Gradient: a line graph that shows how the weights of the alternatives vary according to the weight assigned to a specific criterion. (Use the X-Axis to change the selected criterion.)
- Two-Dimensional: shows how well the alternatives perform with respect to any two criteria.
- Difference: a graph that shows the differences between any two alternatives for any criterion.

EXPERT CHOICE: Sensitivity Analysis

- An important use of sensitivity analysis is to determine how much a given criterion weight must change before there is a change in the rankings of the two highest alternatives.
- This type of breakeven analysis can be easily done in Expert Choice.

EXPERT CHOICE: Sensitivity Analysis

- Choose Dynamic from the Sensitivity-Graphs option.
- Drag the cost criterion bar 30.9% to approximately 45.9%, and see that the Volvo and Honda have the same highest final weight.
- The final rankings are relatively insensitive to a change in the cost criterion weight because the cost weight had to be increased by almost 50% to get a change in the rankings.

NEW PRODUCT INTRODUCTION

- CHOCK-FUL-O-CHIPS developed the following hierarchy and data that can be used to help decide which chocolate chip recipe they should use.

Select the best recipe

Taste Cost Fat Content

Recipe 1

Recipe 2

Recipe 3

Recipe 4

Recipe 1

Recipe 2

Recipe 3

Recipe 4

Recipe 1

Recipe 2

Recipe 3

Recipe 4

RECIPE DATA

- Taste Fat Content
- Recipe Cost* Rating** (Grams)*
- 1 $0.166 54% 8.0
- 2 0.099 24% 7.0
- 3 0.265 20% 3.5
- 4 0.224 43% 6.0
- * Per one ounce cookie
- ** Percentage of people who rated a cookie either an 8 or 9 on a 9-point scale, where 9 means extremely liked, 8 means liked very much, and down to one which means extremely disliked.

TASTE PAIRWISE COMPARISON MATRIX

- 54% 24% 20% 43%
- Recipe 1 Recipe 2 Recipe 3 Recipe 4
- Recipe 1 1
- Recipe 2 1
- Recipe 3 1
- Recipe 41

COST PAIRWISE COMPARISON MATRIX

- 0.166 0.099 0.265 0.224
- Recipe 1 Recipe 2 Recipe 3 Recipe 4
- Recipe 1 1
- Recipe 2 1
- Recipe 3 1
- Recipe 41

FAT CONTENT PAIRWISE COMPARISON MATRIX

- 8.0 7.0 3.5 6.0
- Recipe 1 Recipe 2 Recipe 3 Recipe 4
- Recipe 1 1
- Recipe 2 1
- Recipe 3 1
- Recipe 41

CRITERIA PAIRWISE COMPARISON MATRIX

- Taste Cost Fat Content
- Taste 1
- Cost 1
- Fat Content 1

FINAL WEIGHTS FROM EXPERT CHOICE

- Criteria Weights
- Taste Cost Fat Content
- Final
- Weights
- Recipe 1
- Recipe 2
- Recipe 3
- Recipe 4

SUMMARY

- In this chapter:
- we provided an overview of operations management; and
- offered the AHP as a decision-making process with application in operations management.

SUMMARY

- AHP benefits include:
- natural way to elicit judgments;
- measure degree of inconsistency;
- easy to use;
- allows broad participation; and
- fully supported by Expert Choice.

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