Selection of School

Selection of School

Selection of School:

Academic Reputation, Location,

Placement, Fees, Infrastructure

Analytic

Hierarchy Process

by

G N Patel

Admission

Location PlacementReputation Fees Infrastructure

YX Z

CRITERIA

ALTERNATIVES

Hierarchic

Thinking

Purchase of apple

Purchase of apple

Purchase of Apple:

Taste, Aroma, Ripeness, Size, Price

Purchase of Oven

Purchase of Oven

Choose best oven:

function, economy,

safety and reliability,

convenience

Whom to marry

Whom to marry

Whom to marry:

flexibility, independence,

commitment, humor,

intelligence, physical,

socio-cultural

Selection of Job

Selection of Job

Selection job:

salary, life quality of the city where

job is located, job profile, nearness to home, security,

reputation, flexibility (time, work place), opportunity

(salary potential, top level position)

Evaluation of Employees for Promotion

Evaluation of employees for promotion:

dependability, education, experience,

quality, attitude, leadership

Perhaps the most creative task in making

a decision is to choose the factors that

are important for the decision

Analytic Hierarchy Process (AHP)

A popular mathematical method for solving MCDM problems .

AHP Applications

It has been used in more than 30 diversified field like

1. Planning and development

2. Selection

3. Resource allocation

4. Forecasting

5. Evaluation

6. Priority and ranking.

7. Health and related fields

and many more.

Importance of AHP

It provides a unique way of incorporating qualitative and quantitative judgments.

It is able to rank choices in their order of effectiveness in realizing their objectives.

It allows decision makers to include inconsistency in their choices.

It is versatile and flexible to enable a combination of other mathematical methods not limited to LP, Fuzzy logic

theories and network models.

Analytical Hierarchy Process

1.A multi-attribute analysis technique that

organizes complex systems/unstructured

problems with many elements of different

influence.

2.Easy to use, automatable algorithm,

well-accepted by policy makers.

3.Uses stakeholder perceptions to find the

most important elements influencing

complex decisions (only as good as the

experts).

The Analytic Hierarchy

Process (AHP)

Decision Making involves setting priorities and the AHP is the

methodology for doing that. It is designed for situations in which

ideas, feelings, and emotions affecting the decision process are

quantified to provide a numeric scale for prioritizing the

alternatives.

AHP- Methodology

It has the following steps:

Step 1.

Stating the goal, criteria, sub- criteria, alternatives and

constraints of the problem clearly.

Step 2.

Arrange fragmented decision problems into (tree- like)

hierarchy structure of different levels ( goal, criteria, sub-

criteria, alternatives.)

The Analytic Hierarchy Process (Step 2 contd.)

Objective

Criterion 2Criterion 1 Criterion KLevel 2

Subcriterion 1 Subcriterion 2 Subcriterion K

Alternative 1 Alternative 2 Alternative N

Level 3

Level P

Hierarchy with P Levels

Level 1

Step 2. Decompose the problem into a hierarchy of interrelated

decision criteria and alternatives

.

.

.

GOAL

CRITERIA

ALTERNATIVES

Relative Measurement

The Process of Prioritization

Step 3.

Develop a pair wise comparison matrix using fundamental scale to

measure both tangible and intangible criteria.

In relative measurement a preference, judgment is expressed on

each pair of elements with respect to a common property they

share.

In practice this means that a pair of elements in a level of the

hierarchy are compared with respect to parent elements to which

they relate in the level above.

The Principle of the AHP

This comparison is carried out using the following fundamental scale from 1 to 9 as follows: 1 Equally preferred

2 Equally to Moderately preferred

3 Moderately preferred

4 Moderately to Strongly preferred

5 Strongly preferred

6 Strongly to Very Strongly preferred

7 Very Strongly preferred

8 Very strongly to Extremely preferred

9 Extremely preferred

AHP- Methodology(Contd)

The pairwise comparison matrix looks like

where is the relative importance of criterion i over criterion j number of comparisons required for the pair-wise comparison matrix is

given by n(n-1)/2 where n = number of elements

Diagonal elements are 1 and other elements are reciprocals of earlier comparisons that is

AHP- Methodology(Contd)

Step 4

The priority vector w is obtained by using Additive Normalization as follows:

Consistency of the Comparison Matrix

Step 5 : Testing the consistency of the comparison matrix

If all the columns of the normalized matrix are identical, then the

original matrix is said to be consistent

is a consistent matrix

Consistency implies coherent judgment on the part of the decision

maker regarding the pair-wise comparisons.

R L

A= R 1 5

L 1/5 1

Consistency of the Comparison Matrix

Step 5 : Testing the consistency of the comparison

matrix

Mathematically, A is consistent if

Also it can defined as when n is the size of the matrix

and A is consistent.

When A is not consistent , than , max being the

principal eigen vector

Consistency of the Comparison Matrix

(contd.)

Step 5

Testing of the consistency

Where max = principal eigen vector

CI = consistency index

RI = the random consistency index.

.

Consistency of the Comparison Matrix

(contd.)

It is unusual for all comparison matrices to be consistent.

Indeed, given that human judgment is the basis of the

construction of these matrices, some reasonable degreeof inconsistency is expected and tolerated.

The matrix is accepted as consistent if

AHP- Methodology(Contd)

Step 6: Global weights of alternatives with respect to the goal defined in the AHP model are calculated.

Selection of Management Institute for EDP/FDP

Ms. Y has received information from three Management

institutions A, B, C to attend EDP / FDP on similar topics. She

specifies two main criteria location and academic reputation.

Being a participant believing to enhance knowledge through

attending such programmes, she judges academic reputation to

be five times as important as location. Using the symbols R and

L to represent reputation and location, the associated

comparison matrix is given as

R L

A= R 1 5

L 1/5 1

Example Contd.

The relative weights of the alternatives of A,B and C

within each of the L and R criteria, whose elements

are based on Ms Xs judgment regarding the relative importance are as follows:

L A B C

A 1 1/2 1/5

AL= B 2 1 1/2

C 5 2 1

A B C

A 1 2 3

AR= B 1/2 1 3/2

C 1/3 2/3 1

Pros and cons of AHP

Pros

Hierarchical structuring of a decision problem

Combining multiple inputs from several persons to a consolidated

outcome

People usually agree with the out coming process

Calculations using excel

Pros and cons of AHP

Cons

Pair wise comparison is a quite artificial way a set of items. People

are more use to agree-disagree or ranking

If consistency index is too high: request to reconsider

Recommendations

When using AHP: Try to structure the model in group of max 4-5

criteria or sub criteria. If possible introduce additional hierarchical

levels

Spend time to explain the use of scale for pair wise comparisons

without knowledge of AHP. Ask them to use the whole range 1 to 9.

Even with a consistency value above the recommended limit, the

results usually reflects the correct ranking and still can be used.

Recommendations

AHP is ideal to get a consolidated result for inputs from several

participants using the geometric mean

Once AHP is introduced and used as method for decision making,

results are generally accepted, as the method is based on

mathematics, seen as neutral and objective