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DECISION MAKING USING ANALYTIC HIERARCHY PROCESS (AHP) 1.Mr. Vaibhav S. Gaikwad (B.E. MECH) 2.Mr. Hansraj O. Patil (B.E. MECH) 3.Mr. Pankaj S. Patil (B.E. MECH) 4.Mr. Aniket S. Thakur (B.E. MECH) DEPARTMENT OF MECHANICAL ENGINEERING, K.G.C.E , KARJAT.

Decision Making Using The Analytic Hierarchy Process

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Page 1: Decision Making Using The Analytic Hierarchy Process

NLC-ETFII-2016

DECISION MAKING USING ANALYTIC

HIERARCHY PROCESS (AHP)

1. Mr. Vaibhav S. Gaikwad (B.E. MECH)

2. Mr. Hansraj O. Patil (B.E. MECH)

3. Mr. Pankaj S. Patil (B.E. MECH)

4. Mr. Aniket S. Thakur (B.E. MECH)

DEPARTMENT OF MECHANICAL ENGINEERING,

K.G.C.E , KARJAT.

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► Is a multicriteria decision-making system.

► Was developed by Thomas L. Saaty.

►Used to solve complex decision-making problems.

►Has been applied in variety of decisions and planning projects

in nearly 20 countries.

►Is implemented in the software of Expert Choice©

Analytic Hierarchy Process (AHP)

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►Resource allocation

►Hiring, evaluating and promoting employees

►TQM

►Strategic planning

►Relocation decisions

►Vendor selection

►Evaluating mergers and acquisitions

Applicable in the areas

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A few of the Universities using AHP. Harvard University Colorado State UniversityYale University University of CambridgeMIT American University

IBM NASAGoodyear IRSFord Motor Co. FBI

Citibank Department of Defense

Xerox World Bank

►Goal: To select the best branch (Resultwise).►Criteria: 2015,2014,2013,2012,2011(Yearwise)►Alternatives: MECH, PROD, COMP, IT, EXTC, INSTRU.(Branchwise)

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GOAL

SELECTION OF BEST BRANCH ON BASIS OF RESULTS

2015 2014 2013 2012 2011

MECH PROD COMP IT EXTC INSTRU

Analytic Hierarchy Process (AHP)

►Step 1: Structure a hierarchy. Define the problem, determine the criteria and identify the alternatives.

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►Step 2: Make pairwise comparisons. Rate the relative importance between each pair of decision alternatives and criteria.

AHP uses 1-9 scale for the prioritization process.

Numerical ratings Verbal judgments

1 Equally important (preferred)3 Moderately more important

5 Strongly more important

7 Very strongly more important

9 Extremely more important

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►Step 2 (cont’d):

Intermediate numerical ratings of 2, 4, 6, and 8 can be assigned.

If someone could not decide whether one criterion (alternative) is

moderately more important than the other one or strongly more

important than the other one, 4 (moderately to strongly more important) can be assigned.

►Step 3: Synthesize the results to determine the best alternative. Obtain the finalresults.The output of AHP is the set of priorities of the alternatives.

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Best Branch SelectionPairwise compasrison:

2015 MECH PROD COMP IT EXTC INSTRU

MECH 1 1/7 3 1/3 1/5 1/9

PROD 7 1 7 5 3 1/3

COMP 1/3 1/7 1 1/3 1/5 1/7

IT 3 1/5 3 1 1/3 1/5

EXTC 5 1/3 5 3 1 1/3

INSTRU 9 3 7 5 3 1

2014 MECH PROD COMP IT EXTC INSTRU

MECH 1 9 1/3 7 5 3

PROD 1/9 1 1/9 1/3 1/5 1/7

COMP 3 9 1 7 5 3

IT 1/7 3 1/7 1 1/3 1/5

EXTC 1/5 5 1/5 3 1 1/3

INSTRU 1/3 7 1/3 5 3 1

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2013 MECH PROD COMP IT EXTC INSTRU

MECH 1 1/5 1/3 5 1/7 3

PROD 5 1 3 7 1/3 5

COMP 3 1/3 1 5 1/3 3

IT 1/5 1/7 1/5 1 1/5 1/3

EXTC 7 3 3 5 1 3

INSTRU 1/3 1/5 1/3 3 1/3 1

2012 MECH PROD COMP IT EXTC INSTRUMECH 1 1/5 1/3 3 1/9 1/7

PROD 5 1 3 5 1/5 1/3

COMP 3 1/3 1 3 1/5 1/3

IT 1/3 1/5 1/3 1 1/5 1/3

EXTC 9 5 5 5 1 3

INSTRU 7 3 3 3 1/3 1

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2011 MECH PROD COMP IT EXTC INSTRU

MECH 1 2 7 5 9 3PROD 1/2 1 7 5 9 3COMP 1/7 1/7 1 1/5 3 1/3IT 1/5 1/5 5 1 3 1/3EXTC 1/9 1/9 1/3 1/3 1 1/3INSTRU

1/3 1/3 3 3 3 1

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Synthesizing Procedure – 1Solving for year 2015

Step 1: Sum the values in each column:

2015 MECH PROD COMP IT EXTC INSTRUMECH 1 1/7 3 1/3 1/5 1/9

PROD 7 1 7 5 3 1/3

COMP 1/3 1/7 1 1/3 1/5 1/7

IT 3 1/5 3 1 1/3 1/5

EXTC 5 1/3 5 3 1 1/3

INSTRU 9 3 7 5 3 1

COLUMN TOTAL

76/3 506/105 26 44/3 116/15 668/315

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Synthesizing Procedure - 2Step 2: Divide each element of the matrix by its column total.All columns in the normalized Form.

2015 MECH PROD COMP IT EXTC INSTRU

MECH 3/76 15/506 3/26 1/44 3/116 35/668

PROD 21/76 105/506 7/26 15/44 45/116 105/668

COMP 1/76 15/506 1/26 1/44 3/116 45/668

IT 9/76 21/506 3/26 3/44 5/116 63/668

EXTC 15/76 35/506 5/26 9/44 15/116 105/668

INSTRU 27/76 315/506 7/26 15/44 45/116 315/668

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Synthesizing Procedure - 3

Step 3: Average the elements in each row.

1. The values in the normalized pairwise comparison matrix have been

converted to decimal form.

2. The result is usually represented as the (relative) priority vector.

2015 Row Avg.

MECH 0.04758

PROD 0.27318

COMP 0.03286

IT 0.08015

EXTC 0.15831

INSTRU 0.4079

TOTAL 1.0000

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Consistency Ratio (CR)The AHP provides a measure of the consistency of pairwise comparison

judgments by computing a consistency ratio. The ratio is designed in such a way that values of the ratio exceeding 0.10 are

indicative of inconsistent judgments.

Although the exact mathematical computation of the consistency ratio is

beyond the scope of this text, an approximation of the ratio can be obtained.

Compute the consistency index (CI):

Where n is the number of items being compared

Compute the consistency ratio (CR):RICICR

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Random Index

Random index (RI) is the consistency index of a randomly

generated pairwise comparison matrix.

RI depends on the number of elements being compared (i.e., size of

pairwise comparison matrix) and takes on the following values:

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MECH PROD COMP IT EXTC INSTRU

1 1/7 3 1/3 1/5 1/97 1 7 5 3 1/31/3 1/7 1 1/3 1/5 1/73 1/5 3 1 1/3 1/55 1/3 5 3 1 1/39 3 7 5 3 1

Row Avg

0.04758

0.27318

0.03286

0.08015

0.15831

0.40790

Weighted Sum

0.2888

1.8478

0.2043

0.5104

1.0279

2.761

Divide the elements of the vector of weighted sums by thecorresponding priority value.MECH - 0.288/0.04758 = 6.0697PROD - 1.8478/0.27318 =6.7640COMP - 0.2043/0.03286 =6.2203IT - 0.5104/0.08015 =6.3680EXTC - 1.0279/0.1583 =6.4933INSTRU - 2.761/0.4079 = 6.7688

Compute the average of the values computed in step 2 (lmax).

lmax = = 6.4474

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Compute the consistency index (CI). CI = = =0.08947

Compute the consistency ratio (CR). CR = = 0.07215 ≤ 0.10 (for Year 2015)

2011 2012 2013 2014 2015 Priority vector

2011 1 5 3 7 9 0.5160

2012 1/5 1 1/3 3 5 0.1424

2013 1/3 3 1 3 5 0.2266

2014 1/7 1/3 1/3 1 3 0.0761

2015 1/9 1/5 1/5 1/3 1 0.0381

Calculate Judgement matrix:

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Decision Matrix2011 2012 2013 2014 2015 Final priority

0.5160 0.1424 0.2266 0.0761 0.0381

MECH 0.3842 0.0530 0.0987 0.2776 0.0475 0.2510

PROD 0.3038 0.1582 0.2710 0.0252 0.2731 0.2530

COMP 0.0509 0.0907 0.1511 0.3998 0.0328 0.1050

IT 0.0953 0.0454 0.0354 0.0461 0.0801 0.07022EXTC 0.0320 0.4310 0.3725 0.0871 0.1583 0.1749

INSTRU 0.1334 0.2214 0.07015 0.1640 0.4079 0.1445

T O T A L 1.0000

Conclusions1. Number of failing percentage in IT BRANCH is less as compared

to all other branches. 2. Result of IT BRANCH in last five years is better in terms of result.3. Calculated value of C.R. is also less than 10%. 4. However this paper demonstrate the live example of our college

result (Branchwise).

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Future FindingsWe will compare our results found in AHP with other methods such as :

TOPSIS

FUZZY REFERENCES

[1] Saaty, T.L., 1980. “The Analytic Hierarchy Process.” McGraw-Hill, New York[2] Wikipedia for problem definition of AHP.[3] [email protected][4] T. L. Saaty, Inconsistency and rank preservation. J. math. Psychol. 28(2), 2055214 (1984). [5] R. Venkatarao phd (Decision Making in the Manufacturing Environment)[6] Expert Choice, software package. Decision Support Software, McLean, Va.[7] Exam cell of KGCE from where we collected the result statistics for matrix evaluation

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Thanks