topsis (11ID60R20)

TOPSIS for supplier selection problem.

Submitted By : Pranav Mishra 11ID60R20

Lets considerLuna wants to go on a vacation. She has 3 options

Hogwarts Hogsmead e Azkaban

How to decide..???

Let us considerEach option can be evaluated against certain criteria. Criteria for vacation destinations can be:

Entertainment Facilities Accommodation cost Travel cost

Similarly

Selecting a source of information (library, internet, etc) involves various criteria such as: Reliability of information Time to gather information Cost of acquiring information

These

are examples of MULTICRITERIA problems and requires MCDM approach.

MCDMMultiple Criteria Decision MakingSelection of the best, from a set of alternatives, each of which is evaluated against multiple criteria. Some problem solving techniques are : SAW (Simple Additive Weighting) TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) ELECTRE (Elimination et Choice Translating Reality) AHP (The Analytical Hierarchy Process) SMART (The Simple Multi Attribute Rating Technique ) ANP (Analytic network process)

Important terms

Alternatives These are the options which areto be evaluated for selection of the best.Example: (for vacation problem)Hogwarts, Hogsmeade, Azkaban

Criteria or Attributes These will impact theselection of alternatives.

Example: (for vacation problem) entertainment, facilities, travel cost, accommodation cost

Completeness: It is important to ensure that all of the importantcriteria are included.

Redundancy: In principle, criteria that have been judgedrelatively unimportant or to be duplicates should be removed at a very early stage.

Operationality: It is important that each alternative can be judgedagainst each criterion.

Important terms

Weights These estimates relative importanceof criteria.

Each attribute is given certain points on 0-10 or 0-100 rating scale by a team of experts or decision makers. Example:

criteria scale

weight4 2 6 8

rating

Entertainment Facilities Travel cost Accomodation

10 very good -1 none 10 very good -1 none 10 low-1 very high 10 low-1 very high

Important terms

Decision makers These are experts who areassigned with the task of weighting each attribute.

There can be n number of decision makers. Example:

criteria

rating scaleRon2 3

Entertainment Facilities Travel cost AccomodationHarry

10 very good -1 none 10 very good -1 none 10 low-1 very high 10 low-1 very highAttributes weights= = =4 =2

Criteriaentertainmen t Facilities

Decision makers Hermoine6 1 4 2

Important terms

Decision matrix A table that is used to objectively

make decision about making selection from a range of options.Decision maker rates each attribute of each alternative Example: for alternate 1 ( hogwarts)Criteria Decision makers Attributes weights = = = =

Harryentertainmen t Facilities Travel cost Acc. Cost 10 7 5 9

Ron8 8 6 5

Hermoine9 6 7 7

=9 =7 =6 =7

Similarly

for alternate 2 ( hogsmeade)Criteria Decision makers Harry Ron 6 9 Hermoine 9 4 = = =8 =7 9 8 Attributes weights

entertainmen t Facilities

Travel costAcc. Cost

75

107

106

==

=9=6

for alternate 3 ( azkaban)Criteria entertainmen t Decision makers Harry 9 Ron 4 Hermoine 8 = =7 Attributes weights

FacilitiesTravel cost Acc. Cost

76 7

95 6

87 5

== =

=8=6 =6

Decision matrixCriteria entertainmen t Facilities Travel cost Acc. Cost Hogwarts 9 7 6 7 hogsmeade Azkaban 8 7 9 6 7 8 6 6

Hogwarts (Table 1)

Hogsmeade (Table 2)

Azkaban (Table 3)

TOPSISTechnique for Order Preference by Similarity to Ideal SolutionIn this method two artificial alternatives are hypothesized:

Ideal alternative: One which has the best attributes values (i.e. max. benefit attributes and min. cost attributes) Negative ideal alternative: One which has the worst attribute values. (i.e. min. benefit attributes and max. cost attributes)

TOPSIS selects the alternative that is the closest to the ideal solution and farthest from negative ideal solution.

Steps involved in TOPSIS

Step 1 standardize the decision matrix.

This step transforms various attribute dimensions into non-dimensional attributes, which allows comparisons across criteria. For standardizing, each column of decision matrix, is divided by root of sum of square of respective Criteria Hogwarts Hogsmeade Azkaban columns.entertainmen t Facilities Travel cost Acc. Cost 9 7 6 7 8 7 9 6 7= 8= 6= 6= = 13.93 =12.73 =12.37 = 11.00

DECISION MATRIX







Standardized decision matrix.

Criteria

Hogwarts

Hogsmead e

Azkaban

Entertainmen tFacilities Travel cost Acc. Cost Criteria Entertainmen t Facilities Travel cost

9 / 13.93

Hogwarts 0.65

Hogsmead e

Azkaban


Criteria

Hogwarts

Hogsmead e

Azkaban


9 / 13.93

8 / 13.93

Hogwarts 0.65

Hogsmead e 0.57

Azkaban


Criteria

Hogwarts

Hogsmead e

Azkaban


9 / 13.93

8 / 13.93

7 / 13.93

Hogwarts 0.65

Hogsmead e 0.57

Azkaban 0.50

Standardized decision matrix.Similarly.Criteria Entertainment Facilities Travel cost Acc. Cost Hogwarts 0.65 0.55 0.49 0.64 Hogsmeade 0.57 0.55 0.73 0.55 Azkaban 0.50 0.63 0.49 0.55

Steps involved in TOPSIS Step 2 rating.Criteria Entertainment X Facilities Travel cost Acc. Cost Hogwarts 0.65 0.55 0.49 0.64 Hogsmeade 0.57 0.55 0.73 0.55 Azkaban 0.50 0.63 0.49 0.55

Construct weighted standardized decision matrix by multiplying attributes weight to each

Attributes weights Criteria Entertainmen t Facilities Hogwarts Hogsmead e Azkaban

Standardized decision matrix

2.6

Weighted Standardized decision matrix

Travel cost

Steps involved in TOPSIS Step 2 rating.Criteria Entertainment X Facilities Travel cost Acc. Cost Hogwarts 0.65 0.55 0.49 0.64 Hogsmeade 0.57 0.55 0.73 0.55 Azkaban 0.50 0.63 0.49 0.55

Construct weighted standardized decision matrix by multiplying attributes weight to each



2.6

2.28


Travel cost

Steps involved in TOPSIS Step 2 matrix rating. construct weighted standardized decision by multiplying attributes weight to eachCriteria Entertainment Facilities X Travel cost Acc. Cost Hogwarts 0.65 0.55 0.49 0.64 Hogsmeade 0.57 0.55 0.73 0.55 Azkaban 0.50 0.63 0.49 0.55



2.6 1.1

2.28


Travel cost

Steps involved in TOPSIS Step 2 matrix rating. construct weighted standardized decision by multiplying attributes weight to each

Similarly.Criteria Hogwarts Hogsmead e Azkaban

Entertainmen tFacilities Travel cost

2.61.1 2.94

2.281.1 4.38

21.26 2.94

Acc. Cost

5.12

4.4

4.4


Steps involved in TOPSIS Step 3 Determine ideal solution and negative idealsolution.A set of maximum values for each criteria is Ideal solution. Criteria Hogwarts Max. Entertainmen 2.6 t Facilities Travel cost Acc. Cost 1.1 Max. 2.94 5.12 Hogsmead e 2.28 Max. 1.1 4.4 Azkaban

Max. 21.26 2.94 4.4

4.38

2.6 1.26 4.38 5.12

Ideal solution = {2.6, 1.26, 4.38, 5.12}

Steps involved in TOPSIS Step 3 Determine ideal solution and negative idealsolution.A set of minimum values for each criteria is Negative Ideal solution. Criteria Hogwarts Hogsmead Azkaban e Min. Entertainmen 2.6 2.28 2 Min. t Min. Facilities 1.1 1.1 1.26 Min. Travel cost 2.94 4.38 2.94

2.0 1.1 2.94 4.4

Acc. Cost

5.12

4.4

4.4

Negative Ideal solution = {2.6, 1.26, 2.94, 4.4}

Steps involved in TOPSIS Step 4 Determine separation from ideal solution.CriteriaEntertainment Facilities Travel cost Acc. Cost Criteria Entertainment Facilities Travel cost Acc. Cost

Si*

Hogwarts(2.6-2.6)2 (1.1-1.26) 2 (2.94-2.94) 2 (5.12-4.4) 2 Hogwarts 0.0 0.02 0.0 0.51

Hogsmeade(2.28-2.6) 2 (1.1-1.26) 2 (4.38-2.94) 2 (4.4-4.4) 2 Hogsmeade 0.10 0.02 2.07 0.0

Azkaban(2.0-2.6) 2 (1.26-1.26) 2 (2.94-2.94) 2 (4.4-4.4) 2 Azkaban 0.36 0.0 0.0 0.0

S* =

= = = 1/2 (.1+.02+2.07+0)1/2 (0.+0.02+0+0.51) (0.36+.0+0+0)1/2 0.74 1.48 0.6

Steps involved in TOPSIS Step 5 Determine separation fromsolution.Criteria Hogwarts (2.6-2.0)2 (1.1-1.1) 2 (2.94-4.38) 2 (5.12-5.12) 2 Hogwarts 0.36 0.0 Entertainment Facilities Travel cost Acc. Cost Criteria Entertainment Facilities

negative idealAzkaban (2.0-2.0) 2 (1.26-1.1) 2 (2.94-4.38) 2 (4.4-5.12) 2 Azkaban 0.0 0.02

Hogsmeade (2.28-2.0) 2 (1.1-1.1) 2 (4.38-4.38) 2 (4.4-5.12) 2 Hogsmeade 0.07 0.0

Travel costAcc. Cost

2.070.0

0.00.51

2.070.51 =

Si

= = (0.36+0+2+0)1/2 (.07+0+0+.51)1/2 (0+.02+2+.51)1/2

1.56

0.773

1.618

Steps involved in TOPSIS Step 6 Determine relative closeness to ideal solution.Criteria Si* Si Si*+Si Hogwarts 0.74 1.56 2.3 1.56/2.3 0.68 Hogsmeade Azkaban 1.48 0.773 2.253 0.77/2.25 0.343 0.6 1.618 2.218 1.62/2.21 Max. 0.729

Si /(Si*+Si )

BEST

TOPSIS for supplier selection problem.Consider 3 suppliers S1 S2 S3 3 suppliers are evaluated against 4 COST ATTRIBUTE attributes Special factor (Q1) BENEFIT On time delivery (Q2) ATTRIBUTES Performance history (Q3) Technical capability (Q4)

TOPSIS for supplier selection problem.There are 4 decision makers D1 D2 D3 D4 to express their preferences and ratings to select the best supplier.

TOPSIS for supplier selection problem.Step 1 finding ATTRIBUTE WEIGHTS.Attributes AVERAGE 1 Q AVERAGE Q AVERAGE 2 AVERAGE Q3 Q4

rating given to each attribute by each decision maker is shown in table.D1 D2 D3 D4 W H(.375) VH(.425 ) L(.175) VH(.425 ) M(.275) VL(.125 ) VL(.125 ) L(.175) ML(.225 ) VVL(.05 ) VVL(.05 ) M(.275) VL(.125) ML(.225) MH(.325 ) ML(.225) .25 .21 .17 .28

Normalized W

.25/.91 = 0.275 .21/.91 = 0.230 .17/.91 = 0.187 .28/.91 = 0.308

scale of attribute weightsTotalATTRIBUTE SCALE VVL WEIGHT .05 VL .125 L .175 ML .225 M .275 MH .325

0.9 1 H.375

1.00VH .425 VVH .475

TOPSIS for supplier selection problem.Step 1 finding ATTRIBUTE WEIGHTS.Attributes Q1 Q2 Q3 Q4

rating given to each attribute by each decision maker is shown in table.D1 D2 D3 D4 W H(.375) VH(.425 ) L(.175) VH(.425 ) M(.275) VL(.125 ) VL(.125 ) L(.175) ML(.225 ) VVL(.05 ) VVL(.05 ) M(.275) VL(.125) ML(.225) MH(.325 ) ML(.225) .25 .21 .17 .28

Normalized W

.25/.91 = 0.275 .21/.91 = 0.230 .17/.91 = 0.187 .28/.91 = 0.308

scale of attribute weightsTotalATTRIBUTE SCALE VVL WEIGHT .05 VL .125 L .175 ML .225 M .275 MH .325

0.9 1 H.375

1.00VH .425 VVH .475


Step 2 finding ATTRIBUTE RATINGS.Rating given to each supplier by each decision maker for attribute Q1 .D1 D2 D3 D4 G1 .03 .05 .03 .05 .03 .05 .03 .05 .03 .05

Suppliers AVERAGE 1 S S AVERAGE 2

S AVERAGE 3

.01

.01

.01

.01

.01

SuppliersAVERAGE 1 S S AVERAGE 2 S AVERAGE 3

Rating given to each supplier by each decision maker for attribute Q2 .D1 D2 D3 D4 G2.95 .98 .85 .95 .98 .85 .95 .98 .85 .95 .98 .85 .95 .98 .85


Step 2 finding ATTRIBUTE RATINGS.G(9) MP(3) F(5) P(1) MP(3) MP(3) MP&F(4) F(5) 4 3.75 4.75

rating given to each supplier by each decision maker for attribute Q3 . Suppliers D1 D2 D3 D4 G3AVERAGE 1 S S AVERAGE 2 AVERAGE S3 AVERAGE 1 S S AVERAGE 2 MP&F(4 MP&F(4 ) ) F(5) MP&F(4

rating given to each supplier by each decision maker for attribute ) Suppliers D1 D2 D3 D4 G3 Q4 .G(9) MP(3) G(9) MP(3) MP&F(4 ) G(9) P(1) F(5) MP&G(6 ) P RATINGS 1 MP(3) F(5) 4 4.25

AVERAGE S3

MP&G(6 8.5 ) ATTRIBUTE SCALE MP 3 F 5 MG 7 G 9

scale of attribute ratings

TOPSIS for supplier selection problem.Attributes Suppliers S1 S2 S3 Q1 .03 .05 .01 Q2 .95 .98 .85 Q3 4 3.75 4.75 Q4 4 4.25 8.5

Step 3 construct DECISION TABLE.

Q1

Q3

Q2

Q4

TOPSIS for supplier selection problem.DECISION TABLE

Step 4 STANDARDIZE DECISIONTABLE.Attributes Q1 .03 .05 .01 Q2 .95 .98 .85 Q3 4 3.75 4.75 Q4 4 4.25 8.5

Supplier s S1 S2 S3

(.03+.05+.01 (.95+.98+.85 (4+3.75+4.75 (4+4.25+8.5 ) ) ) )= 0.059 = 1.608 = 7.254 = 10.31



Supplier s S1 S2 S3

(.03+.05+.01 (.95+.98+.85 (4+3.75+4.75 (4+4.25+8.5 ) ) ) )= 0.059 Supplier s S1 S2 S3 STANDARD DECISION TABLE Q1 .03/.059 = .508 = 1.608 Attributes= 7.254 Q2 Q3 = 10.31 Q4



Supplier s S1 S2 S3

(.03+.05+.01 (.95+.98+.85 (4+3.75+4.75 (4+4.25+8.5 ) ) ) )= 0.059 Supplier s S1 S2 S3 Q1 .03/.059 = .508 .05/.059 = .845 STANDARD DECISION TABLE = 1.608 Attributes= 7.254 Q2 Q3 = 10.31 Q4



Supplier s S1 S2 S3

(.03+.05+.01 (.95+.98+.85 (4+3.75+4.75 (4+4.25+8.5 ) ) ) )= 0.059 Supplier s S1 S2 S3 Q1 .03/.059 = .508 .05/.059 = .845 STANDARD DECISION TABLE = 1.608 Attributes= 7.254 Q2 .95/1.608= .591 Q3 = 10.31 Q4



Supplier s S1 S2 S3

(.03+.05+.01 (.95+.98+.85 (4+3.75+4.75 (4+4.25+8.5 ) ) ) )= 0.059 Supplier s S1 S2 S3 Q1 .03/.059 = .508 .05/.059 = .845 = 1.608 Attributes= 7.254 Q2 .95/1.608= .591 .98/1.608= .609 STANDARD DECISION TABLE Q3 = 10.31 Q4



Supplier s S1 S2 S3

(.03+.05+.01 (.95+.98+.85 (4+3.75+4.75 (4+4.25+8.5 ) ) ) )= 0.059 Supplier s S1 S2 Q1 .03/.059 = .508 .05/.059 = .845 = 1.608 Attributes= 7.254 Q2 .95/1.608= .591 Q3 4/7.254= .551 = 10.31 Q4 4/10.31= .388 4.25/10.31= .412

.98/1.608= .609 3.75/7.254= .517 STANDARD DECISION TABLE

TOPSIS for supplier selection problem.AttributesSupplier s S1 S2 S3 Q1 .508 .845 .169 Q2 .591 .609 .529 Q3 .551 .517 .655

Step 4 STANDARD DECISION TABLE.Q4 .388 .412 .824


Step 5 WEIGHTED STANDARD DECISION TABLE.

Multiplying attribute weights as obtained in step-1, with respective attribute values in standard decision matrix. Attributes Supplier s S1 S2 S3 ATTRIBUTES Q1 Q2 Q3 Q4 WEIGHT S 0.275 0.230 0.187 0.308 Q1 .508X.275 Q2 Q3 Q4

Standard decision table as obtained from Step-4

attribute weights as obtained from Step-1



Multiplying attribute weights as obtained in step-1, with respective attribute values in standard decision matrix. Attributes Supplier s S1 S2 S3 ATTRIBUTES Q1 Q2 Q3 Q4 WEIGHT S 0.275 0.230 0.187 0.308 Q1 .508X.275 .845X.275 Q2 Q3 Q4





Multiplying attribute weights as obtained in step-1, with respective attribute values in standard decision matrix. Attributes Supplier s S1 S2 S3 ATTRIBUTES Q1 Q2 Q3 Q4 WEIGHT S 0.275 0.230 0.187 0.308 Q1 .508X.275 .845X.275 Q2 .591X.230 Q3 Q4





Multiplying attribute weights as obtained in step-1, with respective attribute values in standard decision matrix. Attributes Supplier s S1 S2 S3 ATTRIBUTES Q1 Q2 Q3 Q4 WEIGHT S 0.275 0.230 0.187 0.308 Q1 .508X.275 .845X.275 Q2 .591X.230 Q3 .551X.187 Q4





Multiplying attribute weights as obtained in step-1, with respective attribute values in standard decision matrix. Attributes Supplier s S1 S2 S3 Q1 .508X.275 .845X.275 .169X.275 Q2 .591X.230 .609X.230 .529X.230 Q3 .551X.187 .517X.187 .655X.187 Q4 .388X.308 .412X.308 .824X.308 ATTRIBUTES Q1 Q2 Q3 Q4 WEIGHT S 0.275 0.230 0.187 0.308



TOPSIS for supplier selection problem.AttributesSupplier s S1 S2 S3 Q1 0.14 0.232 0.046 Q2 0.135 0.14 0.121 Q3 0.103 0.097 0.122


Q4 0.119 0.126 0.253

TOPSIS for supplier selection problem.Step 6 SOLUTION. Construct the IDEAL SOLUTION & NEGATIVE IDEAL

IDEAL SOLTION Minimum value of Cost Attributes are Ideal. Maximum value of Benefit Attributes are Ideal. Cost attribute Supplier s S1 S2 S3 Q1 0.14 0.232 (min.) 0.046 Q2 0.135 (Max) 0.14 0.121 Benefit attributes Q3 0.103 0.097 (Max) 0.122 Q4 0.119 0.126 (Max) 0.253

Ideal solution = {0.046, 0.14, 0.122, 0.253}

TOPSIS for supplier selection problem.Step 6 SOLUTION. Construct the IDEAL SOLUTION & NEGATIVE IDEAL

NEGATIVE IDEAL SOLTION Maximum value of Cost Attributes are Negative Ideal. Minimum value of Benefit Attributes are Negative Ideal. Cost attribute Supplier s S1 S2 S3 Q1 0.14 (max.) 0.232 0.046 Q2 0.135 0.14 (min.) 0.121 Benefit attributes Q3 0.103 (min.) 0.097 0.122 Q4 (min.) 0.119 0.126 0.253

Negative Ideal solution = {0.232, 0.121, 0.097 0.119}

TOPSIS for supplier selection problem.Step 7 Construct the SEPARATION from Ideal solution & negative ideal solution.

SEPARATION from Ideal solution Si*Ideal solution = {0.046, 0.14, 0.122, 0.253}Cost attribute Supplier s S1 Q1 (0.14 - .046)2 = 0.009 0.232 0.046 Q2 (0.135 0.14)2 = 0.000 0.14 0.121 Benefit attributes Q3 (0.103 0.122)2 = 0.0004 0.097 0.122 Q4 (0.119 0.253)2 = 0.018 0.126 0.253

S2 S3

S1* = (0.009+0.00+0.0004+0.018)1/2 = 0.166


SEPARATION from Ideal solution Si*Ideal solution = {0.046, 0.14, 0.122, 0.253}Cost attribute Supplier s S1 Q1 (0.14 - .046)2 = 0.009 (0.232 - .046)2 = 0.035 Q2 (0.135 0.14)2 = 0.000 (0.14 - 0.14)2 = 0.000 Benefit attributes Q3 (0.103 0.122)2 = 0.0004 (0.097 0.122)2 = 0.0006 Q4 (0.119 0.253)2 = 0.018 (0.126 0.253)2 = 0.016 0.253

S2

S 0.046 0.121 0.122 S1*3 = (0.009+0.00+0.0004+0.018)1/2 = 0.166 S2* = (0.035+0.00+0.0006_0.016)1/2 = 0.227


SEPARATION from Ideal solution Si*Ideal solution = {0.046, 0.14, 0.122, 0.253}Cost attribute Supplier s S1 Q1 (0.14 - .046)2 = 0.009 (0.232 - .046)2 = 0.0352

Benefit attributes Q2 (0.135 0.14)2 = 0.000 (0.14 - 0.14)2 = 0.0002

Q3 (0.103 0.122)2 = 0.0004 (0.097 0.122)2 = 0.0006

Q4 (0.119 0.253)2 = 0.018 (0.126 0.253)2 = 0.016 (0.253 0.253)2 = 0.000

S2

S (0.046 - .046) (0.121- 0.14) (0.122 S1*3 = (0.009+0.00+0.0004+0.018)1/2 = 0.166 2 = 0.000 = 0.0004 0.122) = S2* = (0.035+0.00+0.0006_0.016)1/2 = 0.227 0.000 S3* = (0.00+0.0004+0.00+0.0000)1/2 = 0.02


SEPARATION from Negative ideal solution Si Negative Ideal solution = {0.232, 0.121, 0.0970.119}Supplier s S1 S2 S3 Cost attribute Q1 (0.14 - .232)2 = 0.008 (0.232 - .232)2 = 0.000 (0.046 - .232)2 = 0.035 Q2 (0.135 - .121)2 = 0.0002 (0.14 - .121)2 = 0.0004 (0.121 - .121)2 = 0.000 Benefit attributes Q3 (0.103 - .097)2 = 0.0000 (0.097 - .097)2 = 0.0000 (0.122 - .097)2 = 0.0006 Q4 (0.119 - .119)2 = 0.000 (0.126 - .119)2 = 0.0001 (0.253 - .119)2 = 0.0179

S1 = (0.008+0.0002+0.000+0.000)1/2 = 0.09 S2 = (0.00+0.0004+0.000+0.0001)1/2 = 0.022 S3 = (0.035+0.00+0.0006+0.0179)1/2 = 0.231

TOPSIS for supplier selection problem.Step 8 solution. Calculate the RELATIVE CLOSENESS to Ideal

CLOSENESS to ideal solution Ci* = Si /(Si* +Si )Criteria Si* Si Si*+Si S1 0.166 0.09 0.256 0.09/0.256 0.351 S2 0.227 0.022 0.249 0.022/0.249 0.088 S3 0.02 0.231 0.251 0.231/0.251 0.920

Si /(Si*+Si )

C1* = 0.351 C2* = 0.088 C3* = 0.920

C 3* > C 1* > C 2*


Step 8 RANK THE ORDER of suppliers based on STEP 8 C 3* > C 1* > C 2*

Supplier3 > Supplier1 > Supplier2

topsis (11ID60R20)

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