1 Dr. Shahram Yazdani Multi ‑ Criteria Decision Making.

1

Dr. Shahram Yazdani

Multi‑Criteria Decision Making

2Dr Shahram Yazdani

The Nature of Decision-Making in Healthcare

System Process is interactive - involves group of persons

Multiple criteria (objectives/attributes) Interaction among criteria/objectives Need for a standard process - need for

consistency and continuity Time dependent: both short- and long-term

3Dr Shahram Yazdani

Multi‑Criteria Decision Making

Ben Franklin over 200 years ago recognized the presence of multiple attributes in everyday decisions and suggested a workable solution

Major development in theory and practice since 1970

4Dr Shahram Yazdani

OptimizingOptimizing

SatisficingSatisficing

Elimination-by-aspectsElimination-by-aspects

IncrementalismIncrementalism

Mixed scanningMixed scanning

Analytic Hierarchy ProcessAnalytic Hierarchy Process

Decision-Making Decision-Making StrategiesStrategies

5Dr Shahram Yazdani

Select the alternative that gives the best Select the alternative that gives the best overall valueoverall value

Identify criteria to judge alternativesIdentify criteria to judge alternatives Can be expressed in mathematical terms and Can be expressed in mathematical terms and

implemented using computer programsimplemented using computer programs Difficult to solve when model involves Difficult to solve when model involves

qualitative criteriaqualitative criteria Optimization of “Utility Super Function”

Decision-Making Strategies : Decision-Making Strategies : OptimizationOptimization

6Dr Shahram Yazdani

Recognizes that “utility super functions” are difficult to formulate and In most cases one doesn’t want optimality

Understand decision process (flow) (Sequence in which Sequence in which alternatives are identified and considered; usually governed alternatives are identified and considered; usually governed by by heuristics)heuristics)

Decision maker is therefore part of the multi-objective problem

Select the first alternative that is good enough with respect Select the first alternative that is good enough with respect to some minimal criteriato some minimal criteria

Cutoff level of constraintsCutoff level of constraints Simon: satisficing or finding solutions that are good

enough e.g. Goal Programming Keen: viewed requirement of assigning weights or priorities

to be problematic. Noninferior sets.

Decision-Making Strategies : Decision-Making Strategies : SatisficingSatisficing

7Dr Shahram Yazdani

Elimination of all alternatives that fail with respect Elimination of all alternatives that fail with respect to one aspect, then consider another aspect …to one aspect, then consider another aspect …

An aspect is like a constraint involving one or more An aspect is like a constraint involving one or more criteriacriteria

Order of aspects can strongly influence resultsOrder of aspects can strongly influence results

An alternative that superior in many aspects may An alternative that superior in many aspects may be eliminated be eliminated

Decision-Making Strategies : Decision-Making Strategies : Elimination-by-AspectsElimination-by-Aspects

8Dr Shahram Yazdani

Compare alternative courses of action to the Compare alternative courses of action to the current course of actioncurrent course of action

Look for alternatives that can overcome Look for alternatives that can overcome shortcomings of the current course of actionshortcomings of the current course of action

A decision that results in incremental A decision that results in incremental improvementimprovement

Decision Making Strategies: Decision Making Strategies: IncrementalismIncrementalism

11Dr Shahram Yazdani

Dominance ruleDominance rule Select the alternative that is better than other alternative(s) on at Select the alternative that is better than other alternative(s) on at

least one attribute and not worse on other attributes least one attribute and not worse on other attributes

Lexicographic ruleLexicographic rule Starts with the most important attribute and selects the attribute Starts with the most important attribute and selects the attribute

that ranks highest on that attributethat ranks highest on that attribute If two or more are tied, proceed to the next important attributeIf two or more are tied, proceed to the next important attribute

Maximizing number of attributes with greater Maximizing number of attributes with greater attractiveness ruleattractiveness rule Classify each alternative as Classify each alternative as better, equal or worse better, equal or worse on each on each

attributeattribute Select the alternative with the greater number of favorable Select the alternative with the greater number of favorable

attributesattributes

Decision Making : Decision Making : Other Other StrategiesStrategies


Conjunctive decision makingConjunctive decision making Compare all attributes of one alternative against all criteriaCompare all attributes of one alternative against all criteria

Reject the alternatives that do not meet the criteriaReject the alternatives that do not meet the criteria

Additive linear ruleAdditive linear rule Start with a set of predetermined weights of each alternative on each Start with a set of predetermined weights of each alternative on each

attribute (A)attribute (A)

Allocate weights against the attributes (B)Allocate weights against the attributes (B)

Multiply (A) by (B) to determine the score for each alternativeMultiply (A) by (B) to determine the score for each alternative

Select the alternative having the highest score Select the alternative having the highest score

Decision Making Strategies: Decision Making Strategies: Other StrategiesOther Strategies


Political Approaches

Actions and decisions result from bargaining among players

To predict decision, find out: who the players are what are the players’ interests or stands? what are the players’ relative influence? How does the combined dynamics of the above

affect the decisions


Anarchic Theory of Decision-Making Decision-making in organizations are random and

disjointed e.g. Lindblom: “muddling-through” concept of

decision theory; avoid comprehensive analysis and concentrate on marginal gains

An organization is a collection of: choices looking for problems issues and feelings waiting for decision situations solutions looking for issues they apply to; or decision makers looking for work so-called organized anarchy.

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Dr. Shahram Yazdani

Multiple Attribute Decision Making


Nature ofalternatives

Nature ofCriteria/objective

Concordance analysisAHPRegime MethodEvamix MethodELECTRE

continuous

discrete

quantitative

Qualitative/mixed Multi-attribute utility theory

Weighted summationIdeal point method

Linear programmingGoal programming


Generic process for MCDM

Identifyobjectives

Weight Criteria/attributes

Rank alternatives

Choose alternative

Identify alternatives

Develop Criteria/attributes


MADM MatrixX1 X2 X3 Xn

A1

A2

A3

Am

Alternatives

Attributes


Give Numerical Values to Attributes of Each Alternative Consider simple measures in simple

quantitative attributes Consider decision tree analysis in complex

quantitative attributes Consider pair wise comparison in qualitative

attributes


MADM MatrixX1 X2 X3 Xn

A1 v11 v12 v13 v1n

A2 v21 v22 v23 v2n

A3 v31 v32 v33 v3n

Am vm1 vm2 vm3 vmn

Alternatives

Attributes

vij is the specific value of attribute Xj for alternative Ai


Standardizing the attribute values1. Normalization

2. Linear

3. Fuzzy

jrij =

vij – min vij

maxvij – min vijj j

jrij =

max vij – vij

maxvij – min vijj j

For positive attributesWhere more is better

For negative attributesWhere less is better


Standardized attributes

X1 X2 X3 Xn

A1 r11 r12 r13 r1n

A2 r21 r22 r23 r2n

A3 r31 r32 r33 r3n

Am rm1 rm2 rm3 rmn

Alternatives

Attributes

rij is the standardized value of attribute Xj for alternative Ai


Weight of each attribute

X1 X2 X3 Xn

A1 r11 r12 r13 r1n

A2 r21 r22 r23 r2n

A3 r31 r32 r33 r3n

Am rm1 rm2 rm3 rmn

Alternatives

W1 W2 W3 Wn


Weighting methods for attributes

Fixed Point Scoring Paired Comparisons Judgment Analysis


Fixed Point Scoring

Attribute 1 Attribute 2 Attribute 3

Attribute n

Give to each attribute a weight (<1) that sum up in 1

W1

W2

W3

Wn

1


Paired Comparisons of Attributes Importance


Paired Comparisons

X4X3X2X1

X4

X3

X2

X1

attributes

n×n AHP matrix


Paired Comparisons

EquallyImportant

SlightlyMore

Important

ModeratelyMore

Important

VeryMore

Important

0.1 0.2 0.5 1 2 5 10

Bipolar Scale for positive attributes

SlightlyLess

Important

ModeratelyLess

Important

VeryLess

Important


Paired Comparisons

1 5 5 7

3

9

1

1

31

X4X3X2X1

X4

X3

X2

X1

attributes

Perform Pairwise Comparison


Paired Comparisons

1 5 5 7

3

9

10.110.330.14

1

310.2

0.330.2

X4X3X2X1

X4

X3

X2

X1

attributes

Perform Pairwise ComparisonUsing reciprocals


Paired Comparisons

1 5 5 7

3

9

10.110.330.14

1

310.2

0.330.2

X4X3X2X1

X4

X3

X2

X1

attributes

Totals 1.54 6.66 9.11 20

Sum the columns


Paired Comparisons

0.651

0.755

0.555

0.357

0.153

0.459

0.051

0.010.11

0.050.33

0.090.14

0.111

0.333

0.151

0.130.2

0.050.33

0.130.2

X4X3X2X1

X4

X3

X2

X1

attributes

Totals1.54

16.66

19.11

1201

Normalize the values in each column


Paired Comparisons

0.651

0.755

0.555

0.357

0.153

0.459

0.051

0.010.11

0.050.33

0.090.14

0.111

0.333

0.151

0.130.2

0.050.33

0.130.2

X4X3X2X1

X4

X3

X2

X1

attributes Sum

2.3

0.76

0.74

0.2

Totals 1.54 6.66 9.11 20

Calculate sum of normalized values for Each row


Paired Comparisons

0.651

0.755

0.555

0.357

0.153

0.459

0.051

0.010.11

0.050.33

0.090.14

0.111

0.333

0.151

0.130.2

0.050.33

0.130.2

X4X3X2X1

X4

X3

X2

X1

attributes Sum

2.3

0.76

0.74

0.2

4.00Totals 1.54 6.66 9.11 20

Calculate the Average (weight) for Each Row

Average(W)

0.575

0.19

0.185

0.05

1.00


Analytical hierarchic process



Information is decomposed into a hierarchy of alternatives and criteria

Information is then synthesized to determine relative ranking of alternatives

Both qualitative and quantitative information can be compared using informed judgements to derive weights and priorities



Classifying attributes in a hierarchic model No end branch should contain more than 10

(preferably 8) attribute Begin cross sectional weighting at root side of

three and progress to the end branch side of three

At each level if the number of items are less than 6 (preferably 4) use fixed point scoring otherwise use paired comparison through AHP matrix

Combine cross sectional weights into hierarchical weights which must sum up to 1 for end branches


Hierarchic Organization of Attributes


End Branch Attributes


w1 w2 w3

w11 w12 w13 w14 w31 w32

w321 w322 w323w141 w142 w143w111 w112

Determine simple weight of attributes


w1 w2 w3

w11 w12 w13 w14 w31 w32

w321 w322 w323w141 w142 w143w111 w112

1

1

1

Determine simple weight of attributes


w1 w2 w3

w11 w12 w13 w14 w31 w32

w321 w322 w323w141 w142 w143w111 w112

Wf1

Determine final weight of attributes


w1 w2 w3

w11 w12 w13 w14 w31 w32

w321 w322 w323w141 w142 w143w111 w112

Wf4



w1 w2 w3

w11 w12 w13 w14 w31 w32

w321 w322 w323w141 w142 w143w111 w112

Wf1 Wf2

Wf3

Wf5

Wf4

Wf6

Wf8

Wf7 Wf9 Wf10 Wf11

Wfi = 1i=111



Application areas strategic planning resource allocation source selection, program selection business policy etc., etc., etc..

AHP software (ExpertChoice) computations sensitivity analysis graphs, tables

Group AHP



Weight of each attribute

X1 X2 X3 Xn

A1 r11 r12 r13 r1n

A2 r21 r22 r23 r2n

A3 r31 r32 r33 r3n

Am rm1 rm2 rm3 rmn

Alternatives

W1 W2 W3 Wn


Weighted value of attributes for alternatives

X1 X2 X3 Xn

A1 R11 R12 R13 R1n

A2 R21 R22 R23 R2n

A3 R31 R32 R33 R3n

Am Rm1 Rm2 Rm3 rmn

Alternatives

Attributes

Rij = rij × Wj


Scoring Alternatives: Weighted summation

X1 X2 X3 Xn Score

A1 R11 R12 R13 R1n S1

A2 R21 R22 R23 R2n S2

A3 R31 R32 R33 R3n S3

Am Rm1 Rm2 Rm3 rmn Sm

Alt

erna

tive

sAttributes

Si = ΣRijJ=1 n

Si = Σrij×wj

J=1 n

58

Dr. Shahram Yazdani

Judgement Analysis through Virtual Portfolios


Judgement analysis through virtual portfolios Choosing the right people

Defining objectives and options Determining ranking attributes Defining ranking attributes Scaling ranking attributes Constructing random virtual portfolios Ranking or scoring virtual portfolios by panel performing stepwise regression analysis Finding independent attributes and their weight

(regression coefficient) Formulating ranking equation Assessing the validity and reliability of equation

on a separate set of portfolios


Attribute 1

Attribute 2

Attribute 3

Attribute 4

Attribute 5

Attribute 6

Attribute 7

Level 1 Level 2 Level 3 Level 4 Level 5

S11 S12 S13 S14 S15

S21 S22 S23 S24 S25

S31 S32 S33 S34 S35

S41 S42 S43 S44 S45

S51 S52 S53 S54 S55

S61 S62 S63 S64 S65

S71 S72 S73 S74 S75


Attribute 1

Attribute 2

Attribute 3

Attribute 4

Attribute 5

Attribute 6

Attribute 7

Level 1 Level 2 Level 3 Level 4 Level 5

S11 S12 S13 S14 S15

S21 S22 S23 S24 S25

S31 S32 S33 S34 S35

S41 S42 S43 S44 S45

S51 S52 S53 S54 S55

S61 S62 S63 S64 S65

S71 S72 S73 S74 S75

S11S25S32S54S61S74S74

Random Virtual Portfolio 1



Ranking of virtual portfolios

























5386127349


Perform Stepwise Regression Analysis

Portfolios Rank = iAi Where

Ai = ith Attribute

i = Regression Coefficient (weight) of ith Attribute

Results in the minimal set of independent attributes contributing in the judgment of stakeholders about the topic


Problem:

Diagnosis of malignant tumors of breast Positive Biopsy rate is 10%-31% for cancer Total cost of percutaneous large core biopsy

of a breast nodule is $1000 The total cost of excisional biopsy of a breast

lump is between $3000 and $4500


Alternatives

Magnetic Resonance Imaging Mammography Ultrasonography Positron Emission Tomography


Attributes Sensitivity (SE) Specificity (SP) Positive Predictive Value (PPV) Negative Predictive Value (NPV) Complexity of Interaction with Patients (CIP)

Includes time spent, degree of discomfort, Invasiveness

Complexity of Interaction with Doctors (CID) Includes Time spent, Level of necessary training

and experience, Complexity of protocol Cost (C)


SE SP PPV NPV CIP CID C

MRI 96 69 75 97 9 5 500

Mammography 89 45 57 83 2 2 75

Ultrasonography 48 94 65 90 6 9 200

PET 80 73 41 94 4 7 350


Thank You !

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1 Dr. Shahram Yazdani Multi ‑ Criteria Decision Making.

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