1_Teoria Sobre Processo Decisorio_partes 1 e 2

8/3/2019 1_Teoria Sobre Processo Decisorio_partes 1 e 2

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HIERARCHICAL DECISIONHIERARCHICAL DECISION--MAKINGMAKING

PROCESSESPROCESSES

B. Srdjevic, 2006.

Concepts and ImportanceParts One and Two


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PART ONE:Concepts, Importance, Difficulties, And Necessities Embedded InHierarchical Decision-Making Processes

PART TWO:Some Important Aspects Related To Hierarchical Decision-Making

Contents


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HIERARCHICAL HIERARCHICAL

MeansMeans

Structuring the decisionStructuring the decision--making processmaking process Identifying decision elements (DEs) and key playersIdentifying decision elements (DEs) and key players

decision makers (DMs)decision makers (DMs)

Defining decision lines: vertical and horizontalDefining decision lines: vertical and horizontal

The hierarchical arrangement has been found to be theThe hierarchical arrangement has been found to be the

best way for human beings to cope with complexity.best way for human beings to cope with complexity.

HIERARCHICAL DECISION-MAKING PROCESS


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DECISION DECISION--MAKING MAKING

MeansMeans

Understanding the problem in handUnderstanding the problem in hand Following selected consistent and coherent methodologyFollowing selected consistent and coherent methodology

eligible for evaluating DEseligible for evaluating DEs DMs being responsible in validating objectives, criteria andDMs being responsible in validating objectives, criteria and

alternatives (willingness, good attitude, best knowledgealternatives (willingness, good attitude, best knowledgeetc.)etc.)

Understanding that there will be consequences ofUnderstanding that there will be consequences ofdecisions madedecisions made



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PROCESS PROCESS

MeansMeans

Considering the spatial and temporal component of theConsidering the spatial and temporal component of theproblemproblem

Recognizing the process in selected methodology ofRecognizing the process in selected methodology ofevaluating DEs.evaluating DEs.

Necessity of feedNecessity of feed--back loops envisioned.back loops envisioned.



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Concepts, Importance, Difficulties, AndConcepts, Importance, Difficulties, AndNecessities Embedded In HierarchicalNecessities Embedded In HierarchicalDecisionDecision--Making ProcessesMaking Processes

Part IPart I


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Information Collection and Management

Modelling and Rational Decision Support

Visualization and the Human Interface

Group Decision-Making

Knowledge Capture and Representation

DSS Integration

Typical Stages In The Decision-Making Process

Overlaps and feedback are usual !Overlaps and feedback are usual !

Not necessarilyNot necessarilythat orderthat order


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Procedural StepsWithin The Decision Making Framework

typical in water resources plan/mnmt/cntrl typical in water resources plan/mnmt/cntrl:

1. Selection of an approach and creation of adoptable framework formulticriteria analysis (MCA) and evaluation of decisionelements.

2. Defining sustainability criteria and setting objectives, such as:(a) water availability/suitability criteria; (b) energy output/inputratios; (c) water requirements; (d) environmental costs; (e)economic viability with considerations of governmental and societalviewpoints; (f) net present values from governmental and

social viewpoints; and(g) local entities' acceptability.

3. Formulation of planning or/and management alternatives.

4. Integrating output from spatial analysis using GIS, resourceaccounting and economic valuation for multi-criteria evaluation.

No consensus jet which one is thebest or most suitable for all cases


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cont.

5. Decomposition of criteria set and other decision elements on ahierarchical basis.

6. Development of pay-off (decision) matrix.

7. Development of questionnaires for decision makers.

8. Administering the questionnaires including interviews with entitiesleaders and project officials.

9. Assigning weights to criteria.

10. Applying MCA (multicriteria analysis) and deriving decisions by usingselected decision-making tool(s).

Procedural StepsWithin The Decision Making Framework

e.g. sub-criteria, sub-sub-criteria,alternatives )


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Decision-Making Concepts & Methodologies

Perhaps the most common formal approach to making achoice among alternatives is to list the pros and cons of eachalternative.

A list of pros and cons can often be embedded in amemorandum such as:

Issue: (i.g. Evaluation of alternative scenarios)

Alternative 1Pros:Cons:

Alternative 2Pros:

Cons:


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Define pros and cons of alternatives Discuss the alternatives and their pros and cons Avoid misuse of numbers (cardinal, ordinal, ratios, intervalscardinal, ordinal, ratios, intervals )

Typical misusesTypical misuses

1. Not weighting the factors is commonly an error of omission and isoften fairly obvious.

2. A more serious error is the inappropriate addition of ranks. Thescores given as ordinal numbers represent ranks, but nothing morebut nothing more. It

is wrong to add these numbers because aany results are meaningless!ny results are meaningless!

Question: How one can identify such mistakes?Answer: By thinking about the meaning of the numbers.


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An example:

A scenario scoring a 1 on robustness is ranked better than a

scenario scoring a 2, but how much better?

Is the interval between scenarios ranked 1 and 2 the same asthe interval between scenarios ranked 6 and 7? NotNotnecessarilynecessarily.

The scenario ranked 1 might be 2 million R$ higher than thescenario ranked 2, while the interval between the 6 and 7scenarios might be only 50 thousand R$ (40x less).

The numbers ordinal in nature cannot be addedThe numbers ordinal in nature cannot be added !


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The misuse of numbers is one reason that numerical analysesare sometimes flawed.

But the misuse of numbers is not a reason to forego usingthem.

We just must be careful that a sound theoretical foundation

exists for whatever we do.


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RatioInterval

OrdinalNominal

(Each level has all of the meaning of the levels below plus additional meaning.)

Levels of Measurement


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Nominal numbers

These numbers are just numerical representations for names. Nominalnumbers are used for identification purposes only and imply nothing aboutthe ordering.

Example: Telephone numbers and personal ID numbers are nominal. Is

one is older or better than someone else because his telephone numberis higher? Obviously not.

Remark: People rarely make mistakes with nominal numbers. However,errors arising from the misuse of ordinal numbers are not so rare.


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Ordinal numbers

They imply an order or ranking among elements. The order may be eitherincreasing or decreasing depending on the application. A ranking implies anordering among elements but nothing more. It does not imply anythingabout the differences (or intervals) between items.

Example: If we know only that a professional football team finished insecond place at the end of the season, we do not know if the team wasone game behind the first place team or 15 games behind.

Remark: Care must be taken not to add or multiply ordinal data. Errorsarising from the addition of ordinal data are very common.


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Interval numbers

Interval scale data possesses the meaning of Nominal and Ordinal data,as well as having meaning about the intervals between objects.Corresponding intervals on different parts of an interval scale have thesame meaning.

Example: If we have interval level data then we can infer that the intervalbetween two objects with values of 20 and 5 (an interval of 15) isequivalent to the interval between two objects with values of 80 and 65.

Remark: Interval level data can be used in arithmetic operations such asaddition and multiplication. However, after adding interval level data, one

can not infer that a total of 100 is twice as good as a total of50. If onewere to allocate resources based on this inference, then the allocationwould be incorrect.


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Ratio numbers

Ratio level data (sometimes called ratio scale) have Nominal, Ordinal, andInterval properties, as well as the property of ratios. Corresponding ratioson different parts of a ratio scale have the same meaning.

Example: If we have ratio scale data, then the ratio between two objects

with values of 100 and 50 is equivalent to the ratio of two objects withvalues of 6 and 3.

Remark:A ratio scale is often defined as one having a true zero point.However, it is easier to think of a ratio scale as one for which equivalentratios are considered equal. Temperature measured on the Celsius scale is

not a ratio measure, since it would be wrong to infer that there is twice asmuch heat when the temperature is 40 degrees as when the temperature is20 degrees. (If the Kelvin scale is used instead, which has the ratioproperty, then such an inference would be correct.)


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Mathematical operations allowed

Nominal, Ordinal, Interval, Ratio succeeding scales have additionalmeaning and can be used in more arithmetic operations as summarizedbelow:

Addition/subtraction and multiplication/division require at least

interval level meaning.

An interval level number can be multiplied by a constant or aratio level number but cannot be multiplied by another intervallevel number.

There are no restrictions when using ratio level numbers.

A decision method that produces ratio scale numbers is considered theA decision method that produces ratio scale numbers is considered themost flexible and accuratemost flexible and accurate..


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Weights and Score Matrix

Typical Weights and Scores Matrix


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Usual Procedure

Typical Weights and Scores Matrix

Criteria are assigned weights using a scale such as 0 to 10 or 0 to 100.

Then each alternative is scored against each criterion.

The alternative scores for each criterion are then multiplied by the weightfor the criterion and summed to give a total score for each alternative

This score represents the overall preference for or performance of thealternative.

IfIf used carefully, weights and scores can be an effective methodology.


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Difficulties

There are, however, several practical difficulties:

When assigning weights, what do the numbers really mean?

On a scale of 0 to 100, what is an 80, or what is a 40?

When one give an 80 to one criterion and give a 40 to another, doeshe really mean that the 80 is twice as important as the 40? If theanswer is yes, then the weights possess the ratio scale property.

But how can one be consistent enough to insure this if he is dealing

with 20, 30 or 100 criteria? If he assigned an 80 to the first criterionand later assign a weight of 10 to the 95th criterion, can he rememberwhat he did earlier and does he really mean that the 95th criterion isonly one eighth as important as the first criterion?


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Channel capacity and short term memory

Experiments have proven that the human brain is limited in both itsshort-term memory capacity and its discrimination ability (channelcapacity) to about 7 things.

If a person has to choose from a range of 20 alternatives, he willgive inaccurate answers because the range exceeds the bandwidthof his channel for perception. In many cases, 7 alternatives are theapproximate limit of his channel capacity. -- James Martin


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Martins conclusion is based on the results of numerous psychologicalexperiments, including the well known study The Magical NumberSeven, Plus or Minus Two: Some Limits on Our Capacity for

Information Processing, Psychological Review, (V

ol. 63, No. 2, March1956), pp. 81-97, by G. A. Miller.

The distribution is a bell shaped curve with an average of 7. Somepeople can recall more than 7, some fewer. But only about 11% ofthe population can recall 9 things from their short term memory, still

fewer 10 things, and so on.


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Need for Hierarchical Structure

If we try to assign weights to 20, 30 or 100 columns, we are bound tobe many mistakes! We can cope with this complexity as we do withother complex situations - by arranging the criteria into groups, each

group having sub-groups, and so on.

If one try to recall a sequence of 9 or 11 digits as someone readsthem, he will probably find himself grouping (psychologists call thischunking) the digits into groups in an effort to overcome thelimitations of his own short-term memory.

Again, hierarchical arrangement has been found to be the best wayfor human beings to cope with complexity.


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Orders of Magnitude

Another problem arises when a weights and scores approachinvolves more than a handful of criteria (columns). Some of thecriteria might be orders of magnitude more important than others.

If one criterion is assigned a 0.02 on a scale of 0-10, and another isassigned a 9.0, do we really mean that one is 450 times more (less)important than another?

Our ability to accurately compare things that differ by orders ofmagnitude is not nearly as good as our ability to compare things thatdiffer by less than an order of magnitude.

A hierarchical groupinghierarchical grouping avoids this problem as well.


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Arbitrary assignment

Difficulty with the weights and scores methodology stems from theassignment of weights and scores in what often appears to be anarbitrary fashion.

How can we justify that a criterion (such as customer perception)

was given an 8? What does the 8 really mean? And why not a 7, ora 9?

Similarly, when scoring a particular alternative with respect to acriterion such as customer perception, we may refer to customerinterview studies and past experience and assign a 3. But what

does the 3 really mean?


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Words instead of numbers

Justification would be much easier if we use a less precise way ofexpressing judgments, such as words instead of numbers.

Suppose we use words instead of numbers. By intuition - words areoften easier to justify than numbers.

For example, if you say that, with respect to corporate image,alternative A is 3 times more preferable than alternative B, can youjustify why it is exactly 3? Why not 2.9, or 3.1? But if you said,instead, that A is moderately more preferable than B, this can bejustified with a variety of arguments, including, perhaps, some hard

data.


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But what can be done with the words?

Question: What to do with verbal judgment such as moderate?

Words have different meanings to different people. In fact, anyonecan put arbitrary numbers behind words in a computer program. Butwill the numbers accurately reflect the meaning the words had to

the individual or group making the judgments?

Even if the decision-maker specifies numerical equivalencies forwords, will he or a group of his colleagues consistently remember theassignments accurately enough to insure that the results reflect theiractual judgments?

Will errors due to the use of imprecise words be a problem? Againanswer is YES !

THEREFORE


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We have to introduce sophisticated approaches that recognizenecessity of dealing with rather weak than rigorous optimizationmethods, tolls and supporting (computerized) systems.

We have to accept the truth that there is no best solutionmethodology for all problems encountered.

We have to fund our decisions within correct theoretical framework.

We have to perform valid sensitivity analyses and verify decisionmade by monitoring and evaluating consequences incurred.

Quite often, we have to simultaneously handle individual judgments(subjectivity) of decision makers along with objectivity issues suchas technical (or economical) value of certain decision element withinrelated functional schema in the decision tree.

THEREFORE


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Some Important Aspects RelatedSome Important Aspects RelatedTo Hierarchical DecisionTo Hierarchical Decision--MakingMaking

Part IIPart II


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AspectsAspects

1.1. Individual and Group DecisionIndividual and Group Decision--Making (DMaking (D--M)M)

2.2. Participative DParticipative D--M modelsM models

3.3. DD--M with complete and incomplete informationM with complete and incomplete information

4.4. DD--M with certainty and uncertaintyM with certainty and uncertainty

5.5. DD--M classifications related to problem structureM classifications related to problem structure

6.6. Mathematics, modeling, models, tools, systemsMathematics, modeling, models, tools, systems(decision support)(decision support)


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Hints for implementation of aHints for implementation of ahierarchical decisionhierarchical decision--making processmaking process

1.1. CaCarefully analyse the decision problem in handrefully analyse the decision problem in handand structure it.and structure it.

2. Learn from the others.2. Learn from the others.

3. Use existing software tools (develop additional or3. Use existing software tools (develop additional ornew only if necessary).new only if necessary).

4. Follow4. Follow--up the consequences of the decisionup the consequences of the decisionmade, and be ready to repeat some calculations.made, and be ready to repeat some calculations.


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1.1. ClusteringClustering

2. Groups, aggregations2. Groups, aggregations

3.3. Optimism and pessimism of the DM(s)Optimism and pessimism of the DM(s)

Various issuesVarious issues


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Clustering the decision elementsClustering the decision elements

4 levels

5 criteria/7 sub-criteria

5 alternatives

Total=17 decision elementsL1: Goal

L2: Criteria

L4: Alternatives

L3: Sub-criteria


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cluster 2 criteria into 1

cluster 3 sub-criteria into 1

to reduce total number of elements to 14

First pass


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4 levels

4 criteria/5 sub-criteria

5 alternatives

Total=14 decision elements

to obtain


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Now perform additional clustering

To obtain the final hierarchy


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3 levels (one level lessone level less)

4 criteria (no subno sub--criteriacriteria)

5 alternatives

Total=9 decision elements


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Compare

CLUSTERINGCLUSTERING

EXPANDINGEXPANDING


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Groups, aggregations

- Normalized weight of the k th member of

a group G- Weight of the i th alternative for k th member ofa group G

- Aggregated weight of the i th alternative for agroup G

In either aggregation, WAMM or GMM, the final additivenormalization of the weights of all alternatives is required !


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Optimism and Pessimism of the DMOptimism and Pessimism of the DM

Define the optimism level of alternative i across all criteria j=1,,n be

where vij is the performance of alternative i for criterion j.

Thus, oi is the value of the best consequence that can result if alternative i is taken.

The max-max return criterion is:

Choose alternative k such that:

ijvnjio

,...,1max

!

!

ijji

imi

k voo maxmaxmax,...,1

!!

!


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Hurwicz (1951) argued that the DM should rank alternatives accordingto the weighted average of the security and optimism levels:

si + ( 1 )oi

Where is the optimism-pessimism index of the DM.

Hurwicz recommends the decision rule:

Choose alternative k such that:

10 eeE

})1({max)1( iii

kk osos EEEE !

This is what is known as Hurwiczs optimism-pessimism index


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Fine tuner of optimism v pessimismFine tuner of optimism v pessimism

There are two available decisions: DThere are two available decisions: D11 and Dand D22. Which one. Which oneto use, or how to combine them into the one: D ?to use, or how to combine them into the one: D ?

Who was theWho was thepessimist, Dpessimist, D11 or Dor D22 ??The answer is simple:The answer is simple:That was the DThat was the D22


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1

Not

important

9

Absolutely

important

5

Very

important


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1

Not

important

9

Absolutely

important

5

Very

important

Where is D ?Where is D ?


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1

Not

important

9

Absolutely

important

GeometricGeometric

3

Weak

importance

5

Very

important

AdditiveAdditive


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What would be your preference, 3 or 5 ?

Theory says 3, because the judgments are fairlydivergent.

Theory suggests that there was an inconsistency, sobetter is to be little pessimistic. Therefore 3.

Do you agree ?

Me NOT, because I am an optimist. But I shall followBut I shall follow

the theory rather.the theory rather.


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To be continued withTo be continued with

Parts III and IVParts III and IV

Documents

1_Teoria Sobre Processo Decisorio_partes 1 e 2