curs 2 business decision processes

7/26/2019 Curs 2 Business Decision Processes

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Business Decision Process-

Course 2

Decision Making using

Analytic Hierarchy Processes


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Decision making

in the economic framework of utility theory

a brief history of the development of the utility theory

a reconceptualization of the basic sources of utility.

intangible factors are brought together into

consideration in the formulation of the utility functions,

in the mainstream of economic theory.


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Decision problem

Single-attribute

Decision problem

Each decision alternative

can be assigned

one number

Multiattribute Decision

problem

Multiple attributes which

aretypically uncomensurable

Analytic Hierarchic

Processes

Multiattribute utility

theory

Axiom of additive

independence


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Ordinal Utility

consumershad preferencesfor one combination of goodsover another

Cardinal Utility

original concept of utilitymoral philosopher Jeremy Bentham

formally integratedJevons, Menger and Walras-in the 1870s

cardinally measurablepsychological

ow of satisfactionsattached to goods and services


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A properly conceptualized utility

theory implies measurements

that cannot e inferred fromeha!ior

ut must e otained directly fromconsumers

and this conceptualization can helpto predict eha!ior that is notother"ise understandale#


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$n AHP

order of preferences intensity of

preferences

%i!en t"o alternati!es & A and B

Which of A or B do you prefer ?

On a scale from 1 to 9

'(-e)ually preferred* +-e,tremelypreferred

by how much youprefer

the alternati!e you chose

o!er the other one.


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A hierarchy

Decision Problem

Criterion 1 (C1) Criterion 2 (C2) Criterion 3 (C3)

(Criterions)

Alternative 1 (A1) Alternative 2 (A2)

(Alternatives)


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Decision matri for a decisionproblem with !" #"$$n decisioncriterions

2 decision criterions C(* C2What criterion is more important among %1

and %!?

Ans"er &C(

On a scale from 1 to 9 &1'e(ually important"etremely important) by how much youthin* is more important the criterion you

chose to the other one ?Ans"er & /

Decisional Matri, C( C2

C( ( /C (0/ (


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/ decision criterions C(* C2 *C/

What criterion you thin* is more important&+reference)

%1or %!?Ans"er &C2

On a scale from 1 to 9 &1'e(ually important" 9'etremly important)&,ntensity)

by how much you consider is more important the criterion you chosen to theother one ?

Ans"er & 1

What criterion you thin* is more important"%!or %#?

Ans"er &C2On a scale from 1 to 9 &1'e(ually important" 9'etremly important)

by how much you consider is more important the criterion you chosen to theother one ?

Ans"er &/

What criterion you thin* is more important"%1or %#?

Ans"er &C/On a scale from 1 to 9 &1'e(ually important" 9'etremly important)

by how much you consider is more important the criterion you chosen to theother one ?Ans"er & /


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Decision matri,

C( C2 C/

C( ( (01 (0/C2 1 ( /

C/ / (0/ (

$n general

Decision matri, eciprocity

ai34(0a3i C( C2 C/

C( ( a(2 a(/ Consistency ai3 5 a3k4 aik

C2 a2( ( a2/

C/ a/( a/2 (


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Decision vector'associated with areciprocal" consistent decision matri is the

normali-ed form of the eigenvectorassociated with the highest eigenvalue

Matricea decizionala 'reciproca* consistenta 6ector dedecizie

%1 %! %#%1 ( a(2 a(/ "(%! a2( ( a2/ "2%# a/( a/2 ( "/

cu a(2 4"(0 "2* a(/ 4"(0 "/ * a2/ 4"20 "/

'in general* ai3 4"i0 "3


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$f the decision matri, is not consistent* the associateddecision !ector is the eigen!ector associated "ith the

highest eigen!alue of the normalized matri,

Decision matri, Decision !ector

C( C2 C/C( ( (01 (0/ "(47#(71

C2 1 ( / "247#8/9

C/ / (0/ ( "/ 47#21:

In general, a positive,reciprocal, suare matri!" C" isconsistent if and only if #ma!$dim%C&


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;he computation of a priority !ector correspondingto the


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Conclusion .

Ho" do "e aggregate the results .

Ho" many e,perts are needed to!alidate the results.

$n the AHP original frame"ork

e,perts meet together* discuss*compromise and agree to a commonpoint of !ie"=

is this all the time feasile .

,s a group.s point of viewsuperior to an individual.s one ?


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Disputale points in the AHP theory

numerical scale'(-+* or (-1 or others

individual scale&

an indi!idual "ho prefers C(to C2"ithintensity /

may not e comparale "ith another

indi!idual deli!ering the same ans"er=# >ince di?erent indi!iduals may ha!edi?erent standards coming from di?erente,periences=


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$@&

,t would be a way to decide whether

' the /.s response' declared #' actually means 1$!0

'the .s response'declared #' actually means #$21

so that the decision matrices corresponding to the tworespondents are 3more consistent4 than the initial ones

and this could be somehow etended to the bothhierarchies associated with the two respondents

then the arithmetic mean of the two correspondentcomponents in the decision vector would be arepresentative approimation for the true value" thusma*ing the statistical representatives useless5


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6aaty.s most famous eperiments

7his section reproduces four eamples

from 6aaty &!818) in which the numericalscale using integers from 1 to 9 is appliedand the true vector of priorities is *nown$

7hese eamples refer to single matrivalidation eample$

ou are strongly encouraged toreproduce these eperiments and presenttheir :ndings$


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Optics Example

,n this eperiment participated 6aaty.s *ids of ; and2 years old" to provide one decision matri and

6aaty.s wife to provide the second decision matri$

hehas to loo* at the chair and compare their relativebrightness in pairs" :ll the decision matri andobtain a relationship between the chairs and theirdistance from the light source$

7his eperiment was repeated twice and thecorrespondent decision matrices are given below$


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D1 %1 %! %# %0

%1 ( 1 8 9%! ( 8

%# (

%0 (


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D!

%1 %! %# %0

%1

( 8 9

%! ( /

%# ( 2

%0 (


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7he corresponding priority.svectors &+@)for the relativebrightness are shown in the net

table


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elative

brightness +@1

elative

brightness +@!

8$C1 7#82

8$!0 7#22

8$1 7#2

8$8; 7#78


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7hese results should be comparedwith the so'called inverse s(uarelaw in optics according to which

the brightness is inverseproportional with the s(uare ofthe distance to the source of light

&see 7able !)$


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Dista

nce

ormali

-ed

distanc

e

6(uare of

normali-e

d

distance

ecipr

ocal of

previo

us

column

ormali

-ed

recipro

cal

ounding

oE

9 7#(2/

7#7(1(2+

88#7+:

7#879+

7#8(

1; 7#27

1

7#72

721

2/#9

+

7#2(

::

7#22

!1 7#2:

:

7#7:2

+

(2#7

1

7#((

7:

7#((

!= 7#/:

7#(9

18

8#9: 7#78

2/

7#78


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Relative consumption of drinks

,n this eperiment #8 people" using consensus arrived at thesame Fudgment regarding the dominance of the consumption

of drin*s in the Gnited 6tates &which drin* is consumed morein the G6 and how much more than another drin*?)$

7he priority vector &+@ ) corresponding to a single decisionmatri is compared with the actual consumption" fromstatistical sources $

aybe" after contemplating the ama-ing match of the results"one would want to thin* at the diEerences among consensusand individual opinion &epressed through a survey"eventually) and redo the eperiment$

7he decision matri corresponding to the Foint evaluation of #8individuals for the drin* consumption in the G6 &DDrin*%onsumption) is presented below


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DDrin* %onsumption %oEe Wine 7ea Beer 6odas il* Water

%oEe ( + 1 2 ( (

Wine (

7ea + (

Beer + / ( (

6odas ( + 2 ( 2

il* ( + / ( (

Water 2 + + / 2 / (


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7he comparison among thepriority vector &+@) correspondingto the previous decision matriand the actual consumption &fromstatistical sources) is shown in the

net table


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+@ Actual

consumpti

on%oEee 7#(99 7#(:7Wine 7#7(+ 7#7(77ea 7#72 7#77Beer 7#((8 7#(276odas 7#(+7 7#(:7il* 7#(2+ 7#(7water 7#/29 7#//7


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Pairwise comparisons of the weights of ve objects

7his eperiment gives the

estimated pairwise comparisons ofthe weights of the :ve obFectslifted by hand" made by a friend of

6aaty$

7he decision matri &DWeight)is

presented below


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DWeight adio 7ypewriter Harge

AttachI

%ase

+roFector 6mall AttachI

%ase

adio (

7ypewriter 1 ( 2 2 :

Harge AttachI %ase / (

+roFector 2 (

6mall AttachI %ase (


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7he comparison among thepriority vector &+@) and the actualrelative weights is shown in the

net table


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+@ Actual

elative

Weightsadio 7#7+ 7#(7

7ypewriter

7# 7#/+

Harge

AttachI

%ase

7#(: 7#27

+roFector 7#2+ 7#296mall

AttachI

%ase

7#7 7#7


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Relative Wealth of Seven ations

7his eercise was done by 6aatyand one of his collaborators whiletraveling by plane$

Gsing common *nowledge aboutthe relative power and standing ofseven countries" in the net isshown the decision matri

&Delative Wealth) deduced bypairwise comparisons of therelative wealth of seven nations$


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Delative Wealth G$6$ ussia %hina


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7he comparison among thepriority vector &+@) and thenormali-ed L+ values is shown

in the net table


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+@ Actual

L+

&192!)

orma

li-ed

L+

@aluesG$6$ 7#29 ((89 7#(/ussia 7#2/ 8/1 7#221%hina 7#72( (27 7#7/

curs 2 business decision processes

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