ch19 Decision work

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Chapter 19: Decision Analysis 91

Chapter 19

Decision Analysis

LEARNING OBJECTIVES

Chapter 19 describes how to use decision analysis to improve management decisions, thereby enablingyou to:

1. Learn about decision making under certainty, under uncertainty, and under risk.

. Learn several strategies !or decision"making under uncertainty, including e#pected payo!!,

e#pected opportunity loss, ma#imin, ma#ima#, and minima# regret.

$. Learn how to construct and analy%e decision trees.

&. 'nderstand aspects o! utility theory.(. Learn how to revise probabilities with sample in!ormation.

CA!TER O"TLINE

19.1 )he Decision )able and Decision *aking 'nder Certainty Decision )able

Decision"*aking 'nder Certainty

19. Decision *aking 'nder 'ncertainty

*a#ima# Criterion

*a#imin Criterion

+urwic% Criterion

*inima# egret

19.$ Decision *aking 'nder isk

Decision )rees

-#pected *onetary alue /-*0 -#pected alue o! er!ect 2n!ormation 'tility

19.& evising robabilities in Light o! 3ample 2n!ormation

-#pected alue o! 3ample 2n!ormation

#E$ TER%S

Decision Alternatives +urwic% Criterion

Decision Analysis *a#ima# Criterion

Decision *aking 'nder Certainty *a#imin Criterion

Decision *aking 'nder isk *inima# egretDecision *aking 'nder 'ncertainty 4pportunity Loss )able

Decision )able ayo!!s

Decision )rees ayo!! )able

-*5er isk"Avoider

-#pected *onetary alue /-*0 isk")aker

-#pected alue o! er!ect 2n!ormation 3tates o! 6ature

-#pected alue o! 3ample 2n!ormation 'tility



9 3olutions *anual and 3tudy 7uide

ST"D$ &"ESTIONS

1. 2n decision analysis, decision"making scenarios are divided into three categories: decision"makingunder 88888888888888, decision"making under 888888888888888, and decision"making under

88888888888888.

. *any decision analysis problems can be viewed as having three variables:

1. 888888888888888888888, . 88888888888888888888, and $. 8888888888888888888888.

$. 4ccurrences o! nature that can happen a!ter a decision has been made that can a!!ect the outcome o!

the decision and over which the decision"maker has little or no control are called

888888888888888888888888888888888. )he bene!its or rewards that result !rom selecting a

particular decision alternative are called 888888888888888. )he various choices or options available

to the decision"maker in any given problem situation are called

8888888888888888888888888888888888.

&. -#amine the decision table shown below:

3tate o! 6ature

1 $ &Decision

Alternative

1 ( ( ;( 1(

1 1( (

$ ( 1

)he selected decision alternative using a *a#ima# criterion is 888888888888888888 and the optimal

payo!! is 88888888888.

(. 'se the decision table !rom <uestion &. )he selected decision alternative using a *a#imin criterion is

8888888888888 and the payo!! !or this is 888888888888. 3uppose +urwic% criterion is used to select

a decision alternative and α is .$. )he selected decision alternative is 88888888888888888888 and the

payo!! is 88888888888888888888. +owever, i! α is .=, the selected decision alternative is 88888888888888888888 and the payo!! is 88888888888888888888.

>. 'se the decision table !rom <uestion & to construct an 4pportunity Loss table. 'sing this table and a

*inima# egret criterion, the selected decision alternative is 888888888888888888888 and the

minimum regret is 8888888888888.

;. ?ith decision trees, the decision alternatives are depicted by a 88888888888888 node and the states

o! nature are represented by a 8888888888888888 node.

=. )he decision table presented in <uestion & has been reproduced below with probabilities assigned to

the states o! nature:

3tate o! 6ature

1/.0 /.$(0 $/.&0 &/.(0

Decision

Alternative

1 ( ( ;( 1(

1 1( (

$ ( 1

)he e#pected monetary value o! selecting decision alternative 1 is 888888888888888. )he e#pected

monetary value o! selecting decision alternative is 888888888888888. )he e#pected monetary value

o! selecting decision alternative $ is 888888888888888.



Chapter 19: Decision Analysis 9$

9. An -*5er would choose decision alternative 8888888888 based on the results o! <uestion =.

1. )he e#pected value o! per!ect in!ormation !or the decision scenario presented in <uestion = is

8888888888888888888.

11. )he degree o! pleasure o! displeasure a decision"maker has in being involved in the outcome

selection process given the risks and opportunities available is 888888888888888888.

1. 2! it takes more than the e#pected monetary value to get a player to withdraw !rom a game, then that

person is said to be a 8888888888888888.

1$. Consider the decision table shown below:

3tate o! 6ature

@/.&0 /.>0

Decision 1 (

( =

)he e#pected monetary value o! this decision scenario is 8888888888888888888.

3uppose the decision maker has an opportunity to buy a !orecast to assist himBher in making the

decision. ?hen the state o! nature is @, the !orecaster will predict @ =( o! the time and 1( o!the time. ?hen the state o! nature is , the !orecaster will predict 9( o! the time and will predict

@ ( o! the time. 2! the !orecast is purchased and the !orecaster predicts that @ will occur, then

revised probability o! @ occurring is 8888888888888888 and o! occurring is 8888888888888. 2! the

!orecaster predicts that will occur, then the revised probability o! @ occurring is 8888888888888

and o! occurring is 888888888888888888. )he probability that the !orecaster will predict @ is

888888888888888. )he probability that the !orecaster will predict is 88888888888888. )he

e#pected monetary value with in!ormation is 88888888888888888. )he e#pected value o! sample

in!ormation is 88888888888888888.



9& 3olutions *anual and 3tudy 7uide

ANS'ERS TO ST"D$ &"ESTIONS

1. Certainty, 'ncertainty, isk ;. , !

. Decision Alternatives, 3tates o! =. 1;.(, 1>.(, .;(

6ature, ayo!!s

9. 1$. 3tates o! 6ature, ayo!!s, Decision

Alternatives 1. >

&. 1, 1( 11. 'tility

(. , 1, , 1&.(, 1, 9 1. isk"taker

>. 1, > 1$. (, .91=9, .=11, .9(, .9&=, .$;,.>$, .(&., &.

SOL"TIONS TO ODD(N"%BERED !ROBLE%S IN CA!TER 19

19.1 s1 s s$ *a# *in

d 1 ( 1;( ( ( (

d 11 1 ; 11 ;

d $ $9 1& = $9 =

a.0 *a# (, 11, $9E F )9* decision: 3elect d $

b.0 *a# (, ;, =E F +* decision: 3elect d

c.0 Gor α F .$

d 1: .$/(0 H .;/(0 F (;.(

d : .$/110 H .;/;0 F ,-

d $: .$/$90 H .;/=0 F >1

decision: 3elect d

Gor α F .=

d 1: .=/(0 H ./(0 F 19( d : .=/110 H ./;0 F 1

d $: .=/$90 H ./=0 F -9.

decision: 3elect d $

Comparing the results !or the two di!!erent values o! alpha, with a more pessimist point"o!"view

/α F .$0, the decision is to select d and the payo!! is =. 3electing by using a more optimistic

point"o!"view /α F .=0 results in choosing d $ with a higher payo!! o! 9>.



Chapter 19: Decision Analysis 9(

d.0 )he opportunity loss table is:

s1 s s$ *a#

d 1 1& 9( 1&

d = ;( =

d $ $( 1( 1(

)he minima# regret F min 1&, =, 1(E F 1/*

Decision: 3elect d 1 to minimi%e the regret.

19.$ D 2 *a# *in A > 1( ( > (

I 1 ( $ $ 1

C 1 & 1( & 1

D ( ( ( (

*a#ima# F *a# >, $, &, (E F .*

Decision: 3elect A

*a#imin F *a# (, 1, 1, (E F 1*

Decision: 3elect I

19.(, 19.>



9> 3olutions *anual and 3tudy 7uide

19.; -#pected ayo!! with er!ect 2n!ormation F

(/.1(0 H (/.(0 H /.$0 H =/.10 H >/.0 F )10+

-#pected alue o! er!ect 2n!ormation F $1.( (.( F .0*

19.9 Down/.$0 'p/.>(0 6o Change/.(0 -* Lock"2n 1( =(

6o 1;( ( 11

Decision: Iased on the highest -*02,3, JLock"2nJ

-#pected ayo!! with er!ect 2n!ormation F

1;(/.$0 H /.>(0 H /.(0 F 1,-0

-#pected alue o! er!ect 2n!ormation F 1=.( =( F 9+0

19.11 a.0 -* F ,/.(0 H /(,0/.(0 F +4***

b.0 isk Avoider because the -* is more than the investment /;(, K (,0

c.0 ou would have to o!!er more than ;(, which is the e#pected value.

19.1$

Dec/.>0 2nc/.&0 -*

3 ( &( $(

* 1( 1( 1(

L $( & (

Decision: Iased on -* F *a#imum $(, 1(, (E F *

Gor Gorecast /Decrease0:

rior Cond. oint evised

Decrease .> .;( .&( .==&

2ncrease .& .1( .> .11;>

G/Dec0 F .(1

Gor Gorecast /2ncrease0:

rior Cond. oint evised

Decrease .> .( .1( .$>1

2ncrease .& .=( .$& .>9$9

G/2nc0 F .&9



Chapter 19: Decision Analysis 9;

)he e#pected value with sampling is -//0-+

-32 F -?3 -* F &&.;( ( F 19/0-+

19.1( 4il/.110 6o 4il/.=90 -*

Drill 1,, 1, 1,

Don5t Drill

Decision: )he -* !or this problem is *a# 1,, E F 1,.

)he decision is to Drill.



9= 3olutions *anual and 3tudy 7uide

Actual

4il 6o 4il 4il . .1

Gorecast

6o 4il .= .9

Gorecast 4il:

3tate rior Cond. oint evised

4il .11 . . .19=

6o 4il .=9 .1 .=9 .=1=

/G4il0 F .111

Gorecast 6o 4il:

3tate rior Cond. oint evised 4il .11 .= .== .99

6o 4il .=9 .9 .=1 .91

/G 6o 4il0 F .==9

)he -#pected alue ?ith 3ampling 2n!ormation is -14*1-0)-

-32 F -?32 -* F 1, 1,1.$ F 1-0)-




19.1;

b.0 d 1: &/.$0 H (/.(0 H $/.0 H 1/.(0 F -.+0

d : $/.$0 H /10/.(0 H >/.0 H /.(0 F $(

Decision: 3elect d 1

c.0 -#pected ayo!! o! er!ect 2n!ormation:

&/.$0 H (/.(0 H >/.0 H /.(0 F )-0

alue o! er!ect 2n!ormation F $(.( >;.( F ,

19.19 3mall *oderate Large *in *a#

3mall ( $ $

*odest 1 $ > 1 >

Large $ & $

a.0 *a#ima#: *a# $, >, E F -***

Decision: Large 6umber

*inima#: *a# , 1, $E F -**

Decision: 3mall 6umber




b.0 4pportunity Loss:

3mall *oderate Large *a#

3mall 1( 1; 1;

*odest 1 1 1& 1& Large ( (

*in 1;, 1&, (E F **

Decision: Large 6umber

c.0 *inima# regret criteria leads to the same decision as *a#ima#.

19.1 *ild/.;(0 3evere/.(0 -* eg. ( =;(

?eekend 1 =(

6ot 4pen $ 1

Decision: Iased on *a# -* F

*a#=;(, =(, E F ,+, open regular hours.

-#pected alue with er!ect 2n!ormation F

/.;(0 H 1/.(0 F 1-

alue o! er!ect 2n!ormation F 1(( =;( F .*




19.$ ed./.1(0 Con./.$(0 2nc./.(0 -*

Automate &, 1(, >, 1=,;(

Do 6ot (, 1, $, 1,;(

Decision: Iased on *a# -* F

*a# 1=;(, 1;(E F 1,4+*, 3elect Automate

Gorecast eduction:


.1( .> .9 .>

C .$( .1 .$( .$$$

2 .( .( .( .1>>;

/Ged0 F .1(

Gorecast Constant:


.1( .$ .&( .1

C .$( .= .= .>

2 .( .( .1( .;;=

/GCons0 F .&(

Gorecast 2ncrease:


.1( .1 .1( .$;(

C .$( .1 .$( .=;(

2 .( .; .$( .=;(

/G2nc0 F .&




-#pected alue ?ith 3ample 2n!ormation F -14/-0

-32 F -?32 -* F 1,&(.(( 1=,;( F -4.+0



Chapter 19: Decision Analysis 1$



1& 3olutions *anual and 3tudy 7uide



Chapter 19: Decision Analysis 1(



1> 3olutions *anual and 3tudy 7uide



Chapter 19: Decision Analysis 1;



1= 3olutions *anual and 3tudy 7uide

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