Decision under uncertainty

Topics: Decision theory, Harshad number, Risk Pages: 16 (459 words) Published: October 7, 2013
DECISION UNDER
UNCERTAINTY
MZ510 ANALYTICAL METHODS
23 SEPTEMBER 2013

OUTLINE


Objectives



Introduction



Application (Example)



Decision Criteria



Summary

2

OBJECTIVES


Studysituationswheredecisionsaremadeinan
uncertainenvironment



Introducebasictheoryofdecisionmakingunder
uncertainty



Demonstratehowtocalculateandselectadecision
whenuncertaintiesregardingthefutureexist



Understandthemethodthatwilloptimizethe
resultingpayoffintermsofadecisioncriterion
3

WEDDING ANNIVERSARY?
Mr.Rightisabouttoleaveworkforhome.He
looksathiscalendar.ItisAugust24.This,hefeels,
isanimportantdate.
Isithisweddinganniversary?
Hebetterbuyhiswifesomeflowers(cost$25).
Whatifitisnottheiranniversaryandhearrives
homewiththepresent?
Shewillbecomesuspicious.
Hewouldhavetotakeherouttodinnertoexplain
(cost$125).
Worsestillifhedoesnotbringanythinghomeand
itistheiranniversarytherewillbetrouble;
perhaps$500wouldbeneededtohelppatch
thingsup.Whatshouldhedo?

4

INTRODUCTION


State‐of‐the‐WorldDecision‐MakingModel



PossiblestatesSj ={S1, S2….,Sk}



AssumethatSj happenswithprobabilityPj P={P1,P2….,Pk}





Decisionmakerchoosesanaction,ai A={a1,,a2….,ak}

Ifaction,ai ,ischosenandthestateoftheworldisSj thenthe rewardis,rij

Mr.Right’sWeddingAnniversary?


S={anniversary,noanniversary},Pisequallylikely



A={buy,don'tbuy}
PayOffTable

Anniversary

NoAnniversary

Buy

‐25

‐150

Don’tBuy

‐500

0

5

SCM APPLICATION: NEWSVENDOR EXAMPLE
Needs to decideon an order
quantity
 Demand unknown
 Possibility is equally likely,
P6=p7 =p8 =p9=p10=1/5
 Possible values ofdaily demand
S={6,7,8,9,10}
 A={6,7,8,9,10}
 Cost =20cents
 Selling price =25cents


6

DOMINATED DECISION
o Mathematical definition:


Variablesthatprovidethemostsuitablepayoffthanany
anothervariables



Definition:AnactionAi isdominatedbyanactionAi’if forallSj S,Rij ≤Ri‘j andforsomestateSj ',Rij'<Ri‘j ‘ Ordered
1
2
3
4
5
6
7
8
9
10
11

6
5
10
15
20
25
30
10
‐10
‐30
‐50
‐70

7
5
10
15
20
25
30
35
15
‐5
‐25
‐45

Demand
8
5
10
15
20
25
30
35
40
20
0
‐20

9
5
10
15
20
25
30
35
40
45
25
5

10
5
10
15
20
25
30
35
40
45
50
30

7

MAXIMIN CRITERION

Ordered
6
7
8
9
10

6
30
10
‐10
‐30
‐50

7
30
35
15
‐5
‐25

Demand
8
30
35
40
20
0

9
30
35
40
45
25

10
30
35
40
45
50

Min. Value
30
10
‐10
‐30
‐50

Min. Maximum 
Value
30

8

MAXIMAX CRITERION
Ordered
6
7
8
9
10

6
30
10
‐10
‐30
‐50

7
30
35
15
‐5
‐25

Demand
8
30
35
40
20
0

9
30
35
40
45
25

10
30
35
40
45
50

Max. Value
30
35
40
45
50

Max. Maximum 
Value
50

9

MAXIMIN REGRET CRITERION
Ordered
6
7
8
9
10

6
30
10
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