# 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

uncertainenvironment

Introducebasictheoryofdecisionmakingunder
uncertainty

whenuncertaintiesregardingthefutureexist

Understandthemethodthatwilloptimizethe
3

WEDDING ANNIVERSARY?
looksathiscalendar.ItisAugust24.This,hefeels,
isanimportantdate.
Isithisweddinganniversary?
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

PayOffTable

Anniversary

NoAnniversary

‐25

‐150

‐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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