Quantitative Analysis for Management. Chapter 3 Fundamentals of Decision Theory Models. Chapter Outline. 3.1 Introduction 3.2 The Six Steps in Decision Theory 3.3 Types of DecisionMaking Environments 3.4 Decision Making Under Risk 3.5 Decision Making Under Uncertainty
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Quantitative Analysis for Management
Chapter 3
Fundamentals of Decision Theory Models
31
3.1 Introduction
3.2 The Six Steps in Decision Theory
3.3 Types of DecisionMaking Environments
3.4 Decision Making Under Risk
3.5 Decision Making Under Uncertainty
3.6 Marginal Analysis with a Large Number of Alternatives and States of Nature
32
Students will be able to:
33
34
35
Favorable Market ($)
Unfavorable Market ($)
Construct a
large plant
200,000
180,000
Construct a small plant
20,000
100,000
Do nothing
0
0
36
37
n
=
å
EMV(Altern
ative
i)
(Payoff
*
P(S
))
j
S
j
=
j
1
=
where
j
1
to
the
number
of
states
of
nature,
n
Expected Monetary Value:
38
Favorable Market ($)
Unfavorable Market ($)
Construct a
large plant
200,000
180,000
10,000
Construct a small plant
100,000
20,000
40,000
Do nothing
0
0
0
0.50
0.50
EMV
39
310
n
=
å
EV

PI
(
best
outcome
for
state
of
nature
j)
*
P(S
)
j
=
1
j
=
where
j
1
to
the
number
of
states
of
nature,
n
311
312
Favorable Market ($)
Unfavorable Market ($)
Construct a
large plant
200,000
Construct a small plant
40,000
Do nothing
0
0.50
0.50
EMV
313
EVPI = expected value with perfect information  max(EMV)
= $200,000*0.50 + 0*0.50  $40,000
= $60,000
314
We want to maximize EMV or
minimize EOL
315
316
317
318
EMV(Large Plant) = $200,000P  (1P)$180,000
EMV(Small Plant) = $100,000P  $20,000(1P)
EMV(Do Nothing) = $0P + 0(1P)
319
EMV (Small Plant)
EMV(Large Plant)
320
321
Favorable Market ($)
Unfavorable Market ($)
200,000
180,000
Construct a
large plant
100,000
20,000
Construct a small plant
0
0
Do nothing
Maximax  Choose the alternative with the maximum output
322
Favorable Market ($)
Unfavorable Market ($)
200,000
180,000
Construct a
large plant
100,000
20,000
Construct a small plant
0
0
Do nothing
Maximin  Choose the alternative with the maximum minimum output
323
Favorable Market ($)
Unfavorable Market ($)
200,000
180,000
EMV
Construct a
large plant
10,000
100,000
20,000
Construct a small plant
40,000
0
0
Do nothing
0
0.50
0.50
Equally likely (Laplace)  Assume all states of nature to be equally likely, choose maximum EMV
324
Favorable Market ($)
Unfavorable Market ($)
200,000
180,000
CR
Construct a
large plant
124,000
100,000
20,000
Construct a small plant
76,000
0
0
0
Do nothing
0.50
0.50
Criterion of Realism (Hurwicz):
CR = *(row max) + (1)*(row min)
325
Favorable Market ($)
Unfavorable Market ($)
Max in row
Construct a
large plant
0
180,000
180,000
Construct a small plant
100,000
20,000
100,000
Do nothing
200,000
0
200,000
0.50
0.50
Minimax  choose the alternative with the minimum maximum Opportunity Loss
326
327
328
329
ML
³
P
+
ML
MP
4
4
=
=
=
0
66
.
4
+
2
6
= $6  $4 = $2
330
331
332
ML
=
P
+
ML
MP
*

m
X
=
Z
s
333
334
4
ML
=
=
=
0
40
P
.
+
4
+
6
ML
MP
*

50
X
0
25
=
10
*
=
10
0
25
+
50
=
52
5
53
X
*
.
.
or
newspapers
P = 0.6 (i.e., 1  .04) Z = 0.25,
and
or:
.
335
336
337
8
ML
=
=
=
0
80
P
.
+
8
+
2
ML
MP
*

1000
X

0
84
=
10
*
=

8
4
+
100
=
91
6
92
X
.
.
or
newspapers
Z = 0.84 for an area of 0.80
and
or:
.
338
339