Transcript Document

Decision Making
under
Uncertainty
1
The maximin criterion
A decision table for the food manufacturer
(Daily profits)
Course of action
Produce 1 batch
Produce 2 batches
Demand (no. of batches)
1
2
$200
–$600
$200
$400
2
The Expected Monetary Value (EMV)
criterion
Another decision table for the food manufacturer
(Daily profits)
Course of action
Produce 1 batch
Produce 2 batches
Demand (no. of batches)
1
2
Probability 0.3
0.7
$200
–$600
$200
$400
3
Calculating expected profits
Produce one batch:
Expected daily profit
= (0.3  $200) + (0.7  $200) = $200
Produce two batches:
Expected daily profit
= (0.3  –$600) + (0.7  $400) = $100
4
Sensitivity analysis
5
Limitations of the EMV criterion
• It assumes that the decision maker is neutral
to risk
• It assumes a linear value function for money
• It considers only one attribute - money
6
Single-attribute utility:
A decision tree for the conference organizer
7
Applying utilities to the conference
organizer’s decision
8
A utility function for the conference organizer
- indicating she is risk averse
9
Interpreting utility functions
10
The drug company research department’s
problem
11
Utility function for product development
time
12
Allais’s paradox
13
Multi-attribute Utility
14
Utility independence
Attribute A is utility independent of attribute
B, if the decision maker’s preferences for
gambles involving different levels of A, but
the same level of B, do not depend on the
level of attribute B…
15
Utility independence
16
Utility functions for overrun time and
project cost
17
The project manager’s utilities for
overrun and cost
Overrun
(weeks)
0
1
3
6
Utility
1.0
0.9
0.6
0.0
Cost of
project ($)
50 000
60 000
80 000
120 000
140 000
Utility
1.00
0.96
0.90
0.55
0.00
18
Multi-attribute utility function
u(x1,x2)
=k1u(x1) + k2u(x2) + k3u(x1)u(x2)
where: k3 = 1– k1– k2
19
Determining k1
20
Determining k2
21
The project manager’s decision tree with utilities
22