1

Decision Making

under Uncertainty

2

The maximin criterion

A decision table for the food manufacturer

(Daily profits)           Demand (no. of batches) 1 2

Course of actionProduce 1 batch $200 $200Produce 2 batches –$600 $400

 

3

The Expected Monetary Value (EMV) criterion

Another decision table for the food manufacturer

(Daily profits)   Demand (no. of batches)1 2Probability 0.3 0.7

Course of actionProduce 1 batch $200 $200Produce 2 batches –$600 $400

 

4

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

5

Sensitivity analysis

6

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

7

Single-attribute utility:A decision tree for the conference organizer

8

Applying utilities to the conference organizer’s decision

9

A utility function for the conference organizer - indicating she is risk averse

10

Interpreting utility functions

11

The drug company research department’s problem

12

Utility function for product development time

13

Allais’s paradox

14

Multi-attribute Utility

15

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…

16

Utility independence

17

Utility functions for overrun time and project cost

18

The project manager’s utilities for overrun and cost

Overrun Cost of(weeks) Utility project ($) Utility

0 1.0 50 000 1.00

1 0.9 60 000 0.96

3 0.6 80 000 0.90

6 0.0 120 000 0.55

140 000 0.00

19

Multi-attribute utility function

u(x1,x2)

=k1u(x1) + k2u(x2) + k3u(x1)u(x2)

where: k3 = 1– k1– k2

20

Determining k1

21

Determining k2

22

The project manager’s decision tree with utilities