# Chapter14HWSolutions

Topics: Decision theory, Decision making, Risk Pages: 39 (3460 words) Published: November 12, 2013
﻿Chapter 14
Decision Analysis

Learning Objectives

1.Learn how to describe a problem situation in terms of decisions to be made, chance events and consequences.

2.Be able to analyze a simple decision analysis problem from both a payoff table and decision tree point of view.

3.Be able to develop a risk profile and interpret its meaning.

4.Be able to use sensitivity analysis to study how changes in problem inputs affect or alter the recommended decision.

5.Be able to determine the potential value of additional information.

6.Learn how new information and revised probability values can be used in the decision analysis approach to problem solving.

7.Understand what a decision strategy is.

8.Learn how to evaluate the contribution and efficiency of additional decision making information.

9.Be able to use a Bayesian approach to computing revised probabilities.

10.Know what is meant by utility.

11.Understand why utility could be preferred to monetary value in some situations.

12.Be able to use expected utility to select a decision alternative.

13.Be able to use TreePlan software for decision analysis problems.

14.Understand the following terms:

decision alternatives
decision strategy
chance events
risk profile
states of nature
sensitivity analysis
influence diagram
prior probabilities
payoff table
posterior probabilities
decision tree
expected value of sample information (EVSI)
optimistic approach
efficiency of sample information
conservative approach
Bayesian revision
minimax regret approach
utility
opportunity loss or regret
lottery
expected value approach
expected utility
expected value of perfect information (EVPI)

Solutions:

1.a.

b.
Decision
Maximum Profit
Minimum Profit
d1
250
25
d2
100
75

Optimistic approach: select d1

Conservative approach: select d2

Regret or opportunity loss table:

s1
s2
s3
d1
0
0
50
d2
150
0
0

Maximum Regret: 50 for d1 and 150 for d2; select d1

2.a.
Decision
Maximum Profit
Minimum Profit
d1
14
5
d2
11
7
d3
11
9
d4
13
8

Optimistic approach: select d1

Conservative approach: select d3

Regret or Opportunity Loss Table with the Maximum Regret

s1
s2
s3
s4
Maximum Regret
d1
0
1
1
8
8
d2
3
0
3
6
6
d3
5
0
1
2
5
d4
6
0
0
0
6

Minimax regret approach: select d3

b.The choice of which approach to use is up to the decision maker. Since different approaches can result in different recommendations, the most appropriate approach should be selected before analyzing the problem.

c.
Decision
Minimum Cost
Maximum Cost
d1
5
14
d2
7
11
d3
9
11
d4
8
13

Optimistic approach: select d1
Conservative approach: select d2 or d3

Regret or Opportunity Loss Table

s1
s2
s3
s4
Maximum Regret
d1
6
0
2
0
6
d2
3
1
0
2
3
d3
1
1
2
6
6
d4
0
1
3
8
8

Minimax regret approach: select d2

3.a.The decision to be made is to choose the best plant size. There are 2 alternatives to choose from: a small plant or a large plant.

The chance event is the market demand for the new product line. It is viewed as having 3 possible outcomes (states of nature): low, medium and high.

b.Influence Diagram:

c.

d.
Decision
Maximum Profit
Minimum Profit
Maximum Regret
Small
200
150
300
Large
500
50
100

Optimistic approach: select Large plant

Conservative approach: select Small plant

Minimax regret approach: select Large plant

4. a.The decision is to choose the best lease option; there are three alternatives. The chance event is the number of miles Amy will drive per year. There are three possible outcomes.

b.The payoff table for Amy's problem is shown below. To illustrate how the payoffs were computed, we show how to compute the total cost of the Forno Saab lease assuming Amy...