Quantitative Analysis for Management
Solutions: Decision Analysis Notes
,
, CHAPTER 3
Decision Analysis
ALTERNATIVE EXAMPLES
Alternative Example 3.1: Goleb Transport
George Goleb is considering the purchase of two types of industrial robots. The Rob1 (alternative
1) is a large robot capable of performing a variety of tasks, including welding and painting. The
Rob2 (alternative 2) is a smaller and slower robot, but it has all the capabilities of Rob1. The robots
will be used to perform a variety of repair operations on large industrial equipment. Of course,
George can always do nothing and not buy any robots (alternative 3). The market for the repair
operation could be either favorable (event 1) or unfavorable (event 2). George has constructed a
payoff matrix showing the expected returns of each alternative and the probability of a favorable
or unfavorable market. The data are presented:
EVENT 1 EVENT 2
Probability 0.6 0.4
Alternative 1 50,000 –40,000
Alternative 2 30,000 –20,000
Alternative 3 0 0
This problem can be solved using expected monetary value. The equations are presented here:
EMV (alternative 1) = ($50,000)(0.6) + (–$40,000)(0.4)
= $14,000
EMV (alternative 2) = ($30,000)(0.6) + (–$20,000)(0.4)
= $10,000
EMV (alternative 3) = 0
The best solution is to purchase Rob1, the large robot.
Alternative Example 3.2: George Goleb is not confident about the probability of a favorable or
unfavorable market. (See Alternative Example 3.1.) He would like to determine the equally likely
(Laplace), maximax, maximin, criterion of realism (Hurwicz), and minimax regret decisions. The
Hurwicz coefficient should be 0.7. The problem data are summarized below:
EVENT 1 EVENT 2
Probability 0.6 0.4
Alternative 1 50,000 –40,000
Alternative 2 30,000 –20,000
, Alternative 3 0 0
The Laplace (equally likely) solution is computed averaging the payoffs for each alternative and
choosing the best. The results are shown below. Alternatives 1 and 2 both give the highest average
return of $5,000.
Average (alternative 1) = [$50,000 + (–$40,000)]/2
= $5,000
Average (alternative 2) = [$30,000 + (–$20,000)]/2
= $5,000
Average (alternative 3) = 0
The maximin decision (pessimistic) maximizes the minimum payoff outcome for every alternative:
these are –40,000; –20,000; and 0. Therefore, the decision is to do nothing.
The maximax decision (optimistic) maximizes the maximum payoff for any alternative: these
maximums are 50,000; 30,000; and 0. Therefore, the decision is to purchase the large robot
(alternative 1).
The Hurwicz approach uses a coefficient of realism value of 0.7, and a weighted average of
the best and the worst payoffs for each alternative is computed. The results are as follows:
Weighted average (alternative 1) = ($50,000)(0.7)
+ (–$40,000)(0.3)
= $23,000
Weighted average (alternative 2) = ($30,000)(0.7)
+ (–$20,000)(0.3)
= $15,000
Weighted average (alternative 3) = 0 The
decision would be alternative 1.
The minimax regret decision minimizes the maximum opportunity loss. The opportunity loss
table for Goleb is as follows:
Favorable Unfavorable Maximum
Alternatives Market Market in Row
Rob1 0 40,000 40,000
Rob2 20,000 20,000 20,000
Nothing 50,000 0 50,000
The alternative that minimizes the maximum opportunity loss is the Rob2. This is due to the
$20,000 in the last column in the table above. Rob1 has a maximum opportunity loss of $40,000,
and doing nothing has a maximum opportunity loss of $50,000.
Solutions: Decision Analysis Notes
,
, CHAPTER 3
Decision Analysis
ALTERNATIVE EXAMPLES
Alternative Example 3.1: Goleb Transport
George Goleb is considering the purchase of two types of industrial robots. The Rob1 (alternative
1) is a large robot capable of performing a variety of tasks, including welding and painting. The
Rob2 (alternative 2) is a smaller and slower robot, but it has all the capabilities of Rob1. The robots
will be used to perform a variety of repair operations on large industrial equipment. Of course,
George can always do nothing and not buy any robots (alternative 3). The market for the repair
operation could be either favorable (event 1) or unfavorable (event 2). George has constructed a
payoff matrix showing the expected returns of each alternative and the probability of a favorable
or unfavorable market. The data are presented:
EVENT 1 EVENT 2
Probability 0.6 0.4
Alternative 1 50,000 –40,000
Alternative 2 30,000 –20,000
Alternative 3 0 0
This problem can be solved using expected monetary value. The equations are presented here:
EMV (alternative 1) = ($50,000)(0.6) + (–$40,000)(0.4)
= $14,000
EMV (alternative 2) = ($30,000)(0.6) + (–$20,000)(0.4)
= $10,000
EMV (alternative 3) = 0
The best solution is to purchase Rob1, the large robot.
Alternative Example 3.2: George Goleb is not confident about the probability of a favorable or
unfavorable market. (See Alternative Example 3.1.) He would like to determine the equally likely
(Laplace), maximax, maximin, criterion of realism (Hurwicz), and minimax regret decisions. The
Hurwicz coefficient should be 0.7. The problem data are summarized below:
EVENT 1 EVENT 2
Probability 0.6 0.4
Alternative 1 50,000 –40,000
Alternative 2 30,000 –20,000
, Alternative 3 0 0
The Laplace (equally likely) solution is computed averaging the payoffs for each alternative and
choosing the best. The results are shown below. Alternatives 1 and 2 both give the highest average
return of $5,000.
Average (alternative 1) = [$50,000 + (–$40,000)]/2
= $5,000
Average (alternative 2) = [$30,000 + (–$20,000)]/2
= $5,000
Average (alternative 3) = 0
The maximin decision (pessimistic) maximizes the minimum payoff outcome for every alternative:
these are –40,000; –20,000; and 0. Therefore, the decision is to do nothing.
The maximax decision (optimistic) maximizes the maximum payoff for any alternative: these
maximums are 50,000; 30,000; and 0. Therefore, the decision is to purchase the large robot
(alternative 1).
The Hurwicz approach uses a coefficient of realism value of 0.7, and a weighted average of
the best and the worst payoffs for each alternative is computed. The results are as follows:
Weighted average (alternative 1) = ($50,000)(0.7)
+ (–$40,000)(0.3)
= $23,000
Weighted average (alternative 2) = ($30,000)(0.7)
+ (–$20,000)(0.3)
= $15,000
Weighted average (alternative 3) = 0 The
decision would be alternative 1.
The minimax regret decision minimizes the maximum opportunity loss. The opportunity loss
table for Goleb is as follows:
Favorable Unfavorable Maximum
Alternatives Market Market in Row
Rob1 0 40,000 40,000
Rob2 20,000 20,000 20,000
Nothing 50,000 0 50,000
The alternative that minimizes the maximum opportunity loss is the Rob2. This is due to the
$20,000 in the last column in the table above. Rob1 has a maximum opportunity loss of $40,000,
and doing nothing has a maximum opportunity loss of $50,000.
