Name: Sandra Michelle Andrade Peñafiel

Quiz – Decision Theory

Administración de Operaciones
2023 Tr1

1. If probabilities are available to the decision maker, then the decision-making environment is
called:
a. Certainty
b. Uncertainty
c. Risk
d. None of the above
2. The minimum expected opportunity loss is:
a. Equal to the highest expected payoff.
b. Greater than the expected value with perfect information.
c. Equal to the expected value with perfect information.
d. Computed when finding the minimax regret decision.
3. In assessing utility values:
a. The worst outcome is given a utility of -1.
b. The best outcome is given a utility of 0.
c. The worst outcome is given a utility of 0.
d. The best outcome is given a value of -1.
4. On a decision tree, at each state-of-nature note,
a. The alternative with the greatest EMV is selected.
b. An EMV is calculated.
c. All probabilities are added together.
d. The branch with the highest probability is selected.
5. The efficiency of sample information:
a. Is the EVSI/(maximum EMV without SI) expressed as a percentage.
b. Is the EVPI/EVSI expressed as a percentage.
c. Would be 100% if the sample information were perfect.
d. Is computed using only the EVPI and the maximum EMV.
6. Even though independent gasoline stations have been having a difficult time, Susan
Solomon has been thinking about starting her own independent gasoline station. Susan’s
problem is to decide how large her station should be. The annual returns will depend on
both the size of her station and a number of marketing factors related to the oil industry
and demand for gasoline. After a careful analysis, Susan developed the following table:

Size Good Market ($) Fair Market ($) Poor Market ($)
Small 50,000 20,000 -10,000
Medium 80,000 30,000 -20,000
Large 100,000 30,000 -40,000
Very Large 300,000 25,000 -160,000

a.) What is the maximax decision?

The maximax decision is to choose the option with the maximum possible return in each market
scenario. From the table:

Size Good Market ($) Fair Market ($) Poor Market ($)
Small 50,000 20,000 -10,000
Medium 80,000 30,000 -20,000
Large 100,000 30,000 -40,000
Very Large 300,000 25,000 -160,000

The maximax decision is to choose the Very Large size option, with an expected return of
$300,000 in a Good Market scenario.

b.) What is the maximin decision?

The maximin decision is to choose the option with the maximum guaranteed minimum return
across all market scenarios. From the table:

Size Good Market ($) Fair Market ($) Poor Market ($)
Small 50,000 20,000 -10,000
Medium 80,000 30,000 -20,000
Large 100,000 30,000 -40,000
Very Large 300,000 25,000 -160,000

The maximin decision is to choose the small size option, with a guaranteed minimum return of
$20,000.

c.) What is the equally likely decision?

The equally likely decision is to assign equal probabilities to each market scenario and calculate
the expected return for each option. From the table:

Small: (0.333 * $50,000) + (0.333 * $20,000) + (0.333 * -$10,000) = $19,980

Medium: (0.333 * $80,000) + (0.333 * $30,000) + (0.333 * -$20,000) = $29,970
Large: (0.333 * $100,000) + (0.333 * $30,000) + (0.333 * -$40,000) = $29,970
Very Large: (0.333 * $300,000) + (0.333 * $25,000) + (0.333 * -$160,000) = $54,945

Therefore, based on the equally likely decision, the recommended decision would be to choose
the Very Large size option, as it has the highest expected return of $54,945.
The equally likely decision is to choose the Very Large size option, with an expected return of
$54,945.

d.) What is the criterion of realism decision? Use an alpha value of 0.8.
The criterion of realism decision uses a weighted average approach with an alpha value of 0.8.
From the table:

Small: (0.8 * $50,000) + (0.1 * $20,000) + (0.1 * -$10,000) = $41,000

Medium: (0.8 * $80,000) + (0.1 * $30,000) + (0.1 * -$20,000) = $65,000
Large: (0.8 * $100,000) + (0.1 * $30,000) + (0.1 * -$40,000) = $79,000
Very Large: (0.8 * $300,000) + (0.1 * $25,000) + (0.1 * -$160,000) = $226,500

The criterion of realism decision is to choose the Very Large size option, with an expected return
of $226,500
e.) What is the minimax regret decision?
The opportunity loss table shows the difference between the maximum possible return and the
return for each option in each market scenario:

To calculate the regret for each decision, we subtract the actual return for each size option in each
market scenario from the maximum return in that scenario.

Size Good Market ($) Fair Market ($) Poor Market ($)
Small 50,000 20,000 -10,000
Medium 80,000 30,000 -20,000
Large 100,000 30,000 -40,000
Very Large 300,000 25,000 -160,000

Calculating the regret for each option:

 Small: 300,000 - 50,000 = 250,000 (Good Market)

30,000 - 20,000 = 10,000 (Fair Market)
0 - (-10,000) = 10,000 (Poor Market)

 Medium: 300,000 - 80,000 = 220,000 (Good Market)

30,000 - 30,000 = 0 (Fair Market)
0 - (-20,000) = 20,000 (Poor Market)

 Large: 300,000 - 100,000 = 200,000 (Good Market)

30,000 - 30,000 = 0 (Fair Market)
0 - (-40,000) = 40,000 (Poor Market)

 Very Large: 0 (Good Market)

0 - 25,000 = -25,000 (Fair Market)
0 - (-160,000) = 160,000 (Poor Market)

To determine the minimax regret, we select the option with the minimum maximum regret across
all market scenarios.

Size Value ($)

Small 250,000 (Good Market)
Medium 220,000 (Good Market)

Large 200,000 (Good Market)

Very Large 160,000 (Poor Market)
  The minimax regret decision is to choose the Very Large size option, as it has the
minimum maximum regret of 160,000 in the Poor Market scenario.
 The minimax regret decision is to choose the Very Large size option.

7. What is the overall purpose of utility theory?

Utility theory is a branch of economics that seeks to model and quantify the preferences and
choices of individuals in various situations. It assumes that individuals make decisions to
maximize their overall utility or well-being. It is used to analyze consumer behavior, investment
decisions, insurance choices, portfolio selection, and more. It provides a mathematical framework
to study and predict individual choices and behaviors.

8. What is the difference between prior and posterior probabilities?

Prior probability is the initial probability assigned to an event or hypothesis before any additional
information or evidence is taken into account. Posterior probability is the updated probability of
an event or hypothesis after considering new evidence or information.

9. Sue Reynolds has to decide if she should get information (at a cost of $20,000) to invest in a
retail store. If she gets the information, there is a 0.6 probability that the information will be
favorable and a 0.4 probability that the information will not be favorable. If the information
is favorable, there is a 0.9 probability that the store will be a success. If the information is
not favorable, the probability of a successful store is only 0.2. Without any information, Sue
estimates that the probability of a successful store will be 0.6. A successful store will give a
return of $100,000. If the store is built but is not successful, Sue will see a loss of $80,000. Of
course, she could always decide not to build the retail store. What do you recommend?

We can use decision analysis and calculate the expected values associated with each choice.

Probability of favorable information: 0.6

Probability of a successful store given favorable information: 0.9
Expected return: 0.6 * 0.9 * $100,000 = $54,000
Probability of unfavorable information: 0.4
Probability of a successful store given unfavorable information: 0.2
Expected return: 0.4 * 0.2 * $100,000 = $8,000
Total expected return with information: $54,000 + $8,000 = $62,000
Cost of getting the information: -$20,000 (negative because it's an expense)
If Sue doesn't get the information:

Probability of a successful store without information: 0.6

Expected return: 0.6 * $100,000 = $60,000
Probability of an unsuccessful store without information: 0.4
Expected loss: 0.4 * -$80,000 = -$32,000
Total expected return without information: $60,000 - $32,000 = $28,000
Comparing the expected values:

Expected return with information: $62,000 - $20,000 = $42,000

Expected return without information: $28,000
Based on the expected values, it is recommended that Sue gets the information before deciding
whether to invest in the retail store. The expected return with the information is higher at
$42,000, compared to $28,000 without the information.