Quantitative Chapter 3

What makes the difference between good decisions and bad decisions?

A good decision considers all alternatives.

(b) the expected value of perfect information (EVPI)

EVPI = 13800 -12200 = 1,600

A risk avoider is a person for whom the utility of an outcome

increases at a decreasing rate as monetary value increases.

EVPI (expected value of perfect information)

is a measure of the maximum EMV as a result of additional information.

(a) What would be the best decision based on the Laplace criterion?

large facility - equally weighted payoff = $300

(a) What would be the best decision based on the maximax criterion?

large facility - highest overall payoff = $800

(c) What would be the best decision based on the minimax regret?

large facility - lowest maximum regret = $500

Optimistic decision makers tend to

magnify favorable outcomes, ignore bad outcomes

The following is considered a criteria for decision making under uncertainty?

optimistic, pessimistic, equally likely, minimax regret

Another name for a decision table is a

payoff table

In decision making under ________, there are several possible outcomes for each alternative, and the decision maker knows the probability of occurrence of each outcome.

risk

The three decision-making environments are decision making under

risk, certainty, and uncertainty

(b) What would be the best decision based on the maximin criterion?

small facility - highest minimum potential payoff = $100

In the construction of decision trees, which of the following shapes represents a decision node?

square

Expected monetary value (EMV) is

the average or expected monetary outcome of a decision if it can be repeated a large number of times.

It is sometimes said that, "Those who gamble the most are the ones who can least afford to lose." These people gamble because

there is utility other than monetary to consider.

In decision making under ________, there are several possible outcomes for each alternative, and the decision maker does not know the probabilities of the various outcomes.

uncertainty

Describe the utility curve of a risk avoider.

utility increasing at a decreasing rate as the monetary value increases

Describe the utility curve of a risk seeker.

utility increasing at an increasing rate as the monetary value increases

Briefly describe EVSI.

EVSI = EMV (best decision with sample information) - EMV (of best decision without sample information)

(a) the alternative that provides the greatest expected monetary value (EMV)

For large inventory alternative maximum EMV = $12,200

(b) If the marketing research is unfavorable, what is the revised probability of a successful music store?

(b) 0.11

Briefly describe decision making under uncertainty.

There are several possible outcomes for each alternative, and the decision maker does not know the probabilities of the various outcomes.

Briefly describe decision making under risk.

There are several possible outcomes for each alternative, and the decision maker knows the probability of occurrence of each outcome.

Pessimistic decision makers tend to

discount favorable outcomes

What is the range of the Hurwicz criterion coefficient of realism α?

0 to 1

A market research survey is available for $10,000. Using a decision tree analysis, it is found that the expected monetary value with no survey is $62,000. If the expected value of sample information is -$7,000, what is the expected monetary value with the survey?

$45,000

(a) If the marketing research is favorable, what is the revised probability of a successful music store?

(a) 0.82

List the six steps in decision making.

1. Clearly define the problem at hand. 2. List the possible alternatives. 3. Identify the possible outcomes or states of nature. 4. List the payoff or profit of each combination of alternatives and outcomes. 5. Select one of the mathematical decision theory models. 6. Apply the model and make your decision.

Describe the structure of a payoff table.

All of the alternatives are listed down the left side of the table, and all of the possible outcomes or states of nature are listed across the top. The body of the table contains the actual payoffs.

A rational decision maker must choose between two alternatives. Alternative 1 has a higher EMV than Alternative 2, but the decision maker chooses Alternative 2. What might explain why this occurs?

Alternative 2 may have a higher expected utility.

decision theory.

An analytic and systematic approach to the study of decision making is referred to as

List the five major decision criteria used when making decisions under uncertainty.

Answer: (1) maximax (optimistic), (2) maximin (pessimistic), (3) criterion of realism (Hurwicz), (4) equally likely (Laplace), and (5) minimax regret

A market research survey is available for $5,000. Using a decision tree analysis, it is found that the expected monetary value with no survey is $49,000. If the expected value of sample information is -$4,000, what is the expected monetary value with the survey?

Answer: EV with SI = 49,000 - $4,000 + 5,000 = $50,000

A decision table is sometimes called a payout table.

Answer: TRUE

Any problem that can be presented in a decision table can also be graphically portrayed in a decision tree.

Answer: TRUE

In a decision table, all of the alternatives are listed down the left side of the table, while all of the possible outcomes or states of nature are listed across the top.

Answer: TRUE

It is possible for an alternative to be the best among all decision criteria.

Answer: TRUE

The decision theory processes of maximizing expected monetary value (EMV) and minimizing expected opportunity loss (EOL) should lead us to choose the same alternatives.

Answer: TRUE

The difference in decision making under risk and decision making under uncertainty is that under risk, we think we know the probabilities of the states of nature, while under uncertainty we do not know the probabilities of the states of nature.

Answer: TRUE

The several criteria (maximax, maximin, equally likely, criterion of realism, minimax regret) used for decision making under uncertainty may lead to the choice of different alternatives.

Answer: TRUE

To determine the effect of input changes on decision results, we should perform a sensitivity analysis.

Answer: TRUE

111) Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20 percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation. There are two possible sites under consideration. One is relatively small, while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a profit of $80,000, but he will lose $30,000 if demand is low. He also has the option of not opening either. He believes that there is a 50 percent chance that demand will be high. Mark can purchase a market research study. The probability of a good demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.1. There is a 60 percent chance that the study will be favorable. Should Mark use the study? Why? What is the maximum amount Mark should be willing to pay for this study? What is the maximum amount he should pay for any study?

Answer: Yes, he should use the study. His EMV with the study is $34,800 while the highest EMV without the study is $25,000. He should pay no more than $9,800 for this study. He should pay no more than $10,000 for a "perfect" study.

David N. Goliath is planning to open a sporting goods store. However, the initial investment is $120,000. He currently has this money in a certificate of deposit earning 10 percent. He may leave it there if he decides not to open the store. If he opens the store and it is successful he will generate a profit of $50,000. If it is not successful, he will lose $90,000. What would the probability of a successful store have to be for David to prefer this to investing in a CD?

Answer: p(50,000) - (1 - p)(90,000) > 0.10(120,000), therefore p > 0.7286

Which of the following is true about the expected value of perfect information?

It is calculated as expected value with perfect information minus maximum EMV.

The equally likely criterion is also called the ________ criterion.

Laplace

What is the difference between the Expected Monetary Value and Expected Value with Perfect Information?

The Expected Monetary Value looks at the best long run, weighted average outcome by probability, while the Expected Value with Perfect Information assumes that one will have the ability to select the best alternative, knowing the probabilistic

Robert Weed is considering purchasing life insurance. He must pay a $180 premium for a $100,000 life insurance policy. If he dies this year, his beneficiary will receive $100,000. If he does not die this year, the insurance company pays nothing and Robert must consider paying another premium next year. Based on actuarial tables, there is a 0.001 probability that Robert will die this year. If Robert wishes to maximize his EMV, he would not buy the policy if the EMV were negative for him. He has determined that the EMV is, negative for him, but decides to purchase the insurance anyway. Why?

While the EMV is negative, the utility gained from purchasing the insurance is positive, and high.

Decision trees are particularly useful when

a sequence of decisions must be made

How are decision tables organized?

alternatives down the left, states of nature on top, payoffs inside

the following are characteristics of a good decision?

based on logic, considers all available data, considers all possible alternatives, employs appropriate quantitative techniques

In the construction of decision trees, which of the following shapes represents a state of nature node?

circle

In decision theory, we call the payoffs resulting from each possible combination of alternatives and outcomes

conditional values

Briefly describe decision tree analysis.

define the problem, draw the tree, assign the probabilities to the states of nature, estimate payoffs for each alternative, compute EMV

Expected monetary value (EMV)

is the average or expected monetary outcome of a decision if it can be repeated a large number of times.

(b) What would be the best decision based on Hurwicz's criterion of realism using α = 0.6?

large facility - weighted average = $400

The optimistic decision criterion is the criterion of

maximax

A pessimistic decision making criterion is

maximin

A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd). If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine: minimum expected opportunity loss (EOL).

minimum EOL = $1,600