Exam 12: Decision Analysis

Consider a decision situation with four possible states of nature: s1, s2, s3, and s4. The prior probabilities are P(s1) = 0.35, P(s2) = 0.15, P(s3) = 0.20, P(s4) = 0.30. The conditional probabilities are P(C|s1) = 0.2, P(C|s2) = 0.09, P(C|s3) = 0.15, and P(C|s4) = 0.20. Find the revised (posterior) probabilities P(s1|C), P(s2|C), P(s3|C), and P(s4|C).

The following payoff table shows the profit for a decision problem with three states of nature and three decision alternatives: a. Suppose P(s1) = 0.1, P(S2) = 0.3, and P(S3) = 0.6. What is the best decision using the expected value approach? b. Suppose that the probability of sate of nature, s1, s2, and s3 changes to 0.4, 0.2, and 0.4, respectively. What is the best decision using the expected value approach in this case?

Choosing a decision alternative that maximizes the minimum profit is a feature of the _____ approach.

An intersection or junction point of a decision tree is called a(n) _____.

Which of the following tools is used to create decision trees in Excel?

Lines showing the alternatives from decision nodes and the outcomes from chance nodes are called _____.

The parameter R in an exponential utility function represents

For a minimization problem, the conservative approach often is referred to as the _____ approach.

The following table provides information about the profit payoff of an investment strategy. a. What is the optimal decision strategy if perfect information were available? b. What is the expected value for the decision strategy developed in part a? c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? d. What is the expected value of perfect information?

A Manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars. The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows: P(F|Up) = 0.5; P(F|Stable) = 0.3; P(F|Down) = 0.2 P(U|Up) = 0.2; P(U|Stable) = 0.3; P(U|Down) = 0.5 Use Bayes' theorem to compute the conditional probability of the demand being up, stable, or down, given each market research outcome.

The states of nature are defined so that they are _____. This means that at least one state of nature must occur at a given time for a chance event.

_____ is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.

Meega airlines decided to offer direct service from Akron to Clearwater beach, Florida. Management must decide between full-price service using a company's new fleet of jet aircraft and a discount-service using smaller capacity commuter planes. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service on Clearwater beach: high, moderate, and low. The following table shows the estimated quarterly profits (in thousands of dollars): The probabilities for the demand is P(High) = 0.3, P(Medium) = 0.5, and P(Low) = 0.2, respectively. a. What is the optimal decision strategy if perfect information were available? b. What is the expected value for the decision strategy developed in part a? c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? d. What is the expected value of perfect information?

For a particular maximization problem, the payoff for best decision alternative is $15.7 million while the payoff for one of the other alternatives is $12.9 million. The regret associated with the alternate decision would be

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as _____.

A construction company must decide on the size of the shopping mall, i.e. Large, Medium or Small, that has to be constructed in their acquired plot in the sub-urban area of Seattle. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low. The level of response and the size of the mall will decide the return of investment from the mall. The profit payoff table for management (in millions of dollars) after 5 years is provided below. The probabilities are P(High) = 0.35, P(Moderate) = 0.40, and P(Low) = 0.25. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether the construction company should attempt to obtain a better estimate of the response.

Greentrop Pharmaceutical Products are the world leader in the area of sleep aids. Its major product is "Dozealot". The Research-and-Development Division has defined two alternatives to improve the quality of the product, which are simple reformulations of the product to minimize the side effects and to improve the product efficacy. To conduct an analysis, management has decided to consider the possible demands for the drug under each alternative. The following payoff table shows the projected profit in millions of dollars. a. Construct a decision tree for this problem. b. If the decision maker knows nothing about the probabilities of three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

Bayes' theorem

_____ are possible outcomes for chance events that affect the consequences associated with a decision alternative.

The amount of loss (lower profit or higher cost) from not making the best decision for each state of nature is known as _____.