Exam 13: Decision Analysis

Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.

A decision tree

​When consequences are measured on a scale that reflects a decision maker's attitude toward profit, loss, and risk, payoffs are replaced by

Dollar Department Stores has just acquired the chain of Wenthrope and Sons Custom Jewelers. Dollar has received an offer from Harris Diamonds to purchase the Wenthrope store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future profitability, based on economic outcomes, as: P($80,000) = .2, P($100,000) = .3, P($120,000) = .1, and P($140,000) = .4. a.Should Dollar sell the store on Grove Street? b.What is the EVPI? c.Dollar can have an economic forecast performed, costing $10,000, that produces indicators I₁ and I₂, for which P(I₁ | 80,000) = .1; P(I₁ | 100,000) = .2; P(I₁ | 120,000) = .6; P(I₁ | 140,000) = .3. Should Dollar purchase the forecast?

In an influence diagram, decision nodes are represented by

A chemical company is trying to decide whether to build a pilot plant now for a new chemical process or to build the full plant now. If they build a pilot plant now, they could expand it later to a full plant or license the plant to another company. It would cost them $2 million to build the pilot plant and another $2 million later to expand it. If they build the full plant now it would cost $3.5 million to construct. ​ The returns they expect to get from the full production plant depend upon the market. They estimate there is a 60% chance the market will be robust, a 30% chance it will remain stable, and a 10% chance it will become stagnate. The returns are estimated to be $5 million if it is robust, $3 million if it is stable, and $1 million if it is stagnate. ​ Before they expand the pilot plant, they plan to conduct a comprehensive study. Based on past experience, they expect the study to report a 60% chance of favorable outcome for expansion and a 40% unfavorable chance. In either case they will have to decide whether to expand to a full plant or license the pilot plant. If the report is favorable and they license it, they expect to get $3 million. However, if the report is unfavorable and they license it, they will only get $1 million. ​ Develop a decision tree for this problem and determine the optimal decision strategy.

EVPI is always greater than or equal to EVSI.

Sample information with an efficiency rating of 100% is perfect information.

A decision maker has developed the following decision tree. How sensitive is the choice between N and P to the probabilities of states of nature U and V?

​The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

The efficiency of sample information is

​A risk avoider will have a concave utility function.

​The expected utility is the utility of the expected monetary value.

Use a diagram to compare EVwPI, EVwoPI, EVPI, EVwSI, EVwoSI, and EVSI.

Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature?

The expected value of sample information can never be less than the expected value of perfect information.

The minimum expected opportunity loss provides the best decision, regardless of whether the decision analysis involves minimization or maximization.