Exam 12: Decision Analysis

The Hurwicz criterion is a compromise between the maximax and maximin criteria.

The ________ is the maximum amount a decision maker would pay for additional information.

Use the expected value criterion to select the best alternative. Assume that the probability of S2 is equal to 0.4.

The ________ multiplies the decision payoff for each state of nature by an equal weight.

The difference in the expected value with additional information and without additional information is ________.

If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what investment would be made using the expected value criterion?

A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits $800,000. -Draw a decision tree.

An investor is consider four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{ \text { Economic Condition } } \\ \begin{array} { c} \text { Investment } & \begin{array} { c } \text { Poor } \\ \text { (S1) } \end{array} & \begin{array} { c } \text { Average } \\ \left( \mathbf { S } _ { \mathbf { 2 } } \right) \end{array} & \begin{array} { c } \text { Good } \\ \left( \mathbf { S } _ { \mathbf { 3 } } \right) \end{array} & \begin{array} { c } \text { Excellent } \\ \left( \mathbf { S } _ { \mathbf { 4 } } \right) \end{array} \\ \text { A } & 50 & 75 & 20 & 30 \\ \text { B } & 80 & 15 & 40 & 50 \\ \text { C } & - 100 & 300 & - 50 & 10 \\ \text { D } & 25 & 25 & 25 & 25 \end{array} -What decision would be made under maximin?

The ________ is a measure of the decision makers optimism.

Utiles are units of ________ measures of utility.

Regret and opportunity loss mean the same thing.

The quality control manager for ENTA Inc. must decide whether to accept (A1), further analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). 20 30 90 60 70 10 80 50 40 -Construct the regret table.

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code. \# of Workers Low Compliance Medium Compliance High Compliance 1 50 50 50 2 100 60 20 3 150 70 -10 -If he uses the maximin criterion, how many new workers will he hire?

If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what is the expected value of perfect information?

The minimax regret criterion

A small entrepreneurial company is trying to decide between developing two different products that they believe they can sell to two potential companies, one large and one small. If they develop Product A, they have a 50% chance of selling it to the large company with annual purchases of about 20,000 units. If the large company won't purchase it, then they think they have an 80% chance of placing it with a smaller company, with sales of 15,000 units. On the other hand if they develop Product B, they feel they have a 40% chance of selling it to the large company, resulting in annual sales of about 17,000 units. If the large company doesn't buy it, they have a 50% chance of selling it to the small company with sales of 20,000 units. -What is the probability that Product B will being purchased by the smaller company?

The minimax regret criterion minimizes the maximum regret.

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars. School Scenario 1 Scenario 2 Scenario 3 Vanderbilt 95 20 -10 Texas Tech 55 60 60 Seattle 90 10 80 Northeastern State 65 50 60 -Suppose that the likelihood for each of the scenarios 1 through 3 is 0.3, 0.4, and 0.3, respectively. What is the optimal decision under the expected opportunity loss criterion?

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code. \# of Workers Low Compliance Medium Compliance High Compliance 1 50 50 50 2 100 60 20 3 150 70 -10 -If he uses the minimax regret criterion, how many new workers will he hire?

A decision tree is a diagram consisting of circular decision nodes, square probability nodes, and branches.