Exam 13: Decision Analysis

Super Cola is also considering the introduction of a root beer drink. The company feels that the probability that the product will be a success is .6. The payoff table is as follows: ​ The company has a choice of two research firms to obtain information for this product. Stanton Marketing has market indicators, I₁ and I₂ for which P(I₁ | s₁) = .7 and P(I₁ | s₂) = .4. New World Marketing has indicators J₁ and J₂ for which P(J₁ | s₁) = .6 and P(J₁ | s₂) = .3. a.​What is the optimal decision if neither firm is used? Over what probability of success range is this decision optimal? b.What is the EVPI? c.Find the EVSIs and efficiencies for Stanton and New World. d.If both firms charge $5,000, which firm should be hired? e.​If Stanton charges $10,000 and New World charges $4,000, which firm should Super Cola hire? Why?

Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.

Sensitivity analysis considers

​Characterize each of the non-probabilistic approaches to decision making (i.e. - minimin, minimax, maximin, and maximax) in terms of it relating to a minimization or maximization problem and whether it is a pessimistic or optimistic approach.

If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) =

​Draw the utility curves for three types of decision makers, label carefully, and explain the concepts of increasing and decreasing marginal returns for money.

​When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis), the function appears as

​A high efficiency rating indicates that the sample information is almost as good as perfect information.

​Given two decision makers, one risk neutral and the other a risk avoider, the risk avoider will always give a lower utility value for a given outcome.

Fold back this decision tree. Clearly state the decision strategy you determine. ​

For a maximization problem, the conservative approach is often referred to as the

​A risk neutral decision maker will have a linear utility function.

To find the EVSI,

Transrail is bidding on a project that it figures will cost $400,000 to perform. Using a 25% markup, it will charge $500,000, netting a profit of $100,000. However, it has been learned that another company, Rail Freight, is also considering bidding on the project. If Rail Freight does submit a bid, it figures to be a bid of about $470,000. Transrail really wants this project and is considering a bid with only a 15% markup to $460,000 to ensure winning regardless of whether or not Rail Freight submits a bid. a. Prepare a profit payoff table from Transrail's point of view. b. What decision would be made if Transrail were conservative? c. If Rail Freight is known to submit bids on only 25% of the projects it considers, what decision should Transrail make? d. Given the information in (c), how much would a corporate spy be worth to Transrail to find out if Rail Freight will bid?

If p is the probability of Event 1 and (1 − p) is the probability of Event 2, for what values of p would you choose A? B? C? Values in the table are payoffs.

​The approach to determining the optimal decision strategy involves

The Super Cola Company must decide whether or not to introduce a new diet soft drink. Management feels that if it does introduce the diet soda it will yield a profit of $1 million if sales are around 100 million, a profit of $200,000 if sales are around 50 million, or it will lose $2 million if sales are only around 1 million bottles. If Super Cola does not market the new diet soda, it will suffer a loss of $400,000. a. Construct a payoff table for this problem. b. Construct a regret table for this problem. c. Should Super Cola introduce the soda if the company: (1) is conservative; (2) is optimistic; (3) wants to minimize its maximum disappointment? d. An internal marketing research study has found P(100 million in sales) = 1/3; P(50 million in sales) = 1/2; P(1 million in sales) = 1/6. Should Super Cola introduce the new diet soda? e. A consulting firm can perform a more thorough study for $275,000. Should management have this study performed?

Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.

If sample information is obtained, the result of the sample information will be either positive or negative. No matter which result occurs, the choice to select option A or option B exists. And no matter which option is chosen, the eventual outcome will be good or poor. Complete the table.

A payoff table is given as ​ a.What choice should be made by the optimistic decision maker? b.What choice should be made by the conservative decision maker? c.What decision should be made under minimax regret? d.If the probabilities of d₁, d₂, and d₃ are .2, .5, and .3, respectively, then what choice should be made under expected value? e.What is the EVPI?