Exam 13: Decision Analysis

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(n)

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 it builds a pilot plant now,it could expand later to a full plant or license the plant to another company.It would cost $2 million to build the pilot plant and another $2 million later to expand it.If the company builds the full plant now,it would cost $3.5 million to construct.​ The returns the company expects to get from the full production plant depend on the market.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 the company expands the pilot plant,it plans to conduct a comprehensive study.Based on past experience,it expects the study to report a 60% chance of favorable outcome for expansion and a 40% unfavorable chance.In either case,it will have to decide whether to expand to a full plant or license the pilot plant.If the report is favorable and the company licenses it,the company expects to get $3 million.However,if the report is unfavorable and the company licenses it,the company will only get $1 million.​ Develop a decision tree for this problem and determine the optimal decision strategy.

Three decision makers have assessed utilities for the problem whose payoff table appears below.​ ​ ​ a.Plot the utility function for each decision maker. b.Characterize each decision maker's attitude toward risk. c.Which decision will each person prefer? ​ ​

Use graphical sensitivity analysis to determine the range of values of the probability of state of nature s₁ over which each of the decision alternatives has its largest expected value.

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

Utility reflects the decision maker's attitude toward

Super Cola is also considering the introduction of a root beer drink.The company thinks the probability that the product will be a success is 0.6.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)= 0.7 and P(I₁ | s₂)= 0.4.New World Marketing has indicators J₁ and J₂ for which P(J₁ | s₁)= 0.6 and P(J₁ | s₂)= 0.3. 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 $4000,which firm should Super Cola hire?

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

The expected utility approach

A Pacific Northwest lumber company is considering the expansion of one of its mills.The question is whether to do it now or wait one year and reconsider.If it expands now,the major factors are the state of the economy and the level of interest rates.The combination of these two factors results in five possible situations.If it does not expand now,only the state of the economy is important and three conditions characterize the possibilities.The following table summarizes the situation: ​ ​ a.Draw the decision tree for this problem. b.What is the expected value for expanding? c.What is the expected value for not expanding? d.Based on expected value,what should the company's decision(s)be? ​

The expected value of an alternative can never be negative.

Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores.Information on pricing,sales,and inventory costs has led to the following payoff table,in thousands.Show a regret table.​ ​ a.What decision should be made by the optimist? b.What decision should be made by the conservative? c.What decision should be made using minimax regret?

Given two decision makers,one a risk taker and the other a risk avoider,the risk avoider will show a diminishing marginal return for money.

For a chance node,the expected value is the weighted average of the payoffs,where the weights are the state-of-nature probabilities.​

The efficiency of sample information is

After all probabilities and payoffs are placed on a decision tree,the decision maker calculates expected values at state-of-nature nodes and makes selections at decision nodes.

Utility is the term for a measure of the total worth or relative desirability of a particular outcome.

The utility function for a risk avoider typically shows a diminishing marginal return for money.​

The Dollar Department Store chain has the opportunity of acquiring 3,5,or 10 leases from the bankrupt Granite Variety Store chain.Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years.There are four possible states of the economy as modeled by Dollar Department Stores,and its president estimates P(s₁)= 0.4,P(s₂)= 0.3,P(s₃)= 0.1,and P(s₄)= 0.2.The utility has also been estimated.Given the payoffs (in $1,000,000s)and utility values below,which decision should Dollar make? ​ ​ ​

Decision tree probabilities are primarily used to