Exam 19: Decision Theory

State of Nature The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature: State of Nature Alternative I Prob. = II Prob. = III Prob. = A \ 110 \ 80 -\ 20 B \ 90 \ 85 \ 10 C \ 45 \ 65 \ 45 D \ 30 \ 60 \ 65 E \ 10 \ 25 \ 70 -Calculate the expected payoff with perfect information (in thousands of dollars). ____________________ thousand

The level of doubt regarding the decision situation where both the possible states of nature and their exact probabilities of occurrence are known is which of the following?

When Jessica takes the direct route to work,she gets there in 25 minutes if no train is at the railroad crossing.When a train is using the crossing,her travel time is 10 minutes longer.Her alternative is a route that takes 32 minutes to travel,but has no traffic signals or other delays.Assuming that shorter transit times are more desirable,which route will Jessica select if she uses the minimax regret criterion? Explain.

Canoe rentals John's Canoe Rentals leases canoes each day from a supplier and rents them to customers who use them to float down the Delaware River.Each day,John can lease 10,20,or 30 canoes from his supplier.John assumes daily demand will be either 10,20,or 30 canoes.The payoff table for each lease/demand combination is shown below. PAYoFFE Demand Altemitives \ 140 \ 140 \ 140 -\ 20 \ 280 \ 280 30 -\ 180 \ 120 \ 420 -How many canoes should be leased using the maximin criterion?

A decision situation can be expressed as either a payoff table or a decision tree diagram.

Scenario A company must decide whether or not to change its packaging now to a more environmentally safe material.The impact of the decision on profits depends on which future scenario develops.Scenario 1 is that the media does not focus heavily on concerns about packaging and no new laws requiring changes in packaging are passed.Under this scenario,the company will make $30 million if they change their packaging now,but will make $70 million if they do not change their packaging now.Scenario 2 is that the media does focus heavily on concerns about packaging and no new laws requiring changes in packaging are passed.Under this scenario,the company will make $45 million if they change their packaging now,but will make $50 million if they do not change their packaging now.Scenario 3 is that the media does focus heavily on concerns about packaging and new laws requiring changes in packaging are passed.Under this scenario,the company will make $55 million if they change their packaging now,but will make only $10 million if they do not change their packaging now.The probabilities of the three scenarios are 0.3,0.5,and 0.2,respectively. -What decision will be made using the maximax criterion?

A person bets his remaining savings on a horse race based on the large payoff if his horse wins.Which of the following decision making criteria does this typify?

Decisions can never be made without the benefit of knowledge gained from sampling.

Market Condition Three different designs are being considered for a new refrigerator,and profits will depend on the combination of the refrigerator design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. Market Condition Design I II III 27 16 8 17 18 20 7 12 42 -What decision will be made using the maximin criterion?

The expected opportunity loss for the alternative having the maximum expected payoff is the expected value of perfect information.

Define expected payoff of a decision alternative.

Which of the following represents behavior of risk avoidance?

Market Condition Three different designs are being considered for a new refrigerator,and profits will depend on the combination of the refrigerator design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. Market Condition Design I II III 27 16 8 17 18 20 7 12 42 -What decision will be made using the maximax criterion?

The expected value of perfect information is the same as:

Incremental analysis involves the key terms of ______________________________ and ___________________________________.

What is meant when we say that the states of nature in the payoff table must be mutually exclusive and exhaustive?

Tee shirts Tee Shirts Unlimited is providing shirts for an upcoming sports tournament.They assume demand will be either 2000,3000,4000,or 5000 shirts and they need to decide whether to produce 2000,3000,4000,or 5000 shirts.The payoff for each production/demand combination is shown in the table below. PAYOFFE Demand Altematives \ 10,000 \ 10,000 \ 10,000 \ 10,000 \ \ 15,000 \ 15,000 \ 15,000 -\ 4,000 \ \ 20,000 \ 20,000 -\ 11,000 \ 1,000 \ 13,000 \ 25,000 -How many shirts should be produced using the maximax criterion?

Market Condition Three different designs are being considered for a new refrigerator,and profits will depend on the combination of the refrigerator design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. Market Condition Design I II III 27 16 8 17 18 20 7 12 42 -Convert the payoff table to a regret table

In what way are the minimax regret criterion and the expected opportunity loss (EOL)criterion similar? In what ways do they differ?

Competitor's Price ABC Industries is about to launch a new product and must decide to set the price of the product at either high,medium,or low.The annual payoff for ABC will depend on the price set on a competing product that will be introduced in the near future.The table below shows the annual payout for each combination of prices. Competitor's Price AEC Price High Medium Law High \ 60,000 \ 25,000 -\ 20,000 Medium \ 35,000 \ 46,000 -\ 4,000 Lan \ 18,000 \ 12,000 \ 8,000 -What price should ABC choose using the maximin criterion?