Exam 22: Decision Analysis

Car Audio Store For a car audio store,a payoff table,the prior probabilities for two states of nature,and the likelihood probabilities are shown below: Payoff Table: Alternative state of Natura 20 28 33 32 29 25 -{Car Audio Store Narrative} Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome I₁.

In making decisions,we choose the decision with the largest expected monetary value,or the smallest expected opportunity loss.

Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. States of Nature 12 -2 4 10 5 -{Gross Profits Narrative} The opportunity loss for a₂ when s₁ occurs is________________.

Which of the following is true?

The expected monetary value (EMV)decision is always the same as the expected opportunity loss (EOL)decision because the opportunity loss table is produced directly from the payoff table.

What is meant by the expected monetary value (EMV)of a decision alternative?

Incentive programs for sales staff would be considered a state of nature for a business firm.

Container Company A company must decide whether or not to change its packaging to a more environmentally safe material.The impact of the decision on profits depends on which of the following three possible scenarios develops in the future. Scenario 1: 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 $35 million if they change their packaging now,but will make $75 million if they do not change their packaging now. Scenario 2: 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 $50 million if they change their packaging now,but will make $55 million if they do not change their packaging now. Scenario 3: 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 $60 million if they change their packaging now,but will make only $15 million if they do not change their packaging now. The prior probabilities of the three scenarios are 0.3,0.5,and 0.2,respectively. -{Container Company Narrative} What decision will be made to maximize expected payoff?

Hobby Shop A payoff table and the prior probabilities for two states of nature for a Hobby Shop are shown below: Payoff Table: Alternative state of Natura 20 28 33 32 29 25 Prior Probabilities: P(s₁)= 0.4,and P(s₂)= 0.6. -{Hobby Shop Narrative} Set up the opportunity loss table.

Custom Home Designs Three different designs are being considered for new custom homes,and profits will depend on the combination of the custom home design and market condition.The following payoff table summarizes the decision situation,with amounts in millions of dollars. $\text { Alernative (Design) }$ State of Nature (Market condition) \ 30 \ 20 \ 10 \ 19 \ 21 \ 15 \ 11 \ 23 \ 45 Assume that the following probabilities are assigned to the three market conditions: P(s₁)= 0.1,P(s₂)= 0.6,and P(s₃)= 0.3. -{Custom Home Designs Narrative} Determine the expected payoff that would be realized if perfect information were available.

If EMV(a₁)= $50,000,EMV(a₂)= $65,000,and EMV(a₃)= $45,000,then EMV^* = $160,000.

The expected value of perfect information (EVPI)is always the same as the expected opportunity loss for the best alternative.That is,EVPI = EOL^*.

Gas Company A payoff table for an electric company is shown below: Altrnative State of Nature 7 0 4 6 2 4 3 5 The following prior probabilities are assigned to the states of nature: P(s₁)= 0.3,P(s₂)= 0.7. -{Gas Company Narrative} Calculate the expected opportunity loss for each act with present information.What decision should be made using the EOL criterion?

A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a:

A(n)____________________ tree is helpful in describing the acts and states of nature,and for making calculations involving these items easier.

Food Market The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature for a new food market: The prior probabilities of the states of nature are: P(s₁)= 0.2,P(s₂)= 0.3,and P(s₃)= 0.5. -{Food Market Narrative} Calculate the expected opportunity loss for each act with present information.What decision should be made using the EOL criterion?

The difference between expected payoff under certainty and expected value of the best act without certainty is the:

Maintenance Company For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below: Payoff Table: Alternative syate of Nature 80 120 90 60 130 170 200 140 100 Prior Probabilities: P(s₁)= 0.4,P(s₂)= 0.5,and P(s₃)= 0.1. Likelihood Probabilities: 0.5 0.3 0.2 0.2 0.6 0.2 0.1 0.2 0.7 -{Maintenance Company Narrative} Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome I₁.

Gross Profits The following payoff table shows gross profits (in $1000)associated with a set of 3 acts under 2 possible states of nature. States of Nature 12 -2 4 10 5 -{Gross Profits Narrative} If the probability of s₁ is 0.2 and s₂ is 0.8,then the expected opportunity loss (EOL)for a₁ is ____________________.

Maintenance Company For a maintenance company,a payoff table,the prior probabilities for three states of nature,and the likelihood probabilities are shown below: Payoff Table: Alternative syate of Nature 80 120 90 60 130 170 200 140 100 Prior Probabilities: P(s₁)= 0.4,P(s₂)= 0.5,and P(s₃)= 0.1. Likelihood Probabilities: 0.5 0.3 0.2 0.2 0.6 0.2 0.1 0.2 0.7 -{Maintenance Company Narrative} What is the expected payoff with perfect information?