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Exam 13: Decision Analysis

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Question 21

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Fold back the decision tree and state what strategy should be followed.

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Strategy: Select A....

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Question 22

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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. $\begin{array} { c | c c c } \text { Order Size } & \text { Low } & \begin{array} { c } \text { Demand } \\\text { Medium }\end{array} & \text { High } \\\hline \text { 1 lot } & 12 & 15 & 15 \\\text { 2 lots } & 9 & 25 & 35 \\\text { 3 lots } & 6 & 35 & 60\end{array}$ 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?

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a.3 lots
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Question 23

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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. $\begin{array} { c | r r } && { \text { State of Nature } } \\\text { Decision } & s _ { 1 } & s _ { 2 } \\\hline d _ { 1 } & 8 & 10 \\d _ { 2 } & 4 & 16 \\d _ { 3 } & 10 & 0\end{array}$

A payoff

To find the EVSI,

A payoff table is given as $\begin{array} { c | r r r } & & { \text { State of Nature } } \\\text { Decision } & \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \\\hline d_{1} & 10 & 8 & 6 \\d_{2} & 14 & 15 & 2 \\d_{3} & 7 & 8 & 9\end{array}$ a.What decision should be made by the optimistic decision maker? b.What decision should be made by the conservative decision maker? c.What decision should be made under minimax regret? d.If the probabilities of s₁, s₂, and s₃ are .2, .4, and .4, respectively, then what decision should be made under expected value? e.What is the EVPI?

EVPI $\ge$ EVSI

A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to be determined outcomes of chance events.

Which of the methods for decision making without probabilities best protects the decision maker from undesirable results?

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 decision maker has developed the following decision tree. How sensitive is the choice between N and P to the probabilities of states of nature U and V?

Show how you would design a spreadsheet to calculate revised probabilities for two states of nature and two indicators.

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

Decision alternatives are structured so that several could occur simultaneously.

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.

Dollar Department Stores has received an offer from Harris Diamonds to purchase Dollar's store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future profitability, based on economic outcomes, as: P($80,000) = .2, P($100,000) = .3, P($120,000) = .1, and P($140,000) = .4. a.Should Dollar sell the store on Grove Street? b.What is the EVPI? c.Dollar can have an economic forecast performed, costing $10,000, that produces indicators I₁ and I₂, for which P(I₁ $\mid$ 80,000) = .1; P(I₁ $\mid$ 100,000) = .2; P(I₁ $\mid$ 120,000) = .6; P(I₁ $\mid$ 140,000) = .3.Should Dollar purchase the forecast?

Use a diagram to compare EVwPI, EVwoPI, EVPI, EVwSI, EVwoSI, and EVSI.

Decision tree probabilities refer to

Sample information with an efficiency rating of 100% is perfect information.

The efficiency of sample information is