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Exam 21: Decision-Making Tools

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Question 21

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Earl Shell owns his own Sno-Cone business and lives 30 miles from a beach resort. The sale of Sno-Cones is highly dependent upon his location and upon the weather. At the resort, he will profit $110 per day in fair weather, $20 per day in foul weather. At home, he will profit $70 in fair weather, $50 in foul weather. Assume that on any particular day, the weather service suggests a 60% chance of fair weather. a. Construct Earl's payoff table. b. What decision is recommended by the expected value criterion? c. What is the EVPI?

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(a)The payoff table is

(b) the EMV fo...

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Question 22

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A(n) __________ is a graphical means of analyzing decision alternatives and states of nature.

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If a decision maker knows for sure which state of nature will occur, he/she is making a decision under certainty.

If a decision maker is a pessimist, what decision-making criterion is appropriate? Why?

A plant manager wants to know how much he should be willing to pay for perfect market research. Currently there are two states of nature facing his decision to expand or do nothing. Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant. Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0. If the two states of nature are equally likely, how much should he pay for perfect information?

A toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows. $\begin{array} { | l | c | c | c | } \hline & \text { Light Demand } & \begin{array} { c } \text { Moderate } \\\text { Demand }\end{array} & \text { Heavy Demand } \\\hline \text { Probability } & 0.25 & 0.45 & 0.3 \\\hline \text { Wind-up action } & \$ 325,000 & \$ 190,000 & \$ 170,000 \\\hline \text { Pneumatic action } & \$ 300,000 & \$ 420,000 & \$ 400,000 \\\hline \text { Electrical action } & - \$ 400,000 & \$ 240,000 & \$ 800,000 \\\hline\end{array}$ a. What is the EMV of each decision alternative? b. Which action should be selected? c. What is the expected value with perfect information? d. What is the expected value of perfect information?

Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices. $\begin{array} { | l | c | c | c | } \hline & { \text { States of Nature } } \\\hline \text { Alternatives } & \text { Lower gas prices } & \text { Gas prices unchanged } & \text { Higher gas prices } \\\hline \text { probability } & .3 & .5 & .2 \\\hline \text { Subcompact } & 16,000 & 21,000 & 23,000 \\\hline \text { Compact } & 15,000 & 20,000 & 22,000 \\\hline \text { Full size } & 18,000 & 19,000 & 6,000 \\\hline\end{array}$ Calculate the expected monetary value for each decision alternative. Which decision yields the highest EMV?

All of the following steps are taken to analyze problems with decision trees except

A state of nature is an occurrence of a situation over which the decision maker has little or no control.

Daily sales of bread by Salvador Monella's Baking Company follow the historical pattern shown in the table below. It costs the bakery 50 cents to produce a loaf of bread, which sells for 95 cents. Any bread unsold at the end of the day is sold to the parish jail for 25 cents per loaf. Construct the decision table of conditional payoffs. How many loaves should Sal bake each day in order to maximize contribution? $\begin{array} { | l | c | c | c | c | c | } \hline \text { Demand } & 400 & 500 & 600 & 700 & 800 \\\hline \text { Probability } & .20 & .20 & .40 & .15 & .05 \\\hline\end{array}$

The first step, and a key element, in the decision-making process is to

__________ is the difference between the payoff under perfect information and the payoff under risk.

A retailer is deciding how many of a certain product to stock. The historical probability distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1. The product costs $8 per unit and sells for $25 per unit. The conditional value for the decision alternative "Stock 3" and state of nature "Sell 1" is

What is the EMV for Option 1 in the following decision table? $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{ \text { States of Nature } } \\\begin{array} { | l | c | c | } \hline \text { Alternatives } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } \\\hline \mathrm { p } & .4 & .6 \\\hline \text { Option 1 } & 10,000 & 30,000 \\\hline \text { Option 2 } & 5,000 & 45,000 \\\hline \text { Option 3 } & -4,000 & 60,000 \\\hline\end{array}$

A decision tree is a(n)

What is a conditional value?

What is the EMV for Option 1 in the following decision table? $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{ \text { States of Nature } } \\\begin{array} { | l | c | c | } \hline \text { Alternatives } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } \\\hline \mathrm { p } & .6 & .4 \\\hline \text { Option 1 } & 200 & 300 \\\hline \text { Option } 2 & 50 & 350 \\\hline\end{array}$

A local business owner is a bit uncertain of the demand forecast, and is timidly approaching the capacity decision for a business he is about to open. Here's how he describes the decisions that confront him over the next two years."First, I have to choose between building a large plant initially and building a small one that has room to expand. Or I could rent now, and decide whether to build next year. That one, too, could be the large version or the small. If I build small, then after one year, I can review how good business was, and decide whether to expand. If I build large, there is no further option to enlarge."Do not concern yourself with probabilities or payoff values .Simply draw the tree that illustrates the manager's decision alternatives and the chance events that go along with them. Use standard symbols for decision tree construction, and label all parts of your diagram carefully. To simplify, assume that business in the first year, and in the second, can be only "good" or "bad."

A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a(n)

The expected value of perfect information is the same as the expected value with perfect information.