Exam 21: Decision-Making Tools

A decision-maker using the maximax criterion on the problem below would choose Alternative __________ because the maximum of the row maximums is __________. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{ \text { States of Nature } } \\ \begin{array} { | l | c | c | c | } \hline & 1 & 2 & 3 \\ \hline \text { Alternative A } & 50 & 55 & 60 \\ \hline \text { Alternative B } & 30 & 50 & 80 \\ \hline \text { Alternative C } & 70 & 80 & 70 \\ \hline \text { Alternative D } & - 100 & - 10 & 140 \\ \hline \end{array}

What is the EMV for Option 2 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}

Decision trees and decision tables can both solve problems requiring a single decision, but decision tables are the preferred method when a sequence of decisions is involved.

The following decision tree has how many state of nature nodes

Bratt's Bed and Breakfast, in a small historic New England town, must decide how to subdivide (remodel) the large old home that will become their inn. There are three alternatives: Option A would modernize all baths and combine rooms, leaving the inn with four suites, each suitable for two to four adults. Option B would modernize only the second floor; the results would be six suites, four for two to four adults, and two for two adults only. Option C (the status quo option) leaves all walls intact. In this case, there are eight rooms available, but only two are suitable for four adults, and four rooms will not have private baths. Below are the details of profit and demand patterns that will accompany each option. Which option has the highest expected value? Annual profit under various demand patterns Capacity Average A (Modernize all) \ 90,000 .5 \ 25,000 .5 B (Modernize 2 (nd) \ 80,000 .4 \ 70,000 .6 (Status Quo) \ 60,000 .3 \ 55,000 .7

What is the expected value of perfect information of 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}

Doing nothing would yield how much profit if favorable market conditions prevail according to the following decision table? Alternative Favorable market Unfavorable Market Do Nothing \ 20,000 -\ 10,000

Expected monetary value is most appropriate for problem solving that takes place

A decision maker who uses the maximin criterion when solving a problem under conditions of uncertainty is

The square symbol used in drawing a decision trees represents a __________ node.

If a decision maker can assign probabilities of occurrences to the states of nature, then the decision-making environment is Decision Making under Uncertainty.

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 largest conditional value (profit) in the entire payoff table for this scenario is

There are three equally likely states of nature (High, Medium, and Low demand). If the large factory will post profits of $50,000, $25,000, and - $10,000 under these states of nature, respectively, what is the EMV of the factory?

A square node on a decision tree infers that

A do-it-yourself homeowner is installing a new toilet. While installing the toilet he must decide on what kind of connecting pipe he will install to the water supply. There are two available options, one that has a shut-off valve in case of a leak and a cheaper one without the shut-off valve. Suppose that the shut-off valve pipe costs an extra ten dollars and that the homeowner must buy one of the two. a. Draw a decision tree for this scenario, labeling the cost of a leak as X and the chance of a leak as P. b. If the chance of a leak causing household damage is 1%, at what $ amount of household damage is the owner neutral on which pipe to buy? c. If the cost of a leak would be $10,000 what is the maximum % chance to leak at which the homeowner would prefer to buy the cheaper pipe? d. If the cost of a leak is $1,000 and the chance to flood .1% which pipe should the homeowner buy?

__________ is the criterion for decision making under certainty that assigns equal probability to each state of nature.

The last step in the analytic decision process clearly defines the problem and the factors that influence it.

A decision-maker using the maximin criterion on the problem below would choose Alternative __________ because the maximum of the row minimums is __________. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{ \text { States of Nature } } \\ \begin{array} { | l | c | c | c | } \hline & \underline { 1 } & \underline { 2 } & \underline { 3 } \\ \hline \text { Alternative A } & 50 & 55 & 60 \\ \hline \text { Alternative B } & 30 & 50 & 80 \\ \hline \text { Alternative C } & 70 & 80 & 70 \\ \hline \text { Alternative D } & - 100 & - 10 & 140 \\ \hline \end{array}

How is the expected value of perfect information (EVPI) found?

In terms of decision theory, an occurrence or situation over which the decision maker has no control is called a(n)