Exam 18: Decision-Making Tools

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.

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 $120 per day in fair weather, $10 per day in bad weather. At home, he will profit $70 in fair weather, $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather. a. Construct Earl's decision tree. b. What decision is recommended by the expected value criterion?

A decision-maker using the maximax criterion on the problem below would choose Alternative ________ because the maximum of the row maximums is ________. States of Nature 1 2 3 Alternative A 50 55 60 Alternative B 30 50 80 Alternative C 70 80 70 Alternative D -100 -10 140

Suppose a manufacturing plant is considering three options for expansion. The first one is to expand into a new plant (large), the second to add on third-shift to the daily schedule (medium), and the third to do nothing (small). There are three possibilities for demand. These are high, medium, and low with each having an equal likelihood of occurring. Suppose that the profits for the expansion plans are as follows (respective to high, medium, low demand). The large expansion profits are $100000, $10000, -$10000, the medium expansion choice $40000, $40000, $5000 and the small expansion choice $15000, $15000, $15000. Calculate the EMV of each choice. Which of the expansion plans should the manager choose?

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. Light Demand Moderate Demand Heavy Demand Probability 0.25 0.45 0.3 Wind-up action \ 325,000 \ 190,000 \ 170,000 Pneumatic action \ 300,000 \ 420,000 \ 400,000 Electrical action -\ 400,000 \ 240,000 \ 800,000 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?

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?

The expected value with perfect information is

Decision trees

What is the EMV for Option 2 in the following decision table? States of Nature Alternatives .4 .6 Option 1 10,000 30,000 Option 2 5,000 45,000 Option 3 -4,000 60,000

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

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

Bratt's Bed and Breakfast, in a small historic Prince Edward Island 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 P Average p A (Modernize all) US \ 90,000 5 US \ 25,000 5 B (Modernize 2nd) US \ 80,000 4 US \ 70,000 6 C (Status Quo) US \ 60,000 3 US \ 55,000 7

The EMV of a decision with three states of nature is $33,000. If the profit/value under the states of nature A, B, and C is $10,000, $20,000, and $50,000 and states B and C have equal probabilities, determine the likelihood of state of nature A.

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?

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

A problem that involves a sequence of decisions

In a decision tree, a square symbol represents a state of nature node.

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?

The last step of the decision-making process is to

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?