Exam 18: Statistical Tools for Managers

The maximax criterion of decision making requires that all decision alternatives have an equal probability of occurrence.

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

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

An operations manager's staff has compiled the information below for four manufacturing alternatives (A, B, C, and D) that vary by production technology and the capacity of the machinery. All choices enable the same level of total production and have the same lifetime. The four states of nature represent four levels of consumer acceptance of the firm's products. Values in the table are net present value of future profits in millions of dollars. a. Assuming a maximax strategy, which alternative would be chosen? b. If maximin were used, which would be chosen? c. If the states of nature were equally likely, which alternative should be chosen?

Analytic decision making is based on logic and considers all available data and possible alternatives.

In the context of decision-making, define alternative.

The decision criterion that would be used by an optimistic decision maker solving a problem under conditions of uncertainty would be the

Doing nothing would yield how much profit if favorable market conditions prevail according to the following decision table?

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

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.

__________ is the criterion for decision making under uncertainty that finds an alternative that maximizes the minimum outcome or consequences.

Describe the meaning of EVPI. Provide an example in which EVPI can help a manager.

The last step of the decision-making process is to

A poker player is considering three different options after his opponent bet 200 before him. If the player folds, he will lose instantly. If the player calls, he figures he will win half the time. If he raises he figures that the opposing player will not re-raise him, but rather will either call or fold. He figures the opposing player will call only ¼ of the time, folding the other ¾ of the time. If the opposing player calls his raise, he figures he will never win. The pot size is 1,000 (including the opposing player's bet). a. Draw a decision tree for this scenario including the information provided in part b. b. Suppose that the player is thinking of raising to $400 (he will put in 200 to match the opponent's bet and another 200 as a raise, his opponent would then have to put in 200 more to call the raise). Is this the best option or should he instead call or fold? c. At what raise size is the player's EMV of a raise equivalent to simply calling?

If a decision maker has to make a certain decision only once, expected monetary value is a good indication of the payoff associated with the decision.

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

The construction manager for Acme Construction, Inc. must decide whether to build single family homes, apartments, or condominiums. This is not a product-mix problem, but an all-or nothing decision. He will hire workers and rent equipment appropriate for one action only. He estimates annual profits (in thousands of dollars) will vary with population trends as follows: a. If he uses the maximin criterion, which type of dwellings will he choose to build? Show your supporting calculations. b. If he uses the equally likely criterion, which kind of dwellings will he choose to build? Show your supporting calculations. c. If the construction manager were an optimist, what criterion would he choose? What would be the choice of dwelling for that criterion? Show your supporting calculations.

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 expected monetary value of a decision alternative is the sum of all possible payoffs from the alternative, each weighted by the probability of that payoff occurring.

What is the EMV for Option 1 in the following decision table?