Exam 12: Decision Analysis

Reference - 12.2: Use the data below and Bayes' theorem to answer questions 34-35. -Reference - 12.2: Which of the following would be the posterior probabilities, P(Sj|U)?

The probabilities of both sample information and a particular state of nature occurring simultaneously are termed as _____.

Reference - 12.2: Use the data below and Bayes' theorem to answer questions 34-35. -Reference - 12.2: What would be the joint probabilities, P(U ∩ Sj)?

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars): The indifference probabilities are as follows: If P(s₁) = 0.30, P(s₂) = 0.55, and P(s₃) = 0.15, find a recommended decision for each of the three decision makers.

The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River Basin. The mining company is considering two payment-plan options to buy the mines: I. 100% Payment II. Installment-Payment The payoff received will be based on the quality of coal obtained from the mines which has been categorized as High, Normal, and Poor Quality as well as the payment plan. The profit payoff in million dollars resulting from the various combinations of options and quality are provided below: a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event? b. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

_____ refers to the probability of one event, given the known outcome of a (possibly) related event.

Emil Hansen is interested in leasing a sports-utility vehicle and has contacted three automobile dealers for pricing information. Each dealer offered Emil 24-month lease with no down payment due at the time of signing. Each lease includes a monthly cost, mileage allowances, and the cost for additional miles and the details are given in the below table. Emil decided to choose the lease option that will minimize his total 24-month cost. Emil is not sure how many miles he will drive in the next two years. Hence, for the purpose of decision, assume that Emil wants to evaluate options of driving 20,000 miles per year, 23,000 miles per year, and 25,000 miles per year. a. Construct a decision tree based on the payoff table constructed in the previous problem. b. Recommend a decision based on the use of optimistic, conservative, and minimax regret approaches?

Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R = 6450: -$3000, -$1500, $0, $1500, $3000, $4500, $6000, $7500, $9000.

Reference - 12.1: Use the payoff table given below for a maximization problem to answer questions 18-19. -Reference - 12.1: Which is the recommended decision alternative using the conservative approach?

_____ refer to graphical representations of the decision problems that show the sequential nature of the decision-making process.

Chance nodes are

A _____ is a decision maker who would choose a guaranteed payoff over a lottery with a better expected payoff.

For a minimization problem, the optimistic approach often is referred to as the _____ approach.

No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are _____.

Harold has visited a casino and paid an entry fee of $20,000 to play the game of cards. Below is the payoff table in terms of the decision to play or not to play the game (Note: Harold will not pay the entry fee if he does not want to play and the below payoff table includes the entry fee): a. In his previous visits, Harold has won 1 out of every 5 games that he has played. Use the expected value approach to recommend a decision. b. Assume that the utilities for 50,000 and -20,000 are 10 and 0, respectively. If a particular decision maker assigns an indifference probability of 0.0001 to the $0 payoff, would Harold play the game? Use expected utility to justify your answer.

Which of the following is true of decision trees when used to solve a complex problem?

A manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars. The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether the manufacturing company should attempt to obtain a better estimate of the response.

For a maximization problem, the optimistic approach often is referred to as the _____ approach.

What would be the value added by a market analysis undertaken, if the expected value with sample information is $8.56 million and the expected value without sample information is $6.39 million?

The _____ approach evaluates each decision alternative in terms of the best payoff that can occur.