Exam 13: Decision Analysis

After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state of nature nodes and makes selections at decision nodes.

States of nature

Which of the methods for decision making best protects the decision maker from undesirable results?

How can a good decision maker "improve" luck?

​The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the

?A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(-25000) + (1 - p)(5000). If the utility of -25,000 is 0 and of 5000 is 1, then the utility of -10,000 is

Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a straight commission of $1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month. a. Compute the monthly salary payoff table for Jim. b. For this payoff table find Jim's optimal decision using: (1) the conservative approach, (2) minimax regret approach. c. Suppose that during the past year the following is Jim's distribution of home sales. If one assumes that this a typical distribution for Jim's monthly sales, which salary plan should Jim select?

Show how you would design a spreadsheet to calculate revised probabilities for two states of nature and two indicators.

​When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is

For a minimization problem, the conservative approach is often referred to as the

A payoff table is given as ​ a.What decision should be made by the optimistic decision maker? b.What decision should be made by the conservative decision maker? c.What decision should be made under minimax regret? d.​If the probabilities of s₁, s₂, and s₃ are .2, .4, and .4, respectively, then what decision should be made under expected value? e.What is the EVPI?

​Values of utility

​To assign utilities, consider the best and worst payoffs in the entire decision situation.

Dollar Department Stores has received an offer from Harris Diamonds to purchase Dollar's store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future profitability, based on economic outcomes, as: P($80,000) = .2, P($100,000) = .3, P($120,000) = .1, and P($140,000) = .4. a.Should Dollar sell the store on Grove Street? b.What is the EVPI? c.Dollar can have an economic forecast performed, costing $10,000, that produces indicators I₁ and I₂, for which P(I₁ | 80,000) = .1; P(I₁ | 100,000) = .2; P(I₁ | 120,000) = .6; P(I₁ | 140,000) = .3. Should Dollar purchase the forecast?

​Explain why the decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available.

If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be

Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands. ​ ​ a. What decision should be made by the optimist? b. What decision should be made by the conservative? c. What decision should be made using minimax regret?

Decision tree probabilities refer to

​Explain how utility could be used in a decision where performance is not measured by monetary value.

Use graphical sensitivity analysis to determine the range of values of the probability of state of nature s₁ over which each of the decision alternatives has its largest expected value.