Exam 17: Decision-Making Tools

A decision tree is a(n):

What is a tabular presentation that shows the outcome for each decision alternative under the various possible states of nature called?

What limitation(s) do decision trees overcome compared to decision tables?

The campus bookstore sells highlighters that it purchases by the case. Cost per case, including shipping and handling, is $200. Revenue per case is $350. Any cases unsold will be discounted and sold at $175. The bookstore has estimated that demand will follow the pattern below (a) Construct the bookstore's payoff table. (b) How many cases should the bookstore stock in order to maximize expected profit? (c) How would your answer differ if the clearance price were not $175 per case but $225 per case? (It is not necessary to re-solve the problem to answer this.)

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

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

Steve Gentry, the operations manager of Baja Fabricators, wants to purchase a new profiling machine (it cuts compound angles on the ends of large structural pipes used in the fabrication yard). However, because the price of crude oil is depressed, the market for such equipment is down. Steve believes that the market will improve in the near future and that the company should expand its capacity. The table below displays the three equipment options he is currently considering, and the profit he expects each one to yield over a two-year period. The consensus forecast at Baja is that there is about a 30% probability that the market will pick up "soon" (within 3 to 6 months) and a 70% probability that the improvement will come "later" (in 9 to 12 months, perhaps longer). (a) Calculate the expected monetary value of each decision alternative. (b) Which equipment option should Steve take?

The EMV of a decision with three states of nature is $50. If the profit/value of A is 1/3 of B and B is 1/3 of C, determine the profit from A if all three states of nature are equally likely to occur.

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

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

A decision maker using the maximin criterion on the problem below would choose Alternative ________ because the maximum of the row minimums is ________.

If a decision maker is a pessimist, what decision-making criterion is appropriate? Why?

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 monetary value criterion? (c) What is the EVPI?

An operations manager's staff has compiled the information below for four manufacturing alternatives (E, F, G, and H) 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. Forecasts indicate that there is a 0.1 probability of acceptance level 1, 0.2 chance of acceptance level 2, 0.4 chance of acceptance level 3, and 0.3 change of acceptance level 4. Using the criterion of expected monetary value, which production alternative should be chosen?

The expected value with perfect information is:

Define expected monetary value (EMV).

A retailer is deciding how many units 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 $10 per unit and sells for $33 per unit. What is the smallest conditional value (profit) in the entire payoff table for this scenario?

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?

What is the EMV for Option 3 in the following decision table?

Which decision rule under uncertainty results in an optimistic decision? Why?