Exam 22: Decision-Making Tools

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 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.

The last step in the analytic decision process is to clearly define the problem and the factors that influence it.

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?

Miles is considering buying a new pickup truck for his lawn service firm.The economy in town seems to be growing,and he is wondering whether he should opt for a subcompact,compact,or full-size pickup truck.The smaller truck would have better fuel economy,but would sacrifice capacity and some durability.A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year,a 20% chance of higher gas prices,and a 50% chance that gas prices will stay roughly unchanged.Based on this information,Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices.Develop a decision tree for this situation and indicate which type of truck he should select.

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?

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?

What is the EMV for Option 2 in the following decision table?

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

A branch of a decision tree that is less favorable than other available options may be ________.

Explain the symbols used in decision tree analysis.

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

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?

What is the EMV for Option 2 in the following decision table?

In a decision tree,the expected monetary values are computed by working from right to left.

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

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

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.

What are decision tables?

For the following decision table,the highest value for the equally likely criterion is ________;this occurs with alternative ________.