Exam 22: Decision-Making Tools

Bratt's Bed and Breakfast,in a small historic New England town,must decide how to subdivide (remodel)the large old home that will become an inn.There are three alternatives: Option A would modernize all baths and combine rooms,leaving the inn with four suites,each suitable for two to four adults.Option B would modernize only the second floor; the results would be six suites,four for two to four adults,and two for two adults only.Option C (the status quo option)leaves all walls intact.In this case,there are eight rooms available,but only two are suitable for four adults,and four rooms will not have private baths.Below are the details of profit and demand patterns that will accompany each option.Which option has the highest expected value?

An example of expected monetary value would be the payoff from selecting a particular alternative when a particular state of nature occurs.

Decision trees:

What are decision tables?

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?

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

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

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?

A problem that involves a sequence of decisions:

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

A plant manager wants to know how much he should be willing to pay for perfect market research.Currently there are two states of nature facing his decision to expand or do nothing.Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant.Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0.If the two states of nature are equally likely,how much should he pay for perfect information?

A primary advantage of decision trees compared to decision tables is that decision trees:

A state of nature is an occurrence or a situation over which the decision maker has little or no control.

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

What is the expected value of perfect information of the following decision table?

How is the expected value of perfect information (EVPI)found?

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 $8 per unit and sells for $25 per unit.What is the largest conditional value (profit)in the entire payoff table for this scenario?

In the context of decision making,define an alternative.

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

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.)