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Making Hard Decisions with decision tools 3rd edition Robert Clemen, Terence Reilly - Solutions

When we used Bayes’ theorem to update the probabilities that eKnow would be a Success, Potential, or Failure by counting the number of Definitely-Purchase responses at the National Book Conference, we showed the impact of counting 18 Definitely-Purchase responses in the first hour. Now, suppose
A factory manager must decide whether to stock a particular spare part. The part is absolutely essential to the operation of certain machines in the plant. Stocking the part costs $10 per day in storage and cost of capital. If the part is in stock, a broken machine can be repaired immediately, but
Another useful distribution that is based on the normal is the lognormal distribution. Among other applications, this distribution is used by environmental engineers to represent the distribution of pollutant levels, by economists to represent the distribution of returns on investments, and by
Refer to the discussion of eKnow in the section on the beta distribution. Find the probability that the net contribution of eKnow would be greater than $600,000. What is the probability the net contribution will be less than $100,000?
Use the probability statements that follow to find the value of the random variable. a. PB (R ≤ r | n = 12; p = 0.85) = 0.024; find r. b. PP (K > k | m = 3.2) = 0.62; find k. c. PE (T ≤ t | β = 32) = 0.952; find t. d. PN (Y ≤ y | μ = 30; σ = 8) = 0.10; find y. e. PT (Y ≤ y | Min = 10;
Using the alternative-parameter method, determine the parameters of the following distributions based on the given assessments. Refer to Step 5.5 if necessary.a. Find the parameter value β for the exponential distribution given P E (T≤15|β) = 0.50.b. Find the parameters μ and σ for a normal
An exponential distribution has PE (T ≥ 5 | m) = 0.24. Find m.
A Poisson distribution has PP (X = 0 | m) = 0.175. Calculate m.
It was suggested that five is the minimum number of data points for the least likely category when constructing discrete distributions. In many cases, however, we must estimate probabilities that are extremely small or for which relatively few data are available. For example, the probability of
As discussed in the text, it often is possible to use a theoretical distribution as an approximation of the distribution of some sample data. It is always important, however, to check to make sure that your data really do fit the distribution you propose to use.Consider the solar trash compactor
A scientist collected the following weights (in grams) of laboratory animals:Run @RISK's distribution fitting procedure on the weights of the lab-oratory animals.a. The normal distribution is often used with measurement variables such as height and weight. Compare the normal distribution to the
Explain in your own words the role that data can play in the development of models of uncertainty in decision analysis.
A plant manager is interested in developing a quality-control pro-gram for an assembly line that produces light bulbs. To do so, the manager considers the quality of the products that come from the line. The light bulbs are packed in boxes of 12, and the line produces several thousand boxes of
A retail manager in a discount store wants to establish a policy of the number of cashiers to have on hand and also when to open a new cash register. The first step in this process is to determine the rate at which customers arrive at the cash register. One day, the manager observes the following
An ecologist studying the breeding habits of birds sent volunteers from the local chapter of the Audubon Society into the field to count nesting sites for a particular species. Each team was to survey five acres of land carefully. Because she was interested in studying the distribution of nesting
Decision analyst Sandy Baron has taken a job with an up-and-coming consulting firm in San Francisco. As part of the move, Sandy will purchase a house in the area. There are two houses that are especially attractive, but their prices seem high. To study the situation a bit more, Sandy obtained data
Ransom Global Communications (RGC) Inc., sells communications systems to companies that have worldwide operations. Over the next year, RGC will be instituting important improvements in its manufacturing operations. The CEO and majority stockholder, Thomas Ransom, has been extremely optimistic about
Why might a decision maker be reluctant to make subjective probability judgments when historical data are available? In what sense does the use of data still involve subjective judgments?
Suppose that an analyst for an insurance company is interested in using regression analysis to model the damage caused by hurricanes when they come ashore. The response variable is Property Damage, measured in millions of dollars, and the explanatory variables are Diameter of Storm, Barometric
Estimate the 0.65 and 0.35 fractiles of the distribution of yearly operating costs of the Big Bertha solar trash compactors, based on the CDFin Figure 10.7.Figure 10.7 $Estimate the 0.65 and 0.35 fractiles of the distribution of$
Choose appropriate intervals and create a relative frequency histogram based on the annual operating costs of the Big Bertha data in Table 10.4.Table 10.4
Figure 10.36 shows two empirical CDFs of the residuals of Sales for two regressions. Estimate (roughly) the 0.20 and 0.80 fractiles of both of these empirical CDFs. What do these two intervals say about predicting future sales amount?Figure 10.36
Explain in your own words how Monte Carlo simulation may be useful to a decision maker.
Modify the decision-tree model in Figure 11.13 to use the extended Swanson-Megill (ES-M) approximation for demand instead of the EPT approximation.Use your ES-M model to calculate expected profit for Order-Quantity values 600, 650, 700, 750, and 800. How do your results compare to those in Figure
Use your ES-M model to calculate the standard deviation of Profit for Order-Quantity values 600, 650, 700, 750, and 800. Compare those with the corresponding standard deviations using the extended Pearson-Tukey (EP-T) approximation and the standard deviations from the simulation model using the
Your boss has asked you to work up a simulation model to examine the uncertainty regarding the success or failure of five different investment projects. He provides probabilities for the success of each project individually: p1 = 0.50, p2 = 0.35, p3 = 0.65, p4 = 0.58, p5 = 0.45.Because the projects
A decision maker is working on a problem that requires her to study the uncertainty surrounding the payoff of an investment. There are three possible levels of payoff — $1,000, $5,000, and $10,000. As a rough approximation, the decision maker believes that each possible payoff is equally likely.
In the Monty Hall Problem, the host (Monty Hall) asks a contestant to choose one of three curtains. Behind one and only one of these curtains is a fabulous prize, such as an all-expense paid vacation, and behind the other two curtains are much less valuable prizes; let’s suppose donkeys. At this
Use simulation to solve the Birthday Problem using the data file Observed BirthDays.xls at www.cengagebrain.com. The first three rows of the data are shown in the table that follows. The dataset begins with the number 101 representing Jan 1st and ends with 1231 representing Dec 31,and includes leap
Explain how the simulation process works to produce results that are helpful to a decision maker.
If you were to make Leah Sanchez’s decision of how many calendars to order, what order amount would you chose? Why?
A friend of yours has just learned about Monte Carlo simulation methods and has asked you to do a simulation of a complicated decision problem to help her make a choice. She would be happy to have you solve the problem and then recommend what action she should take. Explain why she needs to be
Explain why a simulation model with only discrete probability distributions produces the same results as the corresponding decision tree model even though it uses very different solution methods.
Consider the statement “In simulation models, the values for the uncertain cells are chosen randomly.” Why is this statement incorrect, strictly speaking?
Why should you not model a decision variable as a random variable with a probability distribution?
Leah Sanchez is concerned that if she orders too few calendars, customers’ disappointment in not finding a calendar might drive them to shop elsewhere, resulting in more of a loss over the long term than just the $9.00 of lost profit on the calendar. Modify the model in Figure11.7 by adding a row
Leah Sanchez might have a different objective than maximizing expected profit. How does her optimal order quantity change if her objective is to minimize leftovers? What if her objective is to maximize the probability of making a profit of at least $5,200? What if her objective is to minimize
Explain why in decision analysis we are concerned with the expected value of information.
Look again at Problem 8.11, which concerns whether you should drop your decision analysis course. Estimate EVPI for your score in the course.
In Problem 9.33, the issue is whether or not to close the plant. If your boss knew exactly how many machines would fail during your absence; he would be able to decide what to do without the fear of making a mistake.a. Find his EVPI concerning the number of machine failures during your absence over
Consider the Texaco – Pennzoil example from Chapter 4.a. What is EVPI to Hugh Liedtke regarding Texaco’s reaction to a counteroffer of $5 billion? Can you explain this resultintuitively?b. The timing of information acquisition may make a difference.(i) For example, suppose that Liedtke could
In the Texaco – Pennzoil case, what is EVPI if Liedtke can learn both Texaco ’ s reaction and the final court decision before he makes up his mind about the current $2 billion offer? Can you explain why the interaction of the two bits of information should have this effect?
In Problem 5.8, assume that the grower’s loss incurred with the burners would be $17,500 and that the loss incurred with the sprinklers would be $27,500.a. Find EVPI for the weather conditions (freeze or not).b. Now assume that the loss incurred with the burners is uniformly distributed between
In Exercise 12.4, is it necessary to assume that the events are independent? What other assumption could be made?
Calculate the EVPI for the decision shown in Figure 12.11.Figure 12.11
What is the EVPI for the decision shown in Figure 12.12? Must you perform any calculations? Can you draw any conclusions regarding the relationship between value of information and deterministic dominance?
For the decision tree in Figure 12.13, assume Chance Events E and F are independent.a. Draw the appropriate decision tree and calculate the EVPI for Chance Event E only.b. Draw the appropriate decision tree and calculate the EVPI for Chance Event F only.c. Draw the appropriate decision tree and
Draw the influence diagram that corresponds to the decision tree for Exercise 12.4. How would this influence diagram be changed in order to answer parts a, b, and c in Exercise 12.4?In exercisea. Draw the appropriate decision tree and calculate the EVPI for Chance Event E only.b. Draw the
The claim was made in the chapter that information always has positive value. What do you think of this? Can you imagine any situation in which you would prefer not to have some unknown information revealed? a. Suppose you have just visited your physician because of a pain in your abdomen. The
Consider another oil-wildcatting problem. You have mineral rights on apiece of land that you believe may have oil underground. There is only a10% chance that you will strike oil if you drill, but the payoff is$200,000. It costs $10,000 to drill. The alternative is not to drill at all, in which case
Consider the preceding oil-wildcatting problem. The basic tree is shown in Figure 12.14.Based on Figure 12.14, work through these steps:a. Change P(Strike Oil) from 0.1 to 1.0 and P(No Oil) to 0.0. What is the EMV for the decision tree? Record this as EMV | Strike Oil.b. Now change P(Strike Oil) to
In Problem 4.16, find:a. EVPI for the cost of making the processor.b. EVPI for the cost of subcontracting the processor.c. EVPI for both uncertain events.
Perhaps at some point in your life you have taken each of the actions a – e that follow. In doing so, you exhibited “options thinking.” For each, explain how the option value arises. Additional questions you might consider: What constitutes the option cost, the exercise window, the trigger
You are acting in a consulting capacity advising a limited partner in a real-estate partnership. The partnership has negative income because of high vacancy rates and discounts on lease rates in the current soft market. The general partner would like to consolidate ownership, and is asking your
A start-up venture owns the rights to new technology for a coated stent. The company is about to begin animal trials that could lead to FDA approval of the use of the stent in humans. The company could conduct those trials in two different ways (for coronary application sand for neurological
Two options are evaluated separately in Figures 13.6 and 13.7. Do the analysis for both options together, calculate the option value for the two options together, and explain your results.Figure 13.6Figure 13.7
Acquisition: The board of directors of Quicker com Inc. is considering an acquisition of Honest Communication Inc. (HCI) for a total price of $3 billion, to be finalized January 1, 2016. After thorough due diligence, the financial experts at Quicker com are concerned that HCI's value could decrease
A hybrid automobile has two motors, gasoline and electric. It switches between motors for power, sometimes using both motors. When accelerating, both electricity and gasoline are providing power to the wheels. When cruising, the electric motor is not being used. The gasoline engine provides power
Ruined Mound Properties is in final negotiations for the rights to mine copper on a tract of land in Indonesia. They must decide about adding an option in their agreement with the government of Indonesia. This option would allow them to develop an identical adjacent tract of land, beginning no
The development of a drug requires Food and Drug Administration (FDA) approval at five stages (a preclinical phase; clinical phases I, II, and III; and a final approval). A pharmaceutical company could commit a lump-sum amount upfront to acquire a prospective compound from another firm and then
Pierre, a book broker, is about to sign a contract to buy the rights to a book about twin teenage computer-security sleuths titled Nan and Dan vs. the Monika Worm. His offer to advance $50,000 for the book has been verbally accepted. Pierre plans to immediately turn over his rights to a publisher
Shu Mei Wang is going to start a new business to provide a geographical-information system (GIS) to be used by small businesses in selecting promotions and for other marketing applications. 2 She will provide her service to on-line subscribers via a sophisticated Internet server. She is considering
The lead time for delivery of the largest offshore platforms for oil and gas drilling and collecting is now 2 years. ConExoco Petroleum is thinking about putting down a $15 million nonrefundable deposit on one in the Gulf of Mexico. This deposit is 15% of what the purchase price would be in 2
A biopharma project being pursued by Hopfer Pharmaceutical has a negative NPV of − $28 million Still, Hopfer may participate in this project as a “pioneer” option, giving the company an option to participate later in a large project that could have an attractive NPV. The large follow-on
Why is it important for decision makers to consider their attitudes toward risk?
Consider the following game that you have been invited to play by an acquaintance who always pays his debts. Your acquaintance will flip a fair coin. If it comes up heads, you win$2. If it comes up tails, he flips the coin again. If heads occurs on the second toss, you win $4. If tails, he flips
Assess your utility function in three different ways. a. Use the certainty-equivalent approach to assess your utility function for wealth over a range of $100 to $20,000. b. Use the probability-equivalent approach to assess U($1,500),U($5,600), U($9,050), and U($13,700). Are these assessments
Assess your risk tolerance (R). Now rescale your exponential utility function—the one you obtain by substituting your R value into the exponential utility function—so that U($100) = 0 and U($20,000) = 1. That is, find constants a and b so that α + β (1 – e – 100 = R) = 0 and α + β (1
Let us return to the Texaco-Pennzoil example from Chapter 4 and think about Liedtke’s risk attitude. Suppose that Liedtke’s utility function is given by the utility function in Table 14.5.a. Graph this utility function. Based on this graph, how would you classify Liedtke’s attitude toward
Of course, Liedtke is not operating by himself in the Texaco-Pennzoil case; he must report to a board of directors. Table 14.6 gives utility functions for three different directors. Draw graphs of these. How would you classify each director in terms of his or her attitude toward risk? What would be
How do you think Liedtke (Problem 14.14) and the directors in Problem 14.15 will be able to reconcile their differences?Problem 14.15Of course, Liedtke is not operating by himself in the Texaco-Pennzoil case; he must report to a board of directors. Table 14.6 gives utility functions for three
Rescale the utility function for Director A in Problem 14.15 so that it ranges between 0 and 1. That is, find constants a and b so that when you multiply the utility function by a and then add b, the utility for $10.30 billion is 1 and the utility for $0 is 0. Graph the rescaled utility function
What if Hugh Liedtke were risk-averse? Based on Figure 4.2, find a critical value for Hugh Liedtke’s risk tolerance. If his risk tolerance is small enough (very risk-averse), he would accept the $2 billion offer. How small would his risk tolerance have to be for EU(Accept$2 billion) to be greater
The idea of dominance criteria and risk aversion come together in an interesting way leading to a different kind of dominance. If two risky gambles have the same expected payoff, on what basis might a risk-averse individual choose between them without performing a complete utility analysis?
We have not given a specific definition of risk. How would you define it? Give examples of lotteries that vary in riskiness in terms of your definition of risk.
This problem is related to the ideas of dominance that we discussed in Chapters 4 and 8. Investment D in the table that follows is said to show "second-order stochastic dominance" over Investment C. In this problem, it is up to you to explain why D dominates C.You are contemplating two alternative
Utility functions need not relate to dollar values. Here is a problem in which we know little about five abstract outcomes. What is important, however, is that a person who does know what A to E represent should be able to compare the outcomes using the lottery procedures we have studied.A decision
You have considered insuring a particular item of property (such as an expensive camera, your computer, or your Stradivarius violin), but after considering the risks and the insurance premium quoted, you have no clear preference for either purchasing the insurance or taking the risk. The insurance
An investor with assets of $10,000 has an opportunity to invest$5,000 in a venture that is equally likely to pay either $15,000 or nothing. The investor’s utility function can be described by the utility function U(x) = ln(x), where x is his total wealth.a. What should the investor do?b. Suppose
A bettor with utility function U(x) = ln(x), where x is total wealth, has a choice between the following two alternatives:A Win $10,000 with probability 0.2Win $1,000 with probability 0.8B Win $3,000 with probability 0.9Lose $2,000 with probability 0.1a. If the bettor currently has $2,500, should
Repeat Problem 14.24 with U (x) = 0.0003 x – 8.48e – x = 2775. A utility function of this form is called linear-plus-exponential, because it contains both linear (0.0003 x) and exponential terms. It has a number of interesting and useful properties, including the fact that it switches only once
Show that the linear-plus-exponential utility function in Problem 14.25 has decreasing risk aversion. Repeat Problem 14.25 With U (x) = 0.0003 x – 8.48e – x = 2775. A utility function of this form is called linear-plus-exponential, because it contains both linear (0.0003 x) and exponential
Buying and selling prices for risky investments obviously are related to CEs. This problem, however, shows that the prices depend on exactly what is owned in the first place! Suppose that Peter Brown’s utility for total wealth (A) can be represented by the utility function U (A) = ln (A). He
We discussed decreasing and constant risk aversion. Are there other possibilities? Think about this as you work through this problem. Suppose that a person ’ s utility function for total wealth is U (A) = 200 A – A2 for 0 ≤ A ≤ 100 where A represents total wealth in thousands of dollars. a.
Suppose that a decision maker has the following utility function:U (x) = €“ 0.000156 x2 + 0.028125 x €“ 0.265625Use this utility function to calculate risk premiums for the gambles shown in Tables 14.3 and 14.4; create a similar table but based on this quadratic utility
Explain in your own words the idea of a certainty equivalent.
The CEO of a chemicals firm must decide whether to develop a new process that has been suggested by the research division. His decision tree is shown in Figure 14.20. There are two sources of uncertainty. The production cost is viewed as a continuous random variable, uniformly distributed between
The year is 2040, and you are in the supercomputer business. Your firm currently produces a machine that is relatively expensive (list price $6million) and relatively slow (for supercomputers in the twenty-first century). The speed of supercomputers is measured in calculations, known asfloating
Show that the value of Y that yields indifference between the two alternatives in Figure 14.12 is within about 4% of the risk tolerance R.Figure 14.12
We stated that to assess the risk tolerance value of R for the exponential utility function, we should find the greatest value of Y such that the decision maker is indifferent between receiving $0 or a 50-50 gamble with payoffs Y and – Y/2. Show why this assessment procedure works.
In the trade-off method for assessing utilities, consider the dollar amount X1 that makes you indifferent between gambles A1 and A2, and X2 that makes you indifferent between gambles B1 and B2. Show that U(X2) = 2U(X1).
Explain what is meant by the term risk premium.
Explain in your own words the idea of risk tolerance. How would it apply to utility functions other than the exponential utility function?
A decision maker’s assessed risk tolerance is $1,210. Assume that this individual’s preferences can be modeled with an exponential utility function. a. Find U ($1,000), U($800), U($0), and U( − $1,250). b. Find the EU for an investment that has the following payoff distribution: P ($1,000) =
Many firms evaluate investment projects individually on the basis of expected value and at the same time maintain diversified holdings in order to reduce risk. Does this make sense in light of our discussion of risk attitudes in this chapter?
A friend of yours, who lives in Reno, has life insurance, homeowner’s insurance, and automobile insurance and also regularly plays the quarter slot machines in the casinos. What kind of a utility function might explain this kind of behavior? How else might you explain such behavior?
In your own words, explain why the axioms that underlie expected utility are important to decision analysis.
Even without a formal assessment process, it often is possible to learn something about an individual’s utility function just through the preferences revealed by choice behavior. Two persons, A and B, make the following bet: A wins $40 if it rains tomorrow and B wins $10 if it does not rain
Assume that you are interested in purchasing a new model of a personal computer whose reliability has not yet been perfectly established. Measure reliability in terms of the number of days in the shop over the first three years that you own the machine. (Does this definition of reliability pass the
You are in the market for a new car. An important characteristic is the life span of the car. (Define lifespan as the number of miles driven until the car breaks down, requiring such extensive repairs that it would be cheaper to buy an equivalent depreciated machine.) Assess your utility function

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