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practical management science
Questions and Answers of
Practical Management Science
In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset.Consider the following simple derivative. A
Amanda has 30 years to save for her retirement. At the beginning of each year, she puts $5000 into her retirement account. At any point in time, all of Amanda’s retirement funds are tied up in the
Based on Kelly (1956). You currently have $100. Each week you can invest any amount of money you currently have in a risky investment. With probability 0.4, the amount you invest is tripled (e.g., if
Each year after year 5, the company examines sales. If fewer than 45,000 cars were sold that year, there is a 50%chance the car won’t be sold after that year. Modify the model and run the
Change the new car simulation from Example 11.5 as follows. It is the same as before for years 1 through 5, including depreciation through year
Modify Example 11.9 so that the portfolio now contains 100 shares of stock and one put option on the stock with the same parameters as in the example.You can assume that the price of an option is
A European put option allows an investor to sell a share of stock at the exercise price on the exercise data.For example, if the exercise price is $48, and the stock price is $45 on the exercise
Referring to the retirement example in Example 11.7, rerun the model for a planning horizon of 10 years;15 years; 25 years. For each, which set of investment weights maximizes the VAR 5% (the 5th
Modify the model from Example 11.7 so that you use only the years 1975 to 2007 of historical data. Run the simulation for the same three sets of investment weights. Comment on whether your results
The simulation output from Example 11.7 indicates that an investment heavy in stocks produces the best results. Would it be better to invest entirely in stocks?Answer this by rerunning the
Run the retirement model from Example 11.7 with a damping factor of 1.0 (instead of 0.98), again using the same three sets of investment weights. Explain in words what it means, in terms of the
In the cash balance model from Example 11.6, is the$250,000 minimum cash balance requirement really“costing” the company very much? Answer this by rerunning the simulation with minimum required
In the cash balance model from Example 11.6, the timing is such that some receipts are delayed by one or two months, and the payments for materials and labor must be made a month in advance. Change
Rerun the new car simulation from Example 11.5, but now use the RISKSIMTABLE function appropriately to simulate discount rates of 5%, 7.5%, 10%, 12.5%, and 15%. Comment on how the outputs change as
Rerun the new car simulation from Example 11.5, but now introduce uncertainty into the fixed development cost. Let it be triangularly distributed with parameters$600 million, $650 million, and $850
In the simulation of Deming’s funnel experiment, the@RISK outputs show how tampering leads to poor results, at least in terms of the mean and standard deviation of the distance of the final drop
In Example 11.3, suppose you want to run five simulations, where the probability of passing inspection is varied from 0.6 to 1.0 in increments of 0.1. Use the RISKSIMTABLE function appropriately to
Do you always get this answer? Find out by (1) running the simulation 10 more times, each with 1000 iterations, and finding the 95th percentile and corresponding date in each, and (2) running the
In Example 11.3, we commented on the 95th percentile on days required in cell I35 and the corresponding date in cell J35. If the company begins production on this date, then it is 95% sure to
In Example 11.2, the gamma distribution was used to model the skewness to the right of the lifetime distribution. Experiment to see whether the triangular distribution could have been used instead.
See how sensitive the results in Example 11.2 are to the following changes. For each part, make the change indicated, run the simulation, and comment on any differences between your outputs and the
Referring to Example 11.1, if the average bid for each competitor stays the same, but their bids exhibit less variability, does Miller’s optimal bid increase or decrease? To study this question,
In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined.a. For each of these, use @RISK’s RISKTARGET function to find the probability that
We are continually hearing reports on the nightly news about natural disasters—droughts in Texas, hurricanes in Florida, floods in California, and so on. We often hear that one of these was the
A technical note in the discussion of @RISK indicated that Latin Hypercube sampling is more efficient than Monte Carlo sampling. This problem allows you to see what this means. The file P10_44.xlsx
In statistics we often use observed data to test a hypothesis about a population or populations. The basic method uses the observed data to calculate a test statistic (a single number). If the
(Note that each of these distributions is very skewed.) Run each simulation with 10 values in each average, and run 1000 iterations to simulate 1000 averages. Create a histogram of the averages to
(By default, RANK gives 1 to the largest number.) If the set of numbers is 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1.c. After using the RANK function, you should be able to determine whether
It is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that
The file has the formulas you might expect for this situation in the range C20:G23. You can check how the RISKCORRMAT function has been used in these formulas. Just so that there is an@RISK output
The annual return on each of four stocks for each of the next five years is assumed to follow a normal distribution, with the mean and standard deviation for each stock, as well as the correlations
For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as
The contract between Jean Hudson and Lemington’s works as follows. At the beginning of the season, Lemington’s reserves x units of capacity.Lemington’s must take delivery for at least 0.8x
Should you switch? Simulate this situation 1000 times. For each replication use an @RISK function to generate the door that leads to the prize. Then use another @RISK function to generate the door
You now have the opportunity to switch and choose door
Before you see whether the prize is behind door 2, host Monty Hall opens a door that has no prize behind it. Specifically, suppose that before door 2 is opened, Monty reveals that there is no prize
You have made it to the final round of the show Let’s Make a Deal. You know that there is a $1 million prize behind either door 1, door 2, or door
The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of
The effect of the shapes of input distributions on the distribution of an output can depend on the output function. For this problem, assume there are 10 input variables. The goal is to compare the
Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely
Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal
Use @RISK to determine the “best” order quantity—in this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be
In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation
Continuing the previous problem, assume, as in Problem 11, that the damage amount is normally distributed with mean $3000 and standard deviation$750. Run @RISK with 5000 iterations to simulate the
In Problem 11 from the previous section, we stated that the damage amount is normally distributed.Suppose instead that the damage amount is triangularly distributed with parameters 500, 1500, and
Your single output variable should be the sum of these three numbers. Verify with @RISK that the distribution of this output is approximately normal with mean 300 and variance 300 (hence, standard
But then an order of 200 calendars must also yield a larger expected profit than 190 calendars. Why?)
In the Walton Bookstore example with a discrete demand distribution, explain why an order quantity other than one of the possible demands cannot maximize the expected profit. (Hint: Consider an order
A sweatshirt supplier is trying to decide how many sweatshirts to print for the upcoming NCAA basketball championships. The final four teams have emerged from the quarterfinal round, and there is now
Suppose you own an expensive car and purchase auto insurance. This insurance has a $1000 deductible, so that if you have an accident and the damage is less than $1000, you pay for it out of your
We all hate to keep track of small change. By using random numbers, it is possible to eliminate the need for change and give the store and the customer a fair deal. This problem indicates how it
Then superimpose a normal distribution on this drawing, choosing the mean and standard deviation to match those from the triangular distribution. (Click on the Add Overlay button and then choose the
Use @RISK to draw a binomial distribution that results from 50 trials with probability of success 0.3 on each trial, and use it to answer the following questions.a. What are the mean and standard
Are the answers close to what they should be (about 68% for k 1, about 95% for k 2, and over 99% for k 3)?c. Create a histogram of the random numbers using 10 to 15 categories of your choice.
Then freeze these random numbers.a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect?b. What fraction of these random numbers are within
Suppose you believe that the price of a particular stock goes up each day with probability p and goes down with probability 1-p. You also believe the daily price changes are independent of one
The ending of the game between the Indianapolis Colts and the New England Patriots (NFL teams) in Fall 2009 was quite controversial. With about two minutes left in the game, the Patriots were ahead
The Ventron Engineering Company has just been awarded a $2 million development contract by the U.S. Army Aviation Systems Command to develop a blade spar for its Heavy Lift Helicopter program. The
Sarah Chang is the owner of a small electronics company. In six months, a proposal is due for an electronic timing system for the next Olympic Games.For several years, Chang’s company has been
A manufacturer must decide whether to extend credit to a retailer who would like to open an account with the firm. Past experience with new accounts indicates that 45% are high-risk customers, 35%
A city in Ohio is considering replacing its fleet of gasoline-powered automobiles with electric cars. The manufacturer of the electric cars claims that this municipality will experience significant
A retired partner from a large brokerage firm has one million dollars available to invest in particular stocks or bonds. Each investment’s annual rate of return depends on the state of the economy
A home appliance company is interested in marketing an innovative new product. The company must decide whether to manufacture this product in house or employ a subcontractor to manufacture it. The
The purchasing agent for a PC manufacturer is currently negotiating a purchase agreement for a particular electronic component with a given supplier.This component is produced in lots of 1000, and
You can think of Washington getting$1 if they win and $0 if they lose. Then the EMV is 1*P(Win) 0*P(lose) P(Win), so maximizing EMV is equivalent to maximizing the probability of winning.
The following situation actually occurred in a 2009 college football game between Washington and Notre Dame. With about 3.5 minutes left in the game, Washington had fourth down and one yard to go for
The Indiana University basketball team trails by two points with eight seconds to go and has the ball. Should it attempt a two-point shot or a three-point shot?Assume that the Indiana shot will end
Suppose now that the bank’s utility function of profit x (in dollars) is. Find the strategy that maximizes the bank’s expected utility in this case.How does this optimal strategy compare to the
Suppose now that Techware’s utility function of net revenue x (measured in dollars), earned from the given marketing opportunities, is.a. Find the decision that maximizes Techware’s expected
Suppose now that, at a cost of $90,000, the landowner can request that a soundings test be performed on the site where natural gas is believed to be present. The company that conducts the soundings
Two construction companies are bidding against one another for the right to construct a new community center building in Bloomington, Indiana. The first construction company, Fine Line Homes,
Consider an investor with $10,000 available to invest.He has the following options regarding the allocation of his available funds: (1) he can invest in a risk-free savings account with a guaranteed
Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither
A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an
Carlisle Tire and Rubber, Inc., is considering expanding production to meet potential increases in the demand for one of its tire products. Carlisle’s alternatives are to construct a new plant,
The SweetTooth Candy Company knows it will need 10 tons of sugar six months from now to implement its production plans. Jean Dobson, SweetTooth’s purchasing manager, has essentially two options for
Do the absolute magnitudes of the monetary outcomes matter in the risky venture example? Consider the following two possibilities. In each case, multiply all monetary values in the example by a
In the risky venture example, suppose there is no riskless alternative; the only two possible decisions are the less risky venture and the more risky venture.Explore which of these is the preferred
The concept behind EVPI is that you purchase perfect information (the envelope), then open the envelope to see which outcome occurs, and then make an easy decision. You do not, however, get to choose
These are values where Acme will make the same decision, regardless of the test-market results it observes. Comment on why the test market is worthless for your particular prior
For the Acme problem, perform the following sensitivity analyses on the three prior probabilities and comment on the results.a. Vary the probability of a great national market in a one-way
Prior probabilities are often educated guesses at best, so it is worth performing a sensitivity analysis on their values. However, you must make sure that they are varied so that all probabilities
The terms prior and posterior are relative. Assume that the drug test has been performed, and the outcome is positive, which leads to the posterior probabilities in row 20 of Figure 9.28. Now assume
Suppose you are a heterosexual white male and are going to be tested to see if you are HIV positive.Assume that if you are HIV positive, your test will always come back positive. Assume that if you
Explain in words what information a two-way sensitivity chart, such as the one in Figure 9.27, provides. Demonstrate how you could provide this same information without PrecisionTree’s sensitivity
The tornado chart in Figure 9.24 and the spider chart in Figure 9.25 show basically the same information in slightly different forms. Explain in words exactly what information they provide. (If
For the SciTools example, once you build the tree as in Figure 9.9 and then run a one-way sensitivity analysis with the dialog box filled in as in Figure 9.22, you obtain three strategy charts. (Try
Besides the maximin, maximax, and EMV criteria, there are other possible criteria for making decisions.One possibility involves regret. The idea behind regret is that if you make any decision and
For the example in Simple Decision Problem.xlsx, we found that decision D3 is the EMV-maximizing decision for the given probabilities. See whether you can find probabilities that make decision D1 the
Use a one-way data table to see how (or whether)the optimal decision changes as p varies from 0.1 to 0.7 in increments of 0.05. Explain your results.Skill-Extending Problems
In the SciTools example, the probabilities for the low bid of competitors, given that there is at least one competing bid, are currently 0.2, 0.4, 0.3, and 0.1.Let the second of these be p, and let
Suppose you are the new supply manager at FedEx.You need to choose three hubs for the company. Each of 28 cities will send all of its outgoing packages to one of the hubs. The packages will then be
Note that job 6 has two precedents, jobs 3 and 4, which means that neither of jobs 3 and 4 can be assigned to a higher-numbered workstation than job 6.The cycle time of the system is the maximum time
This means that job 2 cannot be assigned to a higher-numbered workstation than job
A company has nine jobs that must be assigned to three ordered workstations. The file P08_44.xlsx lists the times required for each job, which are independent of the workstations they are assigned
Based on Meneses et al. (2004). A string is a list of characters such as “1differ%”. The length of the string is the number of characters in the string. The distance between two strings is the
You are the Democratic campaign manager for the state of Indiana. There are 15 fairly large cities in the state of Indiana. The numbers of Democrats and Republican voters in these cities (in
Xerox is trying to determine how many maintenance centers are needed in the mid-Atlantic states. Xerox earns $500 profit (excluding the cost of running maintenance centers) on each copier sale. The
We assume that town k is |k – j| miles from town j. The numbers of people in the towns who want to take the bus each hour are listed in the file P08_34.xlsx. Bus 99 will make two stops and anyone
During the next 12 months, the amounts of electric power needed (in thousands of kwh) are listed in the file P08_33.xlsx. This power can be supplied using four generators. The generating capacity (in
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