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practical management science
Practical Management Science 4th Edition Wayne L. Winston, S. Christian Albright - Solutions
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 stock’s current price is $80 per share. You purchase a derivative whose value to you becomes known 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 stock market. Suppose the annual return on stocks follows a normal distribution with mean 12% and
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 you invest$100, you increase your asset position by $300), and, with probability 0.6, the amount
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 simulation. Keep track of two outputs: NPV (through year 10) and the number of years of sales.
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 $81.Discuss in a brief memo how this portfolio differs from the portfolio in the
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 date, the investor can sell the stock for $48 and then immediately buy it back(that is, cover his
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 percentile) of final cash in today’s dollars? Does it appear that a portfolio heavy in stocks is
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 differ in any important way from those in the example.
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 simulation. Is there any apparent downside to this strategy?
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 simulation, to have a damping factor of
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 cash balances of $50,000, $100,000, $150,000, and$200,000. Use the RISKSIMTABLE function to run all
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 the model so that all receipts are received immediately, and payments made this month for materials
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 the discount rate decreases from the value used in the example, 10%.
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 million. (You can check that the mean of this distribution is $700 million, the same as the cost
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 from the target. However, the results we presented don’t show how the tampering rules, particularly
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 this.Comment on the effect of this parameter on the key outputs. In particular, does the
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 simulation once more, but with 10,000 iterations. Comment on the difference between simulations (1) and
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 complete the order by the due date. We found this date to be August
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. Let its minimum value be 0, and choose its most likely and maximum values so that this triangular
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 outputs in the example.a. The cost of a new camera is increased to $300.b. The warranty period is
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, assume that each competitor’s bid, expressed as a multiple of Miller’s cost to complete the
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 Miller’s profit is positive. Do you believe these results should have any bearing on Miller’s
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 “worst in over 30 years,”or some such statement. Are natural disasters getting worse these days, or
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 gets you started. There is a single output cell, B5. You can enter any random value in this cell,
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 magnitude of this test statistic is sufficiently large, the null hypothesis is rejected in favor of 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 see whether it is indeed bell-shaped. Then repeat, using 30 values in each average. Are the histograms
(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 at least two of the 30 people have the same birthday. What is the(estimated) probability that this
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 if 30 people are in the same room, at least two of them will have the same birthday. You can
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 cell, calculate the average of all returns in cell B25 and designate it as an @RISK output.(This cell
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 between stocks, listed in the file P10_37.xlsx. You believe that the stock returns for these stocks
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 shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should
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 dresses and can, if desired, take delivery on up to x dresses. Each dress sells for $160 and Hudson
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 that Monty will open.Assume that Monty plays as follows: Monty knows where the prize is and will open
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 behind door
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 all lot 1 parking sticker holders show up, an average of 72%of all lot 2 parking sticker holders show
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 case where these 10 inputs each have a normal distribution with mean 1000 and standard deviation 250
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 improbable, and(2) it is a symmetric distribution. Many situations are modeled better with a distribution
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 case, assume that the regular demand is normally distributed with mean 9800 and standard deviation
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 considered best by the car dealer. (The point is that a decision maker can use more than just mean
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 amount you pay for damage. Compare your results with those in the previous problem. Does it appear to
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 7000. That is, the damage in an accident can be as low as $500 or as high as $7000, the most likely
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 deviation).
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 of 190 calendars, for example. If this maximizes expected profit, then it must yield a higher
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 a week left until the semifinals, which are then followed in a couple of days by the finals. Each
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 pocket.However, if the damage is greater than $1000, you pay the first $1000 and the insurance pays the
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 could be done.a. Suppose that you buy something for $0.20. How could you use random numbers (built into
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 distribution to superimpose.)a. What are the 5th and 95th percentiles for these two distributions?b.
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 deviation of this distribution?b. You have to be more careful in interpreting @RISK probabilities with
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. Does this histogram have approximately the shape you would expect?
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 k standard deviations of the mean? Answer for k 1; for k 2; for k
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 another. However, you are not sure of the value of p. Based on your current information, you believe p
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 34 to 28 and had the ball on their own 28-yard line with fourth down and two yards to go. Their
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 blade spar is a metal tube that runs the length of and provides strength to the helicopter blade. Due
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 developing a new microprocessor, a critical component in a timing system that would be superior to any
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% are moderaterisk customers, and 20% are low-risk customers. If credit is extended, the manufacturer
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 cost savings over the life of the fleet if it chooses to pursue the conversion. If the manufacturer
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 in the coming year. The file P09_71.xlsx contains the distribution of returns for these stocks and
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 file P09_69.xlsx contains the estimated probability distribution of the cost of manufacturing one unit
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 the cost of purchasing a lot is $30,000. Unfortunately, past experience indicates that this supplier
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 a touchdown, already leading by two points. Notre Dame had just had two successful goal-line stands
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 the game and that no foul will occur on the shot. Assume that a threepoint shot has a 30% chance of
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 optimal decision with an EMV criterion? Explain any difference between the two optimal strategies.
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 utility. How does this optimal decision compare to the optimal decision with an EMV criterion? Explain
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 concedes that 30% of the time the test will indicate that no gas is present when it actually is. When
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, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according to
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 3% annual rate of return; (2) he can invest in a fairly safe stock, where the possible annual rates
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 product, introduce product 1 only, introduce product 2 only, or introduce both products. Research
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 additional $1,800,000 to the landowner, but this will occur only if natural gas is discovered during the
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, expand the existing plant, or do nothing in the short run. The market for this particular tire product
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 acquiring the needed sugar. She can either buy the sugar at the going market price when she needs
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 factor of A. (For example, double them if A 2.) For each part, briefly explain your findings.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 alternative for a range of risk tolerances. Can you find a cutoff point for the risk tolerance such
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 what information the envelope contains. In contrast, sometimes a company can pay, not to obtain
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 probabilities.Skill-Extending Problems
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 sensitivity analysis from 0 to 0.6 in increments of 0.1. Do this in such a way that the probabilities of the
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 are nonnegative and sum to
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 there is a second test, independent of the first, that can be used as a follow-up. Assume that its
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 are not HIV positive, there is still a 0.001 chance that your test will indicate that you are HIV
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 tools, using only data tables. (You can still use the tree built with PrecisionTree.)
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 necessary, consult PrecisionTree’s online help.)
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 it.) Explain exactly what each of these charts represents. (For this problem, you can ignore the
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 then some outcome occurs, you look at that outcome’s column in the payoff table to see how much more
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 best. If the probabilities in row 10 (for D2) are the same as the probabilities in row 11 (for D3),
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 the others sum to 1 p but keep the same ratios to one another: 2 to 3 to
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 sent from the hubs to their final destinations. The file P08_45.xlsx lists the distances between
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 load assigned to any workstation. Find an assignment of jobs to workstations that minimizes the
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 to. It also lists precedence relationships between the jobs. For example, job 2 is a precedent of job
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 number of positions in which the two strings differ. For example, the distance between the strings
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 thousands) are listed in the file P08_37.xlsx. The Democrats control the state legislature, so they can
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 sales of copiers in each major market (Boston, New York, Philadelphia, Washington, Providence, and
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 who wants to take the bus will walk to the closest bus stop.a. If the goal is to minimize the total
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 thousands of kwh), the operating cost, the startup cost, and the shutdown cost (all costs in
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