Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 10, Problem 47P
If you want to replicate the results of a simulation model with Excel functions only, not @RISK, you can build a data table and let the column input cell be any blank cell. Explain why this works.
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Chapter 10 Solutions
Practical Management Science
Ch. 10.2 - Use the RAND function and the Copy command to...Ch. 10.2 - Use Excels functions (not @RISK) to generate 1000...Ch. 10.2 - Use @RISK to draw a uniform distribution from 400...Ch. 10.2 - Use @RISK to draw a normal distribution with mean...Ch. 10.2 - Use @RISK to draw a triangular distribution with...Ch. 10.2 - Use @RISK to draw a binomial distribution that...Ch. 10.2 - Use @RISK to draw a triangular distribution with...Ch. 10.2 - We all hate to keep track of small change. By...Ch. 10.4 - Prob. 11PCh. 10.4 - In August of the current year, a car dealer is...
Ch. 10.4 - Prob. 13PCh. 10.4 - Prob. 14PCh. 10.4 - Prob. 15PCh. 10.5 - If you add several normally distributed random...Ch. 10.5 - In Problem 11 from the previous section, we stated...Ch. 10.5 - Continuing the previous problem, assume, as in...Ch. 10.5 - In Problem 12 of the previous section, suppose...Ch. 10.5 - Use @RISK to analyze the sweatshirt situation in...Ch. 10.5 - Although the normal distribution is a reasonable...Ch. 10.6 - When you use @RISKs correlation feature to...Ch. 10.6 - Prob. 24PCh. 10.6 - Prob. 25PCh. 10.6 - Prob. 28PCh. 10 - Six months before its annual convention, the...Ch. 10 - Prob. 30PCh. 10 - A new edition of a very popular textbook will be...Ch. 10 - Prob. 32PCh. 10 - W. L. Brown, a direct marketer of womens clothing,...Ch. 10 - Assume that all of a companys job applicants must...Ch. 10 - Lemingtons is trying to determine how many Jean...Ch. 10 - Dilberts Department Store is trying to determine...Ch. 10 - It is surprising (but true) that if 23 people are...Ch. 10 - Prob. 40PCh. 10 - At the beginning of each week, a machine is in one...Ch. 10 - Simulation can be used to illustrate a number of...Ch. 10 - Prob. 43PCh. 10 - Prob. 46PCh. 10 - If you want to replicate the results of a...Ch. 10 - Suppose you simulate a gambling situation where...Ch. 10 - Prob. 49PCh. 10 - Big Hit Video must determine how many copies of a...Ch. 10 - Prob. 51PCh. 10 - Prob. 52PCh. 10 - Why is the RISKCORRMAT function necessary? How...Ch. 10 - Consider the claim that normally distributed...Ch. 10 - Prob. 55PCh. 10 - When you use a RISKSIMTABLE function for a...Ch. 10 - Consider a situation where there is a cost that is...
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- Simulation can be used to illustrate a number of results from statistics that are difficult to understand with nonsimulation arguments. One is the famous central limit theorem, which says that if you sample enough values from any population distribution and then average these values, the resulting average will be approximately normally distributed. Confirm this by using @ RISK with the following population distributions (run a separate simulation for each): (a) discrete with possible values 1 and 2 and probabilities 0.2 and 0.8; (b) exponential with mean 1 (use the RISKEXPON function with the single argument 1); (c) triangular with minimum, most likely, and maximum values equal to 1,9, and 10. (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 based on 10 values qualitatively different from those, based on 30?arrow_forwardSuppose you simulate a gambling situation where you place many bets. On each bet, the distribution of your net winnings (loss if negative) is highly skewed to the left because there are some possibilities of really large losses but not much upside potential. Your only simulation output is the average of the results of all the bets. If you run @RISK with many iterations and look at the resulting histogram of this output, what will it look like? Why?arrow_forwardA common decision is whether a company should buy equipment and produce a product in house or outsource production to another company. If sales volume is high enough, then by producing in house, the savings on unit costs will cover the fixed cost of the equipment. Suppose a company must make such a decision for a four-year time horizon, given the following data. Use simulation to estimate the probability that producing in house is better than outsourcing. If the company outsources production, it will have to purchase the product from the manufacturer for 25 per unit. This unit cost will remain constant for the next four years. The company will sell the product for 42 per unit. This price will remain constant for the next four years. If the company produces the product in house, it must buy a 500,000 machine that is depreciated on a straight-line basis over four years, and its cost of production will be 9 per unit. This unit cost will remain constant for the next four years. The demand in year 1 has a worst case of 10,000 units, a most likely case of 14,000 units, and a best case of 16,000 units. The average annual growth in demand for years 2-4 has a worst case of 7%, a most likely case of 15%, and a best case of 20%. Whatever this annual growth is, it will be the same in each of the years. The tax rate is 35%. Cash flows are discounted at 8% per year.arrow_forward
- Rerun the new car simulation from Example 11.4, 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 given in the example.) Comment on the differences between your output and those in the example. Would you say these differences are important for the company?arrow_forwardBig Hit Video must determine how many copies of a new video to purchase. Assume that the companys goal is to purchase a number of copies that maximizes its expected profit from the video during the next year. Describe how you would use simulation to shed light on this problem. Assume that each time a video is rented, it is rented for one day.arrow_forwardBased 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 you invest is lost. Consider the following investment strategies: Each week, invest 10% of your money. Each week, invest 30% of your money. Each week, invest 50% of your money. Use @RISK to simulate 100 weeks of each strategy 1000 times. Which strategy appears to be best in terms of the maximum growth rate? (In general, if you can multiply your investment by M with probability p and lose your investment with probability q = 1 p, you should invest a fraction [p(M 1) q]/(M 1) of your money each week. This strategy maximizes the expected growth rate of your fortune and is known as the Kelly criterion.) (Hint: If an initial wealth of I dollars grows to F dollars in 100 weeks, the weekly growth rate, labeled r, satisfies F = (I + r)100, so that r = (F/I)1/100 1.)arrow_forward
- Assume that all of a companys job applicants must take a test, and that the scores on this test are normally distributed. The selection ratio is the cutoff point used by the company in its hiring process. For example, a selection ratio of 25% means that the company will accept applicants for jobs who rank in the top 25% of all applicants. If the company chooses a selection ratio of 25%, the average test score of those selected will be 1.27 standard deviations above average. Use simulation to verify this fact, proceeding as follows. a. Show that if the company wants to accept only the top 25% of all applicants, it should accept applicants whose test scores are at least 0.674 standard deviation above average. (No simulation is required here. Just use the appropriate Excel normal function.) b. Now generate 1000 test scores from a normal distribution with mean 0 and standard deviation 1. The average test score of those selected is the average of the scores that are at least 0.674. To determine this, use Excels DAVERAGE function. To do so, put the heading Score in cell A3, generate the 1000 test scores in the range A4:A1003, and name the range A3:A1003 Data. In cells C3 and C4, enter the labels Score and 0.674. (The range C3:C4 is called the criterion range.) Then calculate the average of all applicants who will be hired by entering the formula =DAVERAGE(Data, "Score", C3:C4) in any cell. This average should be close to the theoretical average, 1.27. This formula works as follows. Excel finds all observations in the Data range that satisfy the criterion described in the range C3:C4 (Score0.674). Then it averages the values in the Score column (the second argument of DAVERAGE) corresponding to these entries. See online help for more about Excels database D functions. c. What information would the company need to determine an optimal selection ratio? How could it determine the optimal selection ratio?arrow_forwardThe DC Cisco office is trying to predict the revenue it will generate next week. Ten deals may close next week. The probability of each deal closing and data on the possible size of each deal (in millions of dollars) are listed in the file P11_55.xlsx. Use simulation to estimate total revenue. Based on the simulation, the company can be 95% certain that its total revenue will be between what two numbers?arrow_forwardSoftware development is an inherently risky and uncertain process. For example, there are many examples of software that couldnt be finished by the scheduled release datebugs still remained and features werent ready. (Many people believe this was the case with Office 2007.) How might you simulate the development of a software product? What random inputs would be required? Which outputs would be of interest? Which measures of the probability distributions of these outputs would be most important?arrow_forward
- The IRR is the discount rate r that makes a project have an NPV of 0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function might not find an answer, and you would get an error message. Then you must try the syntax =IRR(range of cash flows, guess), where guess" is your best guess for the IRR. It is best to try a range of guesses (say, 90% to 100%). Find the IRR of the project described in Problem 34. 34. Consider a project with the following cash flows: year 1, 400; year 2, 200; year 3, 600; year 4, 900; year 5, 1000; year 6, 250; year 7, 230. Assume a discount rate of 15% per year. a. Find the projects NPV if cash flows occur at the ends of the respective years. b. Find the projects NPV if cash flows occur at the beginnings of the respective years. c. Find the projects NPV if cash flows occur at the middles of the respective years.arrow_forwardYou are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)arrow_forwardAssume a very good NBA team has a 70% chance of winning in each game it plays. During an 82-game season what is the average length of the teams longest winning streak? What is the probability that the team has a winning streak of at least 16 games? Use simulation to answer these questions, where each iteration of the simulation generates the outcomes of all 82 games.arrow_forward
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