Practical Management Science
5th Edition
ISBN: 9781305734845
Author: WINSTON
Publisher: Cengage
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Chapter 10.6, Problem 24P
Summary Introduction
To determine: Whether the two inputs correlated as expected.
Introduction: Simulation model is the digital prototype of the physical model that helps to
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Johnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives of these tubes is 145 hours.
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A television network earns an average of $25 million each season from a hit program and loses an average of $8 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospec- tive program and issue a report predicting whether the given programwill end up being a hit. If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict the program to be a hit.a. What is the maximum value of C that the network should be willing to pay the market research firm?b. Calculate and interpret EVPI for this decision problem.
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1.Average values generated from a simulation are generally more accurate than expected values computed from a probability distribution
2.Simulated results will differ from expected values more for long simulations than for short simulations
3.Simulation can reproduce the behaviour of a system over several periods .
4.A random number is assigned to each value of the random variable
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 - Prob. 34PCh. 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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- Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poors 500 during 11 of the last 13 years. People use this as an argument that you can beat the market. Here is another way to look at it that shows that Balboas beating the market 11 out of 13 times is not unusual. Consider 50 mutual funds, each of which has a 50% chance of beating the market during a given year. Use simulation to estimate the probability that over a 13-year period the best of the 50 mutual funds will beat the market for at least 11 out of 13 years. This probability turns out to exceed 40%, which means that the best mutual fund beating the market 11 out of 13 years is not an unusual occurrence after all.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_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_forward
- The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.arrow_forwardIn 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 distribution has approximately the same mean and standard deviation as the gamma distribution in the example. (Use @RISKs Define Distributions window and trial and error to do this.) Then run the simulation and comment on similarities or differences between your outputs and the outputs in the example.arrow_forwardIf you add several normally distributed random numbers, the result is normally distributed, where the mean of the sum is the sum of the individual means, and the variance of the sum is the sum of the individual variances. (Remember that variance is the square of standard deviation.) This is a difficult result to prove mathematically, but it is easy to demonstrate with simulation. To do so, run a simulation where you add three normally distributed random numbers, each with mean 100 and standard deviation 10. 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 300=17.32).arrow_forward
- Big 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 Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)arrow_forwardUse @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 a discrete distribution such as this binomial. For example, if you move the left slider to 11, you find a probability of 0.139 to the left of it. But is this the probability of less than 11 or less than or equal to 11? One way to check is to use Excels BINOM.DIST function. Use this function to interpret the 0.139 value from @RISK. c. Using part b to guide you, use @RISK to find the probability that a random number from this distribution will be greater than 17. Check your answer by using the BINOM.DIST function appropriately in Excel.arrow_forward
- You have 5 and your opponent has 10. You flip a fair coin and if heads comes up, your opponent pays you 1. If tails comes up, you pay your opponent 1. The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability that you end up with all the money and the probability that neither of you goes broke in 100 tosses.arrow_forwardA martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.arrow_forwardAssume 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_forward
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