We have separated the examples in this chapter into operations, finance, marketing, and sports categories. List at least one other problem in each of these catego- ries that could be attacked with simulation. For each, identify the random inputs, possible probability distributions for them, and any outputs of interest.

We have separated the examples in this chapter into operations, finance, marketing, and sports categories. List at least one other problem in each of these catego- ries that could be attacked with simulation. For each, identify the random inputs, possible probability distributions for them, and any outputs of interest.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 84P: Software development is an inherently risky and uncertain process. For example, there are many...

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Assume 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.
W. L. Brown, a direct marketer of womens clothing, must determine how many telephone operators to schedule during each part of the day. W. L. Brown estimates that the number of phone calls received each hour of a typical eight-hour shift can be described by the probability distribution in the file P10_33.xlsx. Each operator can handle 15 calls per hour and costs the company 20 per hour. Each phone call that is not handled is assumed to cost the company 6 in lost profit. Considering the options of employing 6, 8, 10, 12, 14, or 16 operators, use simulation to determine the number of operators that minimizes the expected hourly cost (labor costs plus lost profits).
An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors: The fixed cost of developing the Racer is triangularly distributed with parameters 3, 4, and 5, all in billions. Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000. The selling price in year 1 is 25,000. The year 2 selling price will be 1.05[year 1 price + 50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50( 10)] = 25,725. Similarly, the year 3 price will be 1.05[year 2 price + 50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales. The variable cost in year 1 is triangularly distributed with parameters 10,000, 12,000, and 15,000, and it is assumed to increase by 5% each year. Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.
Based 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.)
Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.
Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of 150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of 250 per room. a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100. b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?
Software 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?
The Eagles will play the Falcons on Sunday, September 12, 2021. Suppose the Eagles have a 40% chance of winning the game. Suppose football games cannot end in a tie. (a) What is the random variable associated with this game? (b) What is the mutually exclusive event in this case? (c) Construct a well-labeled probability distribution table based on the outcomes of this game.
Do the following problems using either TreePlan A student is deciding which scholarships (out of two) to accept. The first scholarship is worth $10,000 but carries the condition that recipients cannot accept another other forms of income (such as other scholarships). The second scholarship is awarded in a competition, where this student has a 50% chance of earning $7,000, a 40% chance of earning $10,000, and a 10% chance of earning $15,000. The student must inform the administrator of the first scholarship whether she will be accepting their offer today. A. Develop a decision tree to determine which scholarship this student should accept (using our normal decision criteria). B. Under what circumstance might the student accept the other scholarship?
A grow fast company which is found in Addis Ababa is evaluating four alternative single period investment opportunities whose returns are based on the state of the economy. The possible state of the economy and the associated probability distributions are shown in the table below: State Fair Good Great Probability 0.3 0.4 0.3 Besides, the returns for each investment opportunity and each state of the economy are also clearly indicated in the given below table: Alternatives Fair Good Great Alternative 1 $2000 $4000 $7000 Alternative 2 $600 $4600 $6900 Alternative 3 $100 $5100 $8100 Alternative 4 $-4000 $6000 $8500 Based on the information given the above two tables determine:a. Expected monetary value (EMV) of the Grow fast company b. Expected Opportunity Loss (EOL) of the Grow fast company 2 | P a g ec. Expected value of perfect information (EVPI)
2. A daily demand for loaves of bread at a grocery store is given by the following probability distribution: 100 150 0.20 0.25 200 0.30 250 0.15 300 0.10 p(x) and the cost payoff matrix (in Rs) as: Daily Demand 100 150 200 250 350 100 300 300 300 300 300 150 250 450 450 450 450 200 200 400 600 600 600 250 150 350 550 750 750 350 100 300 500 700 900 i) Determine the best daily stock of loaves of bread using the expected monetary value (EMV) criterion. ii) Determine the best daily stock of loaves of bread using the expected opportunity loss (EOL) criterion. i) How much will the decision maker spend to get additional information? Daily Stock
Cliff Colby wants to determine whether his South Japanoil field will yield oil. He has hired geologist Digger Barnesto run tests on the field. If there is oil in the field, there is a95% chance that Digger’s tests will indicate oil. If the fieldcontains no oil, there is a 5% chance that Digger’s tests willindicate oil. If Digger’s tests indicate that there is no oil inthe field, what is the probability that the field contains oil?Before Digger conducts the test, Cliff believes that there isa 10% chance that the field will yield oil.