The Platinum Star Hotel in Kingston, NY, is considering doing overbooking in order to deal with the constant problem they have with no-shows. The table given below presents the number of no-shows and the probability of each occurring. Number of Shows (d) Probability of No-shows Occurring P(d) 0 0.10 1 0.07 2 0.12 3 0.02 4 0.07 5 0.01 6 0.04 7 0.19 8 0.22 9 0.16 a) What would be your recommendation for overbooking if the average rate per room per night is S125 and the cost of not honoring a reservation is $155? b) What is the expected loss for your overbooking choice? c) State the reasoning for selecting your overbooking choice?

The Platinum Star Hotel in Kingston, NY, is considering doing overbooking in order to deal with the constant problem they have with no-shows. The table given below presents the number of no-shows and the probability of each occurring. Number of Shows (d) Probability of No-shows Occurring P(d) 0 0.10 1 0.07 2 0.12 3 0.02 4 0.07 5 0.01 6 0.04 7 0.19 8 0.22 9 0.16 a) What would be your recommendation for overbooking if the average rate per room per night is S125 and the cost of not honoring a reservation is $155? b) What is the expected loss for your overbooking choice? c) State the reasoning for selecting your overbooking choice?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.4: Simulation With Built-in Excel Tools

Problem 12P: In August of the current year, a car dealer is trying to determine how many cars of the next model...

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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.)
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).
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
A 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.
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 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.)
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?
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?
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.
A new edition of a very popular textbook will be published a year from now. The publisher currently has 1000 copies on hand and is deciding whether to do another printing before the new edition comes out. The publisher estimates that demand for the book during the next year is governed by the probability distribution in the file P10_31.xlsx. A production run incurs a fixed cost of 15,000 plus a variable cost of 20 per book printed. Books are sold for 190 per book. Any demand that cannot be met incurs a penalty cost of 30 per book, due to loss of goodwill. Up to 1000 of any leftover books can be sold to Barnes and Noble for 45 per book. The publisher is interested in maximizing expected profit. The following print-run sizes are under consideration: 0 (no production run) to 16,000 in increments of 2000. What decision would you recommend? Use simulation with 1000 replications. For your optimal decision, the publisher can be 90% certain that the actual profit associated with remaining sales of the current edition will be between what two values?
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.
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.
In August of the current year, a car dealer is trying to determine how many cars of the next model year to order. Each car ordered in August costs 20,000. The demand for the dealers next year models has the probability distribution shown in the file P10_12.xlsx. Each car sells for 25,000. If demand for next years cars exceeds the number of cars ordered in August, the dealer must reorder at a cost of 22,000 per car. Excess cars can be disposed of at 17,000 per car. Use simulation to determine how many cars to order in August. For your optimal order quantity, find a 95% confidence interval for the expected profit.