The length of time between breakdowns of an essential piece of equipment is important in the decision of the use of auxiliary equipment. An engineer thinks that the best “model” for time between breakdowns of a generator is the exponential distribution with a mean of 15 days. If the generator has just broken down, what is the probability that it will break down in the next 12 to 24 days?

The length of time between breakdowns of an essential piece of equipment is important in the decision of the use of auxiliary equipment. An engineer thinks that the best “model” for time between breakdowns of a generator is the exponential distribution with a mean of 15 days. If the generator has just broken down, what is the probability that it will break down in the next 12 to 24 days?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 65P

See similar textbooks

Similar questions

At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
When Apple introduced its mobile payment system in 2014, the company was looking to leverage the popularity of its iPhone by adding more functionality and convenience for millions of customers. With Apple Pay, iPhone owners and Apple Watch wearers first enter their credit- or debit-card information, which Apple confirms with the banks. Once this information is on file, Apple creates a digital token that will be electronically transmitted to the retailer when an iPhone owner pays for something. To complete a purchase, the customer simply waves the phone or taps it at the checkout, uses the iPhones Touch or Face ID security to activate Apple Pay, and the phone instantly transfers the token as payment. Even though Apple Pay offers consumers the benefits of convenience and security, Apple knew it wouldnt succeed without a large network of retailers, restaurants, and other businesses agreeing to accept its mobile payments. Among the earliest businesses to sign up with Apple was McDonalds, which agreed to honor Apple Pay in its 14,000 U.S. restaurants and drive-through locations. We serve 27 million customers every day. This is a clear and compelling business opportunity for us, explained McDonalds chief information officer. Compared with cash transactions, Apple Pay transactions cost McDonalds a few pennies more to process because of bank fees. Yet the fast-food giant was willing to sign on because it saw competitive advantage and profit potential in wooing iPhone users interested in speedy checkout. Another early business supporter was Walgreens, the nationwide drug-store chain with 85 million customers enrolled in its frequent-buyer rewards program. Walgreens sells snacks, household products, and health and beauty items in addition to health-care products. Not only did Walgreens agree to accept Apple Pay at its checkout counters, but it was also the first U.S. retailer to add its rewards program to Apple Pays easy sign-on system. As a result, Walgreens customers tap twice at the checkout, once to activate the rewards account and display their savings, the second time to process the actual payment. By deciding to honor Apple Pay, Walgreens said it was enabling a simple and convenient customer experience. Several hundred thousand businesses had signed on to participate by the time Apple Pay launched in October 2014. Apples ongoing efforts to increase business participation paid off: Eighteen months later, the network of participating businesses topped 2 million, and major companies like Starbucks, Dominos, and Crate Barrel were preparing to participate. Eyeing international expansion, Apple also initiated talks with banks in China to bring Apple Pay to millions of iPhone users there. Today, Apple Pay is accepted at more than 50 percent of all U.S. retail locations and in many retail stores in twenty countries. Even though more consumers are making more mobile payments year after year, not every U.S. retailer is willing or able to work with Apple Pay. Some arent satisfied with the amount of consumer information that Apple Pay shares with participating merchants. Others would have to upgrade to new checkout technology for Apple Pay. Still others are locked into exclusive mobile payment deals with competing services. Today, mobile payments represent a small fraction of all purchase transactions, dwarfed by cash as well as by credit and debit payments. And Apple Pay faces strong competition from Google, Samsung, and others operating in the mobile-payment market. To remain a leader, Apple will have to keep signing more participating businesses and showing consumers the benefits of paying by iPhone or Apple Watch whenever they make a purchase. Which of the four categories of business markets is Apple Pay best suited for, and why?
When Apple introduced its mobile payment system in 2014, the company was looking to leverage the popularity of its iPhone by adding more functionality and convenience for millions of customers. With Apple Pay, iPhone owners and Apple Watch wearers first enter their credit- or debit-card information, which Apple confirms with the banks. Once this information is on file, Apple creates a digital “token” that will be electronically transmitted to the retailer when an iPhone owner pays for something. To complete a purchase, the customer simply waves the phone or taps it at the checkout, uses the iPhone’s Touch or Face ID security to activate Apple Pay, and the phone instantly transfers the token as payment. Even though Apple Pay offers consumers the benefits of convenience and security, Apple knew it wouldn’t succeed without a large network of retailers, restaurants, and other businesses agreeing to accept its mobile payments. Among the earliest businesses to sign up with Apple was McDonald’s, which agreed to honor Apple Pay in its 14,000 U.S. restaurants and drive-through locations. “We serve 27 million customers every day. This is a clear and compelling business opportunity for us,” explained McDonald’s chief information officer. Compared with cash transactions, Apple Pay transactions cost McDonald’s a few pennies more to process because of bank fees. Yet the fast-food giant was willing to sign on because it saw competitive advantage and profit potential in wooing iPhone users interested in speedy checkout. Another early business supporter was Walgreens, the nationwide drug-store chain with 85 million customers enrolled in its frequent-buyer rewards program. Walgreens sells snacks, household products, and health and beauty items in addition to health-care products. Not only did Walgreens agree to accept Apple Pay at its checkout counters, but it was also the first U.S. retailer to add its rewards program to Apple Pay’s easy sign-on system. As a result, Walgreens’ customers tap twice at the checkout, once to activate the rewards account and display their savings, the second time to process the actual payment. By deciding to honor Apple Pay, Walgreens said it was “enabling a simple and convenient customer experience.” Several hundred thousand businesses had signed on to participate by the time Apple Pay launched in October 2014. Apple’s ongoing efforts to increase business participation paid off: Eighteen months later, the network of participating businesses topped 2 million, and major companies like Starbucks, Domino’s, and Crate & Barrel were preparing to participate. Eyeing international expansion, Apple also initiated talks with banks in China to bring Apple Pay to millions of iPhone users there. Today, Apple Pay is accepted at more than 50 percent of all U.S. retail locations and in many retail stores in twenty countries. Even though more consumers are making more mobile payments year after year, not every U.S. retailer is willing or able to work with Apple Pay. Some aren’t satisfied with the amount of consumer information that Apple Pay shares with participating merchants. Others would have to upgrade to new checkout technology for Apple Pay. Still others are locked into exclusive mobile payment deals with competing services. Today, mobile payments represent a small fraction of all purchase transactions, dwarfed by cash as well as by credit and debit payments. And Apple Pay faces strong competition from Google, Samsung, and others operating in the mobile-payment market. To remain a leader, Apple will have to keep signing more participating businesses and showing consumers the benefits of paying by iPhone or Apple Watch whenever they make a purchase. Which environmental influences on the decision process seem to have been most important to McDonald’s when it decided to honor Apple Pay?
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.
In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
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.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.