A Northwest Airlines ticket counter forecasts that 30 people per hour will need to check in. It takes an average of 1.5 minutes to service a customer. Assume that interarrival times and service times are exponential and that all customers wait in a single line for the first avaliable agent.If we want the average time a customer spends in line and in service to be 3 minutes or less, how many ticket agents should be on duty?
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- During nearly four decades of business operations, Memphis-based FedEx has earned a reputation for reliable, on-time delivery of packages to homes and offices around the country. Founder Fred Smith originally focused on overnight deliveries, choosing Memphis as the company’s headquarters because the airport rarely closes due to bad weather. With FedEx’s planes departing and arriving on schedule nearly all the time, its express shipments usually remained on schedule, then and now. To reassure customers that delivery will take place when and where promised, the firm offers a money-back guarantee on time-sensitive express shipments, among other services. FedEx has steadily expanded its portfolio of services since the 1970s. Its original overnight express delivery is currently available to U.S. customers in various forms, including “first-overnight” delivery, next-morning delivery, next-afternoon delivery, and budget-pleasing two- or three-day delivery. The company’s services also include cost-effective ground delivery for parcels and extra-speedy same-day delivery for urgent deliveries within 1,800 cities. Over the years, FedEx has widened its delivery network to more than 220 countries. It has purchased more cargo jets and acquired specialized shipping firms, including Tiger International, Roberts Express, RPS, and TNT Express, to support global growth. For international business customers needing products, parts, or raw materials shipped across countries or continents, the company now offers time-saving services such as commercial freight forwarding and cross-border logistical support. To add the convenience of local drop-off and pickup points for U.S. consumers and small businesses, FedEx acquired the Kinko’s office services company in 2004 and later rebranded it as FedEx Office. This acquisition also added printing and copying to the menu of services offered. Then the company arranged for large U.S. retailers such as Walgreens, Albertsons, Kroger, and Safeway to accept packages for shipment and receive package delivery for customer pickup in thousands of store locations. This means people who want to send a package can head to a nearby retailer and ship where they shop, rather than making a separate trip to the FedEx location. It’s also a safe alternative for packages to be picked up by people who don’t want FedEx shipments left by the front door. Another service FedEx offers to small and mid-sized businesses, including retailers, is FedEx Fulfillment. The purpose is to expedite order fulfillment by having each business store its products in a FedEx warehouse. Then, when the business’s customers place orders, FedEx puts the products into boxes bearing the business’s own logo and ships directly to those customers. The business doesn’t need a separate warehouse or staff for fulfillment, and packages are on their way to customers more quickly because the products were in FedEx’s warehouse, ready to be packed and shipped. This service puts FedEx into direct competition with Amazon.com, which offers a similar service to merchants that sell through the online Amazon Marketplace. But it also gives businesses that don’t sell via Amazon a fast and professional fulfillment alternative. FedEx is careful to let customers know, through media and social-media announcements, when it anticipates that extreme weather or other conditions will cause delays or force it to halt pickups and deliveries. For the duration of Hurricane Irma, for example, FedEx said it would suspend deliveries in Florida. Some Florida customers who had ordered generators to be delivered via FedEx were unhappy, because they worried about being without power during and after the storm. But one FedEx employee loaded several generator orders into his car and took them to customers himself. When a customer posted a grateful compliment to FedEx on Facebook, the message generated thousands of likes, shares, and positive comments. The company also received positive comments for its donations of cash and transportation services to areas devastated by Hurricanes Irma, Harvey, and Maria. According to the American Customer Satisfaction Index (ACSI), FedEx often tops the list of U.S. shipping companies as ranked by customers surveyed. Every day, the company delivers 13 million packages—and during the busy year-end holiday season, it delivers many more. By meeting customers’ expectations for on-time deliveries, FedEx has increased annual revenues beyond $60 billion and positioned itself for continued growth in the future. How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a) Compute the average number of cars in line.Consider the baggage check-in process of a small airline. Check-in data indicate thatfrom 9 a.m. to 10 a.m., 240 passengers checked in. Moreover, based on counting thenumber of passengers waiting in line, airport management found that the average number of passengers waiting for check-in was 30. How long did the average passenger haveto wait in line?
- Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a.Compute the average number of cars in line. b.Calculate the value of probability that there are no car in the system. c.Compute the average time that a car spends in the system.Angkut Deras Hauling Company has two long-trip cars rental servicesinclusive with a driver at Kota Kinabalu International Airport. The companyhas determine during the late-evening hours on weekend, customersrequest driver for cars rental at a rate that follows the Poisson distributionwith a mean of 0.8 per hour. Travel and assistance time is exponential witha mean of 1 request per hour. Find each of the performance measures ofthis waiting line system. a) What is the system utilization rate for Angkut Deras Hauling Company?b) Probability that both drivers will be busy when a customer request.c) The average number of customer waiting in line.d) The average time customers wait for a driver.e) What is the customers average waiting time on arrival?Explain in what kind of situations is queuing analysis is most important under waiting line models ? It's from operations management domain don't sent it to other subjects plz !
- Describe a situation in your daily life that could be improved by waiting line analysis. Explain how the design of a waiting system can negatively affect customers. Visit your local bank and observe the waiting line system. Describe the system in terms of number of lines, number of facilities, and number of phases.13. Movie Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evening, customers arrive at Movies Tonight at the average rate of 1.25 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times.What is the probability that no customers are in the system?What is the average number of customers waiting services?What is the average time a customer waits for service to begin?Do the operating characteristics indicate that the one-clerk check out system provides an acceptable level of service?a. Customers queue at the express aisle of a supermarket checkout at the rate of 16 per hour. Employees can serve one customer every three minutes. Assuming the number of anivals follows a Poisson distribution: i. Calculate the average number of customers in the waiting line. ii. Calculate the average time a customer spends in the waiting line. b. An investment firm is considering whether to invest in the mining sector, property, or fixed interest in the coming year. The research division has provided modelling under various scenarios and estimated the expected profit for each choice depending on whether economic growth is moderate, low, or in recession. It has also estimated the probability for each economic growth scenario, as summarised in the table below: Economic growth Moderate Low Recession Profit for each Mining 100 55 -25 choice (Smillions) 46 25 15 Property Fixed 20 20 20 Probability 0.2 0.35 0.45 i Calculate the expected profit for each choice and state which investment the…
- In an M/M/1 queueing system, the arrival rate is 3 customers per hour and the service rate is 5 customers per hour. a. What is the utilization? (round your answer to 3 decimal places) b. What is the expected number of customers in the system (L)? (round your answer to 3 decimal places) c. What is the expected waiting time in the system (W)? (express the waiting time in hours, round your answer to 3 decimal places) d. What is the expected number of customers in the queue (Lq)? (round your answer to 3 decimal places) e. What is the expected waiting time in the queue (Wq)? (express the waiting time in hours, round your answer to 3 decimal places)To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on the average, 10 persons per hour request a test. Blood pressure measurements can be made following the queuing (waiting line) model we have studied with an average service time of five minutes each. a) What is the expected average number waiting in line for the testing booth? b) What is the average amount of time that a person can expect to spend waiting in line? c) On average, how long will a person spend in the system (waiting for the testing booth and having the blood pressure test)? d) What is the probability that a person arriving will have to wait for the testing booth?Customers in LineWestern National Bank is considering opening a drive-thru window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.Part 1 Assuming Poisson arrivals and exponential service, find1. Utilization of the teller.2. The average number in the waiting line.3. The average number in the system.4. The average waiting time in line.5. The average waiting time in the system, including service.