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Shauna’s Fast-food Service is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poison probability distribution, with an arrival rate of 24 cars per hour and the service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered:
- A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes.
- A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes
- A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each server. Answer the following questions and recommend one of the design options
Respond to the following:
- What is the probability that no cars are in the system?
- What is the average number of cars waiting for service?
- What is the average number of cars in the system?
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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?A company is considering opening a fast-food service operation (drive through). Prior research shows that customer arrivals would follow a Poisson process, with an arrival rate of 24 cars per hour, and that service times would follow a negative exponential probability distribution. Arriving customers would place orders at an intercom station at the back of the parking lot and then drive to the service area to pay for and receive their orders. The following service alternatives are being considered: Q1. A single-server operation in one service window in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. - What is the average number of cars waiting for service in the line? Ans= 3.2 Cars - What is the average number of cars in the system? Ans = 4 cars - What is the average time a car waits for service in the line? Ans = 0.13 hours = 7.8 mins - What is…given the following: A typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screeneach passenger that arrives at the security gate. During the day, a passenger arrives at the gate onaverage every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based onthis information and the assumption that only one screening line is open at the security gate, answer thefollowing questions with the given information: a) average number of passengers waiting in line to be screened is 7 b) average amount of time (in minutes) passengers spend waiting in line is .147 minutes c) average amount of time (in minutes) passengers spend in the screening system?.166 minutes 1. What is percent of the time does the typical TSA agent spend actively screening passengers? 2. Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45 minutes before a flight is expected to depart. If during this…
- The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes.A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained?C. How many trucks are lined up in front of the station on the average?D. How long on the average does a truck driver have to wait in line for the truck to beinspected?Shauna’s Fast-food Service is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poison probability distribution, with an arrival rate of 24 cars per hour and the service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered: A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from…Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = fill in the blank 1 What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = fill in the blank 2 What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = fill in the blank 3
- Instructions Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of 1 car every 10 minutes and the service times follow an exponential probability distribution, with a service rate of 8 cars per hour. What is the probability that the station will be idle? What is the average number of cars that will be waiting for service? What is the average time a car will be waiting for service? What is the average time a car will be at the gas and wash station?A grocery store checkout counter operates with a single server to process customertransactions. Customers arrive at the counter with an average rate of 20 customers perhour, following a Poisson distribution. The average service time per customer is 2.5minutes, following an exponential distribution. Calculate the following performancemeasures for the checkout counter: a. Average time a customer spends in the system (waiting time + service time).b. Probability that the server is idle (not serving any customer).c. Determine the probability that there will be exactly two customers in the system(both in the queue and being served) at any given moment. What does thisprobability indicate about the checkout counter's efficiency in handling customerflow?d. Discuss how the probability in part f above might change if the average servicetime per customer increases or decreases.A car mechanic, Carlos, can install new mufflers at an average rate of 3 every hour (following an exponential distribution). Customers needing this service arrive at the shop (following a Poisson distribution) on an average of 2 per hour. They are served on a first-in, first-out basis and come from the very large (almost infinite) population of possible buyers. Calculate the following operating characteristics of the service system: a. The probability there are no cars in the system. b. The average number of cars waiting in line. c. The average number of cars in the system. d. The average time a car spends waiting in line. e. The average time a car spends in the system.