Plot the percentage of machines not running as a function of the service factor for a popula- tion of 20 machines with exponential arrivals and services (a) if a single channel is employed and (b) if two channels are employed.
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Plot the percentage of machines not running as a function of the service factor for a popula-
tion of 20 machines with exponential arrivals and services (a) if a single channel is employed
and (b) if two channels are employed.
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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 study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS.a. Calculate the percentage utilization of the graduate student.b. Calculate the average number of students in the system, excluding the graduate student service.c. Calculate the average time in the system.d. Calculate the probability of four or more students being in line or being served.e. Before a test, the arrival of students increases to six per hour, on average. What will the new average line length be?A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Calculate the percentage utilization of the graduate student. Note: Round your answer to 1 decimal place. Calculate the average number of students in the system, including the graduate student service desk. Note: Round your answer to the nearest whole number. Calculate the average time in the system. Note: Round your answer to the nearest whole number. Calculate the probability of four or more students being in line or being served. Note: Round your intermediate calculations to 3…
- Mr. E's cabinet-making shop, in Memphis, has five tools that automate the drilling of holes for the installation of hinges. These machines need setting up for each order of cabinets. The orders appear to follow the Poisson distribution, averaging 3 per 8-hour day. There is a single technician for setting these machines. His service times are exponential, averaging 2 hours each. a)What is the service factor for this system? b)What is the average number of these machines in service? c) What impact on machines in service would there be if a second technician were available?4.) The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?Pls help ASAP. Pls do part D only from this question. only do part d pls.
- Plz solve !!The Seaboard Shipping Company has a warehouse terminalin Spartanburg, South Carolina. The capacity of each terminal dock is three trucks. As trucks enter the terminal, the drivers receive numbers, and when one of the three dock spacesbecomes available, the truck with the lowest number entersthe vacant dock. Truck arrivals are Poisson distributed, andthe unloading and loading times (service times) are exponentially distributed. The average arrival rate at the terminalis five trucks per hour, and the average service rate per dockis two trucks per hour (30 minutes per truck).a. Compute L, Lq, W, and Wq.b. The management of the shipping company is considering adding extra employees and equipment to improvethe average service time per terminal dock to 25 minutes per truck. It would cost the company $18,000 peryear to achieve this improved service. Managementestimates that it will increase its profit by $750 per yearfor each minute it is able to reduce a truck’s waitingtime. Determine…Dimeco, Inc., a small manufacturer of punching die sets has four high speed machines. Because of the age of these machines, they need minor repairs after 30 hours of use. Analysis of previous breakdowns indicates that breakdowns follow a Poisson distribution. The facility employs one repairman specifically to repair these machines. Average repair time is two hours following an exponential distribution. What is the service factor for this system? What is the average number of these machines in service? What is the impact of adding a second repairman?
- Give reason that why do waiting lines form even though a service system is underloaded .Demand at the Krispy Kreme drive-through has jumped up with the new restrictions on inside dining. Customers are arriving according to a Poisson process, at an average of 5 minutes between customers. It takes 4 minutes to serve a car. There is only one drive through channel. Answer the following questions. a. What model best matches this situation? Model used: (time units) |(time units) arrival rate: per population: ("infinite" or a number) service rate: per servers: b. What is the average number cars in the drive-through, including the one being served? c. How long does it take, on average, for a customer to get the product? (time units) d. What is the probability that a customer will show up and not find anyone in the drive-through? e. What is the probability that there will be 3 or more cars in the drive through when a customer arrives? (don't count the customer who is arriving)Pls help with beloew homework :
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