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MindTap Business Statistics for Ragsdale's Spreadsheet Modeling & Decision Analysis, 8th Edition, [Instant Access], 2 terms (12 months)
8th Edition
ISBN: 9781337274876
Author: Cliff Ragsdale
Publisher: Cengage Learning US
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A large industrial pier has two cranes that load container ships. Trucks arrive in a single line and then go to the next available crane when it is clear to do so. The arrival rate of the trucks is Poisson distributed. They arrive at a rate of 20 trucks per hour. Each crane works independently and can attach to the truck-pulled container and place it on the container ship in 4.8 minutes, on average. Crane loading activities follow an exponential distribution.
How many trucks are on the pier on average?
The Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A patrol car requires
repairs every 30 days, on average, according to an exponen-tial distribution. When a patrol car is in need of repair it is
driven into the motor pool, which has a repairperson on
duty at all times. The average time required to repair a pa-trol car is 12 hours (exponentially distributed). Determine
the average time a patrol car is not available for use and theaverage number of patrol cars out of service at any onetime, and indicate if the repair service seems adequate.
Partially completed products arrive at a workstation in a manufacturing operation at a mean rate of 40 per hour (Poisson distributed). The processing time at the workstation averages 1.2 minutes per unit (exponentially distributed). The manufacturing company estimates that each unit of work-inprocess inventory at the workstation costs $31 per day (on average). However, the company can add extra employees and reduce the processing time to 0.90 minute per unit, at a cost of $52 per day. Determine whether the company should continue the present operation or add extra employees.
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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?arrow_forwardThe new-accounts officer at the Bank enrolls all new customers in checking accounts. During the three-week period in August encompassing the beginning of the new school year at UTT, the bank opens many new accounts for students. The bank estimates that the arrival rate during this period will be Poisson distributed with an average of five (5) customers per hour. The service time is exponentially distributed with an average of 15 minutes per customer to set up a new account. The bank wants to determine the operating characteristics for this system to determine if the current person is sufficient to handle the increased traffic. What is the probability of no customers in the system? What is the average number of customers waiting in the bank? What is the average time the customer spends in the bank? What is the average number of customers waiting in the line? What is the average time that a customer spends in the line? Is the number of tellers sufficient to handle the increase…arrow_forwardThe Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A patrol car requiresrepairs every 30 days, on average, according to an exponential distribution. When a patrol car is in need of repair it isdriven into the motor pool, which has a repairperson onduty at all times. The average time required to repair a patrol car is 12 hours (exponentially distributed). Determinethe average time a patrol car is not available for use and theaverage number of patrol cars out of service at any onetime, and indicate if the repair service seems adequatearrow_forward
- McBurger’s fast-food restaurant has a drive-through window with a single server who takes orders from an intercom and also is the cashier. The window operator is assisted by other employees who prepare the orders. Customers arrive at the ordering station prior to the drivethrough window every 4.5 minutes (Poisson distributed), and the service time is 2.8 minutes (exponentially distributed). Determine the average length of the waiting line and the waiting time. Discuss the quality of the service.arrow_forwardThe computer laboratory at a State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On the average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by a constant distribution. Calculate the following characteristics of the system: The average utilization of the help desk server. The average number of students waiting in line. The average number of students waiting in the system. The average time a student spends in the systemarrow_forwardThe Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can service 15 customers per minute . Cars arrive at the regular unleaded pump at a rate of 12 per minute Determine the average queue length, The average number of car in the queuing system, the average time a car is in the system, and the average time a car must wait.arrow_forward
- A single-server queuing system with an infinite calling population and a first-come, first-served queue discipline has the following arrival and service rates (poisson distributed): l = 16 customers per hour m = 24 customers per hour Determine P0, P3, L, Lq,W,Wq, and U.arrow_forwardThe 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…arrow_forwardCustomers arrive at Cochinito Bank according to a Poisson distribution, with a mean of 45 customers per hour. Transactions per customer take around 5 minutes and are distributed exponentially. The bank wants to use a single line and several boxes, similar to those used in airports and some dependencies. The manager is aware that customers may go to other banks if they perceive their waiting in line to be “excessive”. For this reason, the manager wants to limit the average wait time in the queue to no more than 30 seconds. How many boxes should the bank put into service?arrow_forward
- Please build and simulate the following model in ARENA.In this model, car loan applications arrive at processing center approximately every 5 minutes. At this point, 1 of 5 loan officers will review the application to ensure that it is complete. This review step usually takes 15 minutes, but can be as short as 12 minutes or as long as 18 minutes. Applications are sent to an automatic processing machine where they are processed. This process can take from 0.5 to 1.5 hours to complete, but usually requires 1 hour. It is assumed that the automatic processor can process as many applications as needed.After processing, the results are reviewed by a loan officer who will write either an acceptance or rejection document. This task usually takes 7 minutes, but can require anywhere from 5 to 10 minutes to complete.At this point the loan application process is complete, and the acceptance or rejection document is sent to the customer.Run this simulation for one 8-hour day (5 replications).arrow_forwardHow does an event improve the smooth queue management?arrow_forwardBill First, general manager of Worthmore Department Store, has estimated that every hour of customer time spent waiting in line for a sales clerk to become available costs the store $100 in lost sales and goodwill. Customers arrive at the checkout counter at the rate of 30 per hour, and the average service time is 3 minutes. The Poisson distribution describes the arrivals and the service times are exponentially distributed. The number of sales clerks can be 2, 3, or 4, with each one working at the same rate. Bill estimates the salary and benefits for each clerk to be $10 per hour. The store is open 10 hours per day. (a) Find the average time in the line if 2, 3, and 4 clerks are used. (b) What is the total time spent waiting in line each day if 2, 3, and 4 clerks are used? (c) Calculate the total of the daily waiting cost and the service cost if 2, 3, and 4 clerks are used. What is the minimum total daily cost?arrow_forward
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