Spreadsheet Modeling & Decision Analysis: A Practical Introduction to Business Analytics (MindTap Course List)
8th Edition
ISBN: 9781305947412
Author: Cliff Ragsdale
Publisher: Cengage Learning
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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 one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4
What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5
What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours
The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air trafficcontroller to land planes. It takes an airplane 12 minutes to land and clear the runway. Planes arriveat the airport at the rate of four per hour. The FAA has a rule that an air traffic controller can, on average, land planes a maximum of 45 minutes out of every hour. There must be 15 minutes of idle time available to relieve the tension. Will this airport have to hire an extra air traffic controller?
Describe at least 4 operating characteristics you can determine by performing queue analysis. What is the purpose of doing queue analysis to the business owner, i.e., what are possible actions (at least 2) that a business owner or manager might want to take, once the operating characteristics are understood?
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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_forwardCustomers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. Assume that service times are exponentially distributed and that the queuing system model is (M/M/1):(GD/infinity/infinity). Does this queuing system have a steady state? It cannot be determined. Yes none of the other choices Noarrow_forwardA 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…arrow_forward
- The Seaboard Shipping Company has a warehouse terminal in Spartanburg, South Carolina. The capacity of each termi-nal dock is three trucks. As trucks enter the terminal, the dri-vers receive numbers, and when one of the three dock spaces becomes available, the truck with the lowest number entersthe vacant dock. Truck arrivals are Poisson distributed, and the unloading and loading times (service times) are expo-nentially distributed. The average arrival rate at the terminal is 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 consider-ing adding extra employees and equipment to improve the average service time per terminal dock to 25 min-utes per truck. It would cost the company $18,000 per year 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.…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_forwardWorkers come to tool store room to enquire about special tools (required by them) for accomplishing a particular project assigned to them. The average time between two arrivals is 60 seconds and the arivals are assumed to be in Poisson distribution. The average service time (of the tool room attendant) is 40 seconds. Determine: (1) average queue length, (i) average length of non-empty queues, (ii) average number of workers in system including the worker being attended (iv) mean waiting time of an arrival, (v) average waiting time of an arrival who waits.arrow_forward
- A chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for their jobs. The warehouse receives a request for supplies, on average, every 2 minutes (Poisson distributed). The average request requires 1.7 minutes to fill (exponential service times). Maintenance employees are paid $20 per hour, and warehouse employees are paid $12 per hour. The warehouse is open 8 hours each day. What is the optimal number of warehouse employees to hire? (Hint: Time spent by maintenance workers waiting in line for supplies should be considered an expense.) What is the total cost per hour (waiting plus warehouse employee labor cost) of your solution?arrow_forwardMarty's Barber Shop has one barber. Customers have an arrival rate of 1.1 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 one customer is receiving a haircut and two customers are waiting? Round your answer to four decimal places.P3 = What is the probability that more than two customers are waiting? Round your answer to four decimal places.P(More than 2 waiting) = What is the average time a customer waits for service? Round your answer to four decimal places.Wq = minutesarrow_forwardThe Escargot is a small French restaurant with six waiters and waitresses. The average service time at the restaurant for a table (of any size) is 85 minutes (Poisson distributed). The restaurant does not take reservations, and parties arrive for dinner (and stay and wait) every 18 minutes (negative exponential distribution). The restaurant owner is concerned that a lengthy waiting time might hurt its business in the long run. What are the current waiting time and queue length for the restaurant? Discuss the business implications of the current waiting time and any actions the restaurant owner might take.arrow_forward
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