Robert Olney's Barbershop is a popular haircutting and styling salon near the campus of the University of New Haven. Four barbers work full-time andspend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. Arrivals tend to follow thePoisson distribution, and service times are negative exponentially distributed. The software described in this quantitative module may be used to answerthe following questions.a) The probability that the shop is empty isb) The average number of customers in the barber shop isc) The average time spent in the shop ishours (round your response to three decimal places).d) The average time that a customer waits to be called to the barber chair is hours (round your response to three decimal places).e) The average number waiting to be served iscustomers (round your response to two decimal places).f) Robert is thinking of adding a fifth barber. The utilization rate of his shop will be (round your response to four decimal places).(round your response to four decimal places).customers (round your response to two decimal places).

Answered: Robert Olney's Barbershop is a popular…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

See similar textbooks

Similar questions

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?
Peter's International Barbershop is a popular haircutting and styling saloon near the campus of the Brooklyn College. One barber is available to work full time and spend an average of 3 minutes on each customer. Customers arrive all day long at an average rate of 2 customers every 10 minutes. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. Explain your results. What is the probability that the shop is empty? What is the average number of customers in the barbershop? What is the average time spent in the shop? What percentage of time the barber is busy? What is the average number of customers waiting to be served? What is the probability that there will be more than two customers in the shop?
The Fast Shop Drive-In Market has one checkout counter where one employee operates the cash register. The combination of the cash register and the operator is the checkout counter in this waiting line system. Customers arrive at a rate of one every 3 minutes according to a Poisson distribution, and service times are exponentially distributed, with a mean rate of 30 customers per hour. a) The market manager wants to determine the following for this waiting line system: Average number of customers in the total system Average time spent in the system per customer Probability that there are more than 2 customers waiting in line
Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 87 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following: a. The average time customers spend at the machine, including waiting in line and completing transactions b. The probability that a customer will not have to wait upon arriving at the automatic teller machine c. The average number waiting to use the machine
Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes, One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: i) Compute the average number of cars in line

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Marketing

ISBN:

9780357033791

Author:

Pride, William M

Publisher:

South Western Educational Publishing

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Marketing

ISBN:

9780357033791

Author:

Pride, William M

Publisher:

South Western Educational Publishing

SEE MORE TEXTBOOKS