Concept explainers
Drivers who come to get their licenses at the department of motor vehicles have their photograph taken by an automated machine that develops the photograph onto the license card and laminates the complete license. The machine requires a constant time of 4.5 minutes to develop a completed license. If drivers arrive at the machine at the mean rate of 11 per hour (Poisson distributed), determine the average length of the waiting line and the average waiting time.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
OPERATIONS AND SUPPLY CHAIN MANAGEMENT
Additional Business Textbook Solutions
Business in Action
Operations Management, Binder Ready Version: An Integrated Approach
Principles of Operations Management: Sustainability and Supply Chain Management (10th Edition)
Business in Action (8th Edition)
Operations Management: Processes and Supply Chains (12th Edition) (What's New in Operations Management)
- 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_forwardStudents arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?arrow_forwardA toll tunnel has decided to experiment with the use of a debit card for the collection of tolls. Initially, only one lane will be used. Cars are estimated to arrive at this experimental lane at a rate of 750 per hour. It will take exactly four seconds to verify the debit card. (Answers in Appendix D)a. In how much time would you expect the customer to wait in line, pay with the debit card, and leave?b. How many cars would you expect to see in the system?arrow_forward
- Customers arrive at the lobby of the exclusive and expensive Ritz Hotel at the rate of 40 per hour (Poisson distributed) to check in. The hotel normally has three clerksavailable at the desk to check guests in. The average timefor a clerk to check in a guest is four minutes (exponentially distributed). Clerks at the Regency are paid $12 perhour and the hotel assigns a goodwill cost of $2 per minutefor the time a guest must wait in line. Determine if the present check-in system is cost effective; if it is not, recommend what hotel management should doarrow_forwardat the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machines to be sorted for loading onto the appropriate truck for the parcel address. the arrival rate at the sorting machines is at the rate of 100 per hour following Poisson distribution. the machine sorts at the constant rate of 150 per hour.a. what is the utilization rate of system? b. what is the average number of packages waiting to be sorted? c. what is the average number of packages in the sorting system? d. how long must the average package wait until it gets sorted? e. what would Lq and wq be if the service rate were exponential, not constant?arrow_forwardThe Universal Manufacturing Company produces a particular product in an assembly-line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, on average, according to an exponential distribution. The machine operator can process an average of 10 parts per hour (Poisson distributed). Determine the average number of parts waiting to be worked on, the percentage of time the operator is working, and the percentage of time the machine is idle. The management of Universal Manufacturing Company likes to have its operators working 90% of the time. What must the assembly line arrival rate be in order for the operators to be as busy as management would like?arrow_forward
- Circle Electric Supply is considering opening a second service counter to better serve their electrical contractor customers. The arrival rate is 11 per hour. The service rate is 16 per hour. If the cost of waiting is $31 and the cost of each service counter is $23 per hour, should the second counter be opened? (Give your numerical values in dollars per hour. Round your answers to two decimal places.) With one counter, the cost per hour is $ . With two counters, the cost per hour is $ . The second counter ---Select--- should should not be opened.arrow_forwardStudents arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the utilization factor?arrow_forwardMelanie is the manager of the Clean Machine car washand has gathered the following information. Customers arriveat a rate of eight per hour according to a Poisson distribution.Th e car washer can service an average of ten cars per hour withservice times described by an exponential distribution. Melanie isconcerned about the number of customers waiting in line. She hasasked you to calculate the following system characteristics:(a) Average system utilization(b) Average number of customers in the system(c) Average number of customers waiting in linearrow_forward
- Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from…arrow_forwardA student arrive in a photocopy service. There is only one photocopy operator, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem? Select one: a. 2.28 minutes b. 4.35 minutes c. 3 minutes d. 1 minutearrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,MarketingMarketingISBN:9780357033791Author:Pride, William MPublisher:South Western Educational Publishing