As an interested student, you have volunteered to study the operation of the Sunbucks during a typical weekday. You arrive at 8 am just as Sunbucks is opening, and you diligently record information over the next hour. According to the manager, Sunbucks should be able to serve an average of 1 customer every 2 minutes and during the period you were collecting data 25 customers arrived to make a purchase. Based on your data, What was the average waiting time for a customer in line during this period? a) 25 .16 b)3.67 c) 1.0 d)4.167
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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?Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag. If Joe does not want the average waiting time in the queue to exceed 5 minutes, what would you tell Joe about his current system? Back up your statement with quantitative information and assumptions.Customers arrive at the company's service office at an average of one every 20 minutes. Their requests take, on average, 15 minutes to be processed. The service counter is staffed by only one employee, who works six hours per day. Assume Poisson arrivals and exponential service times. What model should you use? What percentage of time is the employee idle? How long is the waiting line, on average? How much time, on average, does a customer spend waiting in line? What is the probability that an arriving customer, just before entering the office, will find at least one other customer waiting in line?
- One field representative services 5 customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every 3.1 working days. The field representative can handle an average (Poisson-distributed) of 1.0 call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round "X" value to 2 decimal places. Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s)A typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screeneach passenger that arrives at the security gate. During the day, a passenger arrives at the gate onaverage every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based onthis information and the assumption that only one screening line is open at the security gate, answer thefollowing questions. Round calculations to at least 3 decimal places.Note: Round each calculation to at least 3 decimal places. a) What is the average number of passengers waiting in line to be screened? b) What is the average amount of time (in minutes) passengers spend waiting in line? c) What is the average amount of time (in minutes) passengers spend in the screening system? d) What is percent of the time does the typical TSA agent spend actively screening passengers? e) Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45…A nice psychologist is providing free consultations to each individual in her town. Each patient comes in to her office on average of every 27 minutes, and she spends an average of 19 minutes with each one of them. Assume that both patient inter-arrival times and the times that she spends with the patient are exponentially distributed. Keep in mind of the system including the psychologist and the patients come to her for help, who when necessary, waiting in line for their turn. 1. What's the throughput, and the capacity of this system? 2. Now assuming that once each patient comes in, no consultation ever finishes before receiving her help. How much time, on average, do consultation last in the system, from the moment it begins until finishing?
- When customers arrive at Gilley’s Ice Cream Shop, theytake a number and wait to be called to purchase ice creamfrom one of the counter servers. From experience in pastsummers, the store’s staff knows that customers arrive atthe rate of 35 per hour (Poisson distributed) on summerdays between 3:00 P.M. and 10:00 P.M. and a server canserve 15 customers per hour on average (Poisson distributed). Gilley’s wants to make sure that customers wait nolonger than 5 minutes for service. Gilley’s is contemplatingkeeping three servers behind the ice cream counter duringthe peak summer hours. Will this number be adequate tomeet the waiting time policy?Students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take, on average, 4 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. a. What percentage of time is Judy idle? (Round your answer to 1 decimal place.) b. How much time, on average, does a student spend waiting in line? (Do not round intermediate calculations. Round your answer to 1 decimal place.) c. How long is the (waiting) line on average? (Round your answer to 2 decimal places.) d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Do not round intermediate calculations. Round your answer to 4 decimal places.)Customers arrive at the lone check-out desk of a certain convenience store at the average rate of 0.23 per minute. If it takes on average four minutes for the store manager to serve each customer, how many customers will on average find themselves waiting in the queue? A. 10.58 B. 0.00024 C. 3.20 D. 0.00351
- A new customer walks into SLC Barber Shop every 60 minutes on average, with a standard deviation of the interarrival times being 60 minutes. At SLC Barber Shop, the average service time is 30 minutes, with a standard deviation of service times being 45 minutes. 1.What is the demand for SLC Barber shop in [customer/minute]? 2.What is the average waiting time of a customer in minutes?Josh’s Hot Dogs is a one-person hot dog stand, and normally gets about 14 customers per hour. Assuming that Josh can serve one customer in about 3 minutes. What impact does this have on the queuing characteristics? Specifically, the following questions:a. Mean number of customer in the queue b. Mean number of customer in the system: c. Mean waiting time in the queue:d. Mean waiting time in the system:e. Utilization factor for the system:f. Probability of more than 1 customer in the system at any given time.g. Do you think he has an acceptable queuing system?Customers arrive at Rich Dunn's Styling Shop at a rate of 4 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 8 haircuts per hour. a) The average number of customers waiting for haircuts = 0.500.50 customers (round your response to two decimal places). b) The average number of customers in the shop = nothing customers (round your response to two decimal places).