A small call center normally has four employees answering calls while open. On average, seven calls arrive every four minutes. Undernormal operating conditions, each employee on average handles each call in 3.3 minutes. But today, one employee has the flu, so thecenter needs to operate with three employees during this time. The manager is nervous that it may be supply-constrained and so shedirects her employees to hurry up their processing of calls today.What is the maximum average processing time for each call that they need to achieve today so that they have a stable queue?Note: Round your answer to 2 decimal places.Answer is complete but not entirely correct.Maximum average processing time4,73 minutes

Processing time refers to the duration taken for an entire procedure to run and the number of…

Answered: A small call center normally has four…

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

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An engineering i rm retains a technical specialist to assist four design engineers workingon a project. The help that the specialist gives engineers ranges widely in time consumption.The specialist has some answers available in memory, others require computation,and still others require signii cant search time. On the average, each request for assistancetakes the specialist one hour.The engineers require help from the specialist on the average of once each day. Becauseeach assistance takes about an hour, each engineer can work for seven hours, on the average,without assistance. One further point: Engineers needing help do not interrupt if thespecialist is already involved with another problem.Treat this as a i nite queuing problem and answer the following questions:a. How many engineers, on average, are waiting for the technical specialist for help?b. What is the average time that an engineer has to wait for the specialist?c. What is the probability that an engineer will have to wait…
Do: 12-21 Truck drivers working for Juhn and Sons (see Problems 12-19 and 12-20) are paid a salary of $20 per hour on average. Fruit loaders receive about $12 per hour. Truck drivers waiting in the queue or at the loading gate are drawing a salary but are productively idle and unable to generate revenue during that time. What would be the hourly cost savings to the firm associated with employing two loaders instead of one? Not this: 12-19 Juhn and Sons Wholesale Fruit Distributors employs one worker whose job is to load fruit on outgoing company trucks. Trucks arrive at the loading gate at an average of 24 per day, or 3 per hour, according to a Poisson distribution. The worker loads them at a rate of 4 per hour, following approximately the exponential distribution in service times. Not this: 2-20 Juhn believes that adding a second fruit loader will substantially improve the firm’s efficiency. He estimates that a two-person crew, still acting like a single-server system, at the loading…
Experience the Tour de France (ETF) is a specialty travel agent. It arranges vacations for amateur cyclists who want to experience the Tour de France by riding through one or more stages in the race. It has five people who take calls from clients. Each call lasts on average 25 minutes, with a standard deviation of 50 minutes. A call arrives on average every 20 minutes with a standard deviation of 20 minutes. (Do not round intermediate calculations. Round your answer to two decimal places.) On average, how many minutes does a caller wait before talking to an agent? minutes
A graphics reproduction firm has four units of equipment that are automatic but occasionally become inoperative because of the need for supplies, maintenance, or repair. Each unit requires service roughly twice each hour, or, more precisely, each unit of equipment runs an average of 30 minutes before needing service. Service times vary widely, ranging from a simple service (such as pressing a restart switch or repositioning paper) to more involved equipment disassembly. The average service time, however, is five minutes. Equipment downtime results in a loss of $20 per hour. The one equipment attendant is paid $6 per hour.Using finite queuing analysis, answer the following questions: a. What is the average number of units in line? b. What is the average number of units still in operation? c. What is the average number of units being serviced?d. The fi- rm is considering adding another attendant at the same $6 rate. Should the firm do it?
The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers’ parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers don’t get in until after the feature has started.) (Use the Excel spreadsheet Queue Models.) What is the average customer time in the system? What would be the effect on customer time in the system of having a second ticket taker doing nothing but validations and card punching, thereby cutting the average service time to 20 seconds? Note: Round your answer to 3 decimal places. What would be the customer time in the system if instead of the change in part (b), a second window was opened with each server doing all three tasks? Note: Do not round intermediate calculations. Round your answer to 3 decimal places. Would system waiting time which is obtained…
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?
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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…
The Shady Farm Milk Company can process milk at a fixed rate of 6,200 gallons/hour. The company’s clients request 104,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a.m. to 6 p.m. The company starts producing at 8 a.m. and continues to work until all of the demand has been satisfied. How long does an average unit milk have to wait between its arrival at the dairy until it is processed?
A graphics reproduction i rm has four units of equipment that are automatic but occasionallybecome inoperative because of the need for supplies, maintenance, or repair. Eachunit requires service roughly twice each hour, or, more precisely, each unit of equipmentruns an average of 30 minutes before needing service. Service times vary widely, rangingfrom a simple service (such as pressing a restart switch or repositioning paper) to moreinvolved equipment disassembly. The average service time, however, is i ve minutes.Equipment downtime results in a loss of $20 per hour. The one equipment attendant ispaid $6 per hour.Using i nite queuing analysis, answer the following questions:a. What is the average number of units in line?b. What is the average number of units still in operation?c. What is the average number of units being serviced?d. The i rm is considering adding another attendant at the same $6 rate. Should the i rmdo it?
Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 10 per hour. The clerk can take an order in an average of 4.0 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential. The cost of the clerk is $8 per hour, but because of lost goodwill and sales, Janson's loses about $25 per hour of customer time spent waiting for the clerk to take an order. a) The average time that catalog customers must wait before their calls are transferred to the order clerk = minutes (round your response to two decimal places). b) The average number of callers waiting to place an…

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