6. The Garrett-Tompkins Company provides three copy machines in its copying room for the use ofits employees. However, due to recent complaints about considerable time being wasted waitingfor a copier to become free, management is considering adding one or more additional copymachines.During the 2,000 working hours per year, employees arrive at the copying room according to aPoisson process at a mean rate of 40 per hour. The time each employee needs with a copymachine is believed to have an exponential distribution with a mean of 4 minutes. The lostproductivity due to an employee spending time in the copying room is estimated to cost thecompany an average of $40 per hour. Each copy machine is leased for $4,000 per year.Find the following values for this system: λ, μ, Cs, Cw. Then use the Excel template to determinehow many copy machines the company should have to minimize its expected total cost per hour.List your result in the following table.:S345PE(TC) = E(SC) + E (WC)

Find the given details below: Arrival rate λ 40 Service rate μ 15.00 Service rate (60/4)…

Answered: The Garrett-Tompkins Company provides…

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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8. The parts department of a large automobile dealership has a counter used exclusively for mechanics’requests for parts. The time between requests can be modeled by a negative exponential distributionthat has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, andthis can be modeled by a Poisson distribution that has a mean of 15. Suppose there are two clerksat the counter.a. On average, how many mechanics would be at the counter, including those being served?b. What is the probability that a mechanic would have to wait for service?c. If a mechanic has to wait, how long would the average wait be?d. What percentage of time are the clerks idle?e. If clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what numberof clerks would be optimal in terms of minimizing total cost?
Eat Well is a tiny drive-through quick food restaurant in a shopping malltown, manned by an efficient employee named John. Customers arrive at the counter at a rate of one per 15 minutes on average, with a Poisson delivery for customer entry. Each food order takes John no more than ten minutes to process. a) How many customers are handled on average at any given time? b) The anticipated amount of clients that would be represented. c) Determine the average consumer wait time in the scheme. d) How much of the day is John Idle idle?
5. Eat well is a small drive through fast food restaurant, staffed by an efficient employee John, is located in a super mall area. Customers arrive at the counter at an average of one every 15 minutes, and the customer arrival follows a Poisson distribution. John takes at most 10 minutes to process each food order. a) What is average number of customer being served at any time? b) The expected number of customers waiting to be served. c) Compute the average time customer wait in the system. d) What percentage of time is John Idle?
(10 Points) Eat well is a small drive through fast food restaurant, staffed by anefficient employee John, is located in a super mall area. Customers arrive at thecounter at an average of one every 15 minutes, and the customer arrival followsa Poisson distribution. John takes at most 10 minutes to process each foodorder.a) What is average number of customer being served at any time?b) The expected number of customers waiting to be served.c) Compute the average time customer wait in the system.d) Compute the average time customer wait in the line.e) What percentage of time is John Idle?
You are in charge of a quarry that supplies sand and stone aggregates to your company’s construction sites. Empty trucks from construction sites arrive at the quarry’s huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. Atthe station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, nine empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 6 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and to add a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. Thearrival rate of trucks would change to six per hour, and…
What is suitable model for factory in queuing theory?
Explain in what kind of situations is queuing analysis is most important under waiting line models ? It's from operations management domain don't sent it to other subjects plz !
Joe Hammer is thinking about setting up a special counter for the do-it-yourself customers at which they can get, not only help where to find products in the store ,but also some quick advice about the best way to handle their upcoming projects. Experience has taught Joe that six minutes is a good figure to allow for the average time required to serve a “do-it-yourselfer” and that these customers will arrive every 15 minutes throughout the day. a.) If joe sets up the counter under these conditions, what operating characteristics might he expect ? b.) What might Joe do to avoid the costs of idleness ? c.) What is the likelihood(probability) that three or more customers will be at the counter, either waiting or being served ,at any given time ? Calculate the Utilization rate, idleness rate ,Average time in queue, Average time in system, Average number in queue, Average number in system,and probability that three or more customers will be in the counter system at the same time.
A priority waiting system assigns arriving customers to one of four classes. Arrival rates (Poisson) of the classes are shown in the following table. Five servers process the customers, and eachcan handle three customers per hour.a. What is the system utilization?b. What is the average wait for service by customers in the various classes? How many are waiting in each class, on average?c. If the arrival rate of the second priority class could be reduced to three units per hour by shifting some arrivals into the third priority class, how would your answers to part b change?d. What observations can you make based on your answers to part c?
An average of 40 cars per hour arrive to be painted at asingle-server GM painting facility. 95% of the cars require1 minute to paint; 5% must be painted twice and require 2.5minutes to paint. Assume that interarrival times areexponential. a On the average, how long does a car wait before be-ing painted? b If cars never had to be repainted, how would youranswer to part (a) change?
at 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?
Drivers who come to get their licenses at the department ofmotor vehicles have their photograph taken by an automatedmachine that develops the photograph onto the license cardand laminates the complete license. The machine requires aconstant time of 4.5 minutes to develop a completed license.If drivers arrive at the machine at the mean rate of 11 perhour (Poisson distributed), determine the average length ofthe waiting line and the average waiting time.

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