Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 12.5, Problem 29P
Summary Introduction
To determine: The machine that the bank should rent.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
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In the production shop of a company, the breakdown of the machines is found to be Poisson distributed with an average rate of 3 machines per hour. Breakdown time at one machine cost 400 birr per hour to the company. There are two choices before the company for hiring the repairmen. One of the repairmen is slow but cheap, the other is fast but expensive. The slow cheap repairman demands 200 birr per hour and will repair the broken down machines exponentially at the rate of 5 per hour. The fast expensive man demands 300 birr per hour and will repair machines exponentially at an average rate of 6 per hour. Which repairman should be hired?
You are considering to invest in a franchise for
a coffee shop in your neighborhood. To
understand the revenue potential, you decide
to visit a coffee shop from the same chain next
to your neighborhood. In the next few months,
you visit this coffee shop at random times
between 6am and 9am. You observe that the
line (queue) averages about 9 customers and it
takes about 3 minutes to get in and out of the
coffee shop. Assuming this is a typical
experience and each customer spends about
$5 per visit, what is the revenue potential per
hour of this coffee shop?
Hint: Calculate the number of customers
arriving per minute (i.e., λ). Convert this to
customers per hour. Then, calculate the
revenue from these customers (each customer
spends about $5, on average)
Toolco operates a machine shop with 22 machines. On the
average, a machine breaks down every 2 hours. It takes an
average of 12 minutes to complete a repair. When a machine
breaks down, one of four repairpersons is called upon to do the
repair. Both the time between breakdowns and the repair time are
exponential. Toolco is interested in analyzing this situation and
knowing the number of repairpersons needed to keep the shop
running "smoothly."
A = 12 = 0.5 breaks down per hour
μ = 60/12 = 5 breaks down per hour
System limit = K = 22 machines
Source limit= K = 22 machines
R = 1, 2, 3, 4.
(M/M/R: GD/ K /K),
Chapter 12 Solutions
Practical Management Science
Ch. 12.3 - Prob. 1PCh. 12.3 - Explain the basic relationship between the...Ch. 12.3 - Prob. 3PCh. 12.3 - Prob. 4PCh. 12.4 - Prob. 5PCh. 12.4 - Prob. 6PCh. 12.4 - Prob. 7PCh. 12.4 - Prob. 8PCh. 12.5 - Prob. 9PCh. 12.5 - Prob. 10P
Ch. 12.5 - Prob. 11PCh. 12.5 - Prob. 12PCh. 12.5 - Prob. 13PCh. 12.5 - Prob. 14PCh. 12.5 - Prob. 15PCh. 12.5 - Prob. 16PCh. 12.5 - Prob. 17PCh. 12.5 - Prob. 18PCh. 12.5 - Prob. 19PCh. 12.5 - Prob. 20PCh. 12.5 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.5 - On average, 100 customers arrive per hour at the...Ch. 12.5 - Prob. 24PCh. 12.5 - Prob. 25PCh. 12.5 - Prob. 26PCh. 12.5 - Prob. 27PCh. 12.5 - Prob. 28PCh. 12.5 - Prob. 29PCh. 12.5 - Prob. 30PCh. 12.5 - Prob. 31PCh. 12.5 - Prob. 32PCh. 12.5 - Prob. 33PCh. 12.5 - Prob. 34PCh. 12.5 - Prob. 35PCh. 12.5 - Two one-barber shops sit side by side in Dunkirk...Ch. 12.5 - Prob. 37PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 54PCh. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61P
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