Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
12th Edition
ISBN: 9781259580093
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 18, Problem 3P
a)
Summary Introduction
To determine: The average time customers spend at the machine, including waiting in line and completing transaction.
Queuing theory: It is a mathematical study of queues or waiting lines. Using queuing model, length of a queue and waiting time can be determined. In operations management, queuing theory is used for decision making about the resources required to offer services.
b)
Summary Introduction
To determine: Probability that a customer will not have to wait.
c)
Summary Introduction
To determine: Average time customers spend at the machine (Lq)
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Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each
customer spends an average of 87 seconds completing his or her transactions. Transaction time is
exponentially distributed. Determine the following:
a. The average time customers spend at the machine, including waiting in line and completing
transactions
b. The probability that a customer will not have to wait upon arriving at the automatic teller
machine
c. The average number waiting to use the machine
Note: Formulas to solve the following problems are given in the
class and example problems were solved in the class. Follow the
examples described in the class and read the literature posted on
blackboard.
1. Huntsville Bank (a fictitious one) has a drive-through teller
window and observed that customers arrive for service one
every three minute, on an average, and the average service
time per customer is 2.4 minutes. Assume inter-arrival time
and service time follow a negative Exponential distribution.
The bank hires you as a consultant. You guess that this is an
M|M|1 system and you are required to determine the
following:
a. Probability (teller is busy)
b. Probability (teller is idle)
c. Average number of customers waiting for service, that is,
number of autos in the line excluding the one at the teller
window.
d. Average number of customers in the system, that is,
number of autos in the line including the one at the teller
window.
e. Average time a customer spends in the waiting…
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Chapter 18 Solutions
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
Ch. 18 - Prob. 1DRQCh. 18 - Why do waiting lines form even though a service...Ch. 18 - Prob. 3DRQCh. 18 - Prob. 4DRQCh. 18 - What approaches do supermarkets use to offset...Ch. 18 - Prob. 6DRQCh. 18 - Prob. 7DRQCh. 18 - Prob. 8DRQCh. 18 - Prob. 9DRQCh. 18 - Prob. 1TS
Ch. 18 - Prob. 2TSCh. 18 - Prob. 3TSCh. 18 - Prob. 1CTECh. 18 - Prob. 2CTECh. 18 - Prob. 3CTECh. 18 - The owner of Eat Now Restaurant implemented an...Ch. 18 - Prob. 5CTECh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Prob. 4PCh. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - Prob. 7PCh. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - Prob. 15PCh. 18 - A priority waiting system assigns arriving...Ch. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - Prob. 1CQ
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