Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 7.3, Problem 15P
Summary Introduction
Interpretation:estimate the squared coefficient of variation of the arrival process.
Concept introduction:Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.
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Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-
up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival
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(a) What is the mean or expected number of customers that will arrive in a six-minute period?
(b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a six-minute period. (Round your answers to four decimal places.)
X
0
1
2
3
P(x)
(c) Delays are expected if more than three customers arrive during any six-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)
The following data has been collected on the number of customers seen to arrive to a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1, 5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. If this data was known to come from a Poisson process, what would be your estimate of λ, the rate of customer arrivals?
Granos, Inc. purchased new automated coffee vending machines, the Preso 2000. This Preso
2000 requires a constant 45 seconds to produce a coffee. It has been estimated that customers
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machine, Granos, Inc. would like to know the expected average time in the system, the average
line length (in costumers), and the average number of costumers in the system (both in line and
at the vending machine).
Chapter 7 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Prob. 6PCh. 7.1 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10P
Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Prob. 27PCh. 7.8 - Prob. 28PCh. 7.8 - Prob. 29PCh. 7.8 - Prob. 30PCh. 7.8 - Prob. 32PCh. 7.8 - Prob. 34PCh. 7.8 - Prob. 35PCh. 7.8 - Prob. 36PCh. 7 - Prob. 38APCh. 7 - Prob. 39APCh. 7 - Prob. 40APCh. 7 - Prob. 41APCh. 7 - Prob. 42APCh. 7 - Prob. 43APCh. 7 - Prob. 44APCh. 7 - Prob. 45APCh. 7 - Prob. 46AP
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