Operations Management
Operations Management
13th Edition
ISBN: 9780135173626
Author: HEIZER, Jay, RENDER, Barry, Munson, Chuck
Publisher: Pearson,
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Chapter D, Problem 8P

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• D.8 Virginia’s Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on average λ = 3 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 8 machines per workday, with a repair time distribution that resembles the exponential distribution.

  1. a. What is the utilization rate of this service system?
  2. b. What is the average downtime for a broken machine?
  3. c. How many machines are waiting to be serviced at any given time?
  4. d. What is the probability that more than 1 machine is in the system? The probability that more than 2 are broken and waiting to be repaired or being serviced? More than 3? More than 4?
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Q.11 An example of a leading performance measure is: a.Number of new customers b. Average response time for  service call
QUESTION 5 A post office has a counter for customers' drive-through to get the services. The design of the drive-through lane allows for unlimited queue length. The arrival and service rate are Poisson distributed with A= 20 customers per hour arriving on average and u=25 customers per hour can be served on average. a) Compute the average number of arrivals. b) Compute the average time a customer waits. c) Compute the average number of arrivals in the system. d) Compute the average time a customer is in the system. e) Compute the probability that less than or equal to 3 customers are in the system. f) If the single counter for the customer drive-through has been replaced with the automatic operation, service rates are constant with A= 20 and u =25. Compute (a), (b), (c) and (d).
QUESTION 1 A multiple channel queuing system with a Poisson arrival rate, and an exponential service time distribution has an average arrival rate of 2.5 customers per hour and an average service time of eighty minutes per customer. A queuing system is described as unstable or overloaded if its utilization rate is greater than, or equal to one. For the system just described, what is the minimum number of servers required to retain stability i.e., to avoid overloading? A. 3 B. 2 C. 4 D. 1 QUESTION 2 Customers arrive at the lone check-out desk of a certain convenience store at the average rate of 0.23 per minute. If it takes on average four minutes for the store manager to serve each customer, how many customers will on average find themselves waiting in the queue? A. 3.20 B. 0.00351 C. 0.00024 D. 10.58

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