Operations Management
14th Edition
ISBN: 9781260238891
Author: Stevenson
Publisher: MCG
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Question
Chapter 18, Problem 11P
a)
Summary Introduction
To determine: Average hourly output of each machine, when waiting and service times are taken into account.
b.
Summary Introduction
To determine: The optimum number of operators.
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оооо
[Queuing Theory - Operation research]
The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following:
(a) probability that the system is idle
(b) average number of customers in the system
(c) amount of time a customer should expect to wait before service
(d) probability that a customer will have to spend more than 15 minutes in the queue
Chapter 18 Solutions
Operations Management
Ch. 18.1 - Prob. 1.1RQCh. 18.1 - Prob. 1.2RQCh. 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. 8DRQ
Ch. 18 - Prob. 9DRQCh. 18 - Prob. 1TSCh. 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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- A supermarket has four girls ringing sales at the counters. If the service time for each customer is exponential with mean 4 minutes, and if people arrive in a Poisson fashion at the rate of 10 per hour, calculate i. The average number of customers in the system. ii. The average time a customer spends in the system. iii. The average queue length iv. The average waiting time for customers. v. The expected percentage of idle time for each girl vi. The probability that at least a girl is waiting for the customer.arrow_forwardDescribe two examples of unethical behavior related to waiting line management, and state whichethical principles they violate.CRITICAL THINKINGEXERCISES1. a. λ = 3 customers/hourμ = 5 customers/hourM = 1(1) What is the system utilization?(2) What is the average number of customers waiting for service?(3) What is the average time customers wait in line for service? b. Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copier repairscome in at a mean rate of three per eight-hour day (assume Poisson). Determine:(1) The average number of customers awaiting repairs.(2) System utilization.(3) The amount of time during an eight-hour day that the repairman is not out on a call.(4) The probability of two or more customers in the system.c. An average of 18 customers arrive at a service center each hour. There are two servers on duty,and each server can process 12…arrow_forwardA vending machine dispenses hot chocolate or coffee. Service time is 15 seconds per cup and is constant. Customers arrive at a mean rate of 55 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)arrow_forward
- A vending machine dispenses hot chocolate or coffee. Service time is 45 seconds per cup and is constant. Customers arrive at a mean rate of 59 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customersarrow_forwardA server operates with 90 % utilization. Coefficient of variation of service process is 0.6. Coefficient of variation of arrival process is 0.8. Average processing time is 4 minutes. What is the average time a customer spends in the system using the single server queuing model ? Show all formulas used, calculations and results.arrow_forward13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.arrow_forward
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