Operations Management
13th Edition
ISBN: 9781259667473
Author: William J Stevenson
Publisher: McGraw-Hill Education
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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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An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed byone ticket agent. It is estimated that requests for tickets and information will average15 per hour, and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggeststhat mean service time should average about three minutes per request. Determine each ofthe following:a. System utilizationb. Percentage of time the server (agent) will be idlec. The expected number of customers waiting to be servedd. The average time customers will spend in the systeme. The probability of zero customers in the system and the probability of four customersin the system
The parts department of a large automobile dealership has a counter used exclusively for mechanics’ requests for parts. The time between requests can be modeled by a negative exponential distribution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, andthis can be modeled by a Poisson distribution that has a mean of 15. Suppose there are two clerksat the counter.a. On average, how many mechanics would be at the counter, including those being served?b. What is the probability that a mechanic would have to wait for service?c. If a mechanic has to wait, how long would the average wait be?d. What percentage of time are the clerks idle?e. If clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what numberof clerks would be optimal in terms of minimizing total cost?
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Chapter 18 Solutions
Operations Management
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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- The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?arrow_forward4) Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come 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.arrow_forward12-11 The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ=3 per day (approximately Poisson in nature). The crew can service an average of μ=8 machines per day, with a repair time distribution that resembles the exponential distribution. a. What is the utilization rate of this service system? b. What is the average downtime for a machine that is broken? c. How many machines are waiting to be serviced at any given time? d. What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?arrow_forward
- One field representative services 5 customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every 1.5 working days. The field representative can handle an average (Poisson-distributed) of 1.0 call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round "X" value to 2 decimal places. Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s)arrow_forwardIn a M/M/1 queueing system, the arrival rate is 8 customers per hour and the service rate is 11 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate). What will be the resulting performance measurements? (Round your ansers to 3 decimal places) a. What is the expected number of customers in the queue (Lq)? b. What is the expected waiting time (in hours) in the queue (Wq)?arrow_forwardAli Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a) Compute the average number of cars in line.arrow_forward
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