Operations Management
14th Edition
ISBN: 9781260238891
Author: Stevenson
Publisher: MCG
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Chapter 18, Problem 13P
a)
Summary Introduction
To determine: Whether the third crew member will be economical.
b.
Summary Introduction
To determine: Would the fourth member be justifiable.
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Trucks arrive at the loading dock of a wholesale grocer at the rate of 1.2 per hour. A single crewconsisting of two workers can load a truck in about 30 minutes. Crew members receive $10 perhour in wages and fringe benefits, and trucks and drivers reflect an hourly cost of $60. The manager is thinking of adding another member to the crew. The service rate would then be 2.4 trucksper hour. Assume rates are Poisson.a. Would the third crew member be economical?b. Would a fourth member be justifiable if the resulting service capacity were 2.6 trucks per hour?
In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds. Assume the Poisson and exponential distributions.
a.
What is λ?
b.
What is μ?
c.
Find probability of no units in the system.
d.
Find average number of units in the system.
e.
Find average time in the waiting line.
f.
Find average time in the system.
g.
Find probability that there is one person waiting.
h.
Find probability an arrival will have to wait.
Please show a corrct solution and answer. Thank you.
A 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.
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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- Benny's arcade has six video game machines. The average time between machine failures is 50 hours. Jimmy, the maintenance manager can repair a machine in 5 hours on average. The machines have an exponential failure distribution, and Jimmy has an exponential service-time distribution. a. Jimmy's utilization is? b. what is the average number of machines out of service, that is, waiting to be repaired or being repaired? c. what is the average time a machine is out of service?.arrow_forwardA vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 76 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 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
- Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22arrow_forwardA local fast food restaurant wants to analyze its drive-thru window. At this time, the only information known is the average number of customers in the system (4.00) and the average time a customer spends at the restaurant (1.176 minutes). What is the arrival rate (λ) and the service rate (μ)? Group of answer choices Arrival rate = 4.25 customers/min. Service rate = 3.4 customers/min. Arrival rate = .29 customers/min. Service rate = .24 customers/min. Arrival rate = 3.4 customers/min. Service rate = 4.25 customers/min. Arrival rate = .24 customers/min. Service rate = .29 customers/min. None of the above answers are correctarrow_forward[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 queuearrow_forward
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