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You are in charge of a quarry that supplies sand and stone aggregates to your company's construction sites. Empty trucks from construction sites arrive at the quarry's huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, seven empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 5 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and to add a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. The arrival rate of trucks would change to five per hour, and the filling time would be reduced to 4 minutes. The second alternative is to add another loading station at a cost of $80,000. The trucks would wait in a common line and the truck at the front of the line would move to the next available station. The average waiting time in the system under the current system is 6.67 minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) The average waiting time in the system for the first alternative is The average waiting time in the system for the second alternative is Therefore, not factoring in costs, if you want to reduce the current average time the trucks spend in the system, including service, would be recommended.

You are in charge of a quarry that supplies sand and stone aggregates to your company's construction sites. Empty trucks from construction sites arrive at the quarry's huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, seven empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 5 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and to add a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. The arrival rate of trucks would change to five per hour, and the filling time would be reduced to 4 minutes. The second alternative is to add another loading station at a cost of $80,000. The trucks would wait in a common line and the truck at the front of the line would move to the next available station. The average waiting time in the system under the current system is 6.67 minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) The average waiting time in the system for the first alternative is The average waiting time in the system for the second alternative is Therefore, not factoring in costs, if you want to reduce the current average time the trucks spend in the system, including service, would be recommended.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
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You are in charge of a quarry that supplies sand and stone aggregates to your company's construction sites. Empty trucks from construction sites arrive at the quarry's huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, seven empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 5 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and to add a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. The arrival rate of trucks would change to five per hour, and the filling time would be reduced to 4 minutes. The second alternative is to add another loading station at a cost of $80,000. The trucks would wait in a common line and the truck at the front of the line would move to the next available station. The average waiting time in the system under the current system is 6.67 minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) The average waiting time in the system for the first alternative is The average waiting time in the system for the second alternative is Therefore, not factoring in costs, if you want to reduce the current average time the trucks spend in the system, including service, would be recommended.
Transcribed Image Text:You are in charge of a quarry that supplies sand and stone aggregates to your company's construction sites. Empty trucks from construction sites arrive at the quarry's huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, seven empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 5 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and to add a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. The arrival rate of trucks would change to five per hour, and the filling time would be reduced to 4 minutes. The second alternative is to add another loading station at a cost of $80,000. The trucks would wait in a common line and the truck at the front of the line would move to the next available station. The average waiting time in the system under the current system is 6.67 minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) minutes. (Enter your response rounded to two decimal places.) The average waiting time in the system for the first alternative is The average waiting time in the system for the second alternative is Therefore, not factoring in costs, if you want to reduce the current average time the trucks spend in the system, including service, would be recommended.
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