An excavation company has been contracted to supply 10 million cubic feet (cu. ft.) of dirt to a construction site. The company uses a bulldozer to collect dirt, which is then moved by a dump truck to the construction site. It costs the company $100 per hour to use the bulldozer, and it rents dump trucks at a rate of $40 per hour per truck. Each dump truck can hold 1,000 cu. ft. of dirt, and it takes an average of 12 minutes for the bulldozer to load a dump truck with dirt. It takes an average of five minutes for a fully loaded dump truck to deliver the dirt to the construction site and returns to the bulldozer for another load. Assume that the time to load a dump truck and the time for a dump truck to deliver the dirt to the construction site and return to the bulldozer follow exponential distributions. Moreover, a usual trip of the truck involves load with dirt, deliver the dirt, return to the bulldozer where it joins a queue for another load of dirt. Then, determine the most appropriate queuing model for the dirt-moving process and then use that model to determine how many dump trucks to rent in order to minimize the expected cost of fulfilling the contract.
An excavation company has been contracted to supply 10 million cubic feet (cu. ft.) of dirt
to a construction site. The company uses a bulldozer to collect dirt, which is then moved by a
dump truck to the construction site. It costs the company $100 per hour to use the bulldozer,
and it rents dump trucks at a rate of $40 per hour per truck. Each dump truck can hold 1,000
cu. ft. of dirt, and it takes an average of 12 minutes for the bulldozer to load a dump truck
with dirt. It takes an average of five minutes for a fully loaded dump truck to deliver the dirt
to the construction site and returns to the bulldozer for another load.
Assume that the time to load a dump truck and the time for a dump truck to deliver the dirt
to the construction site and return to the bulldozer follow exponential distributions. Moreover,
a usual trip of the truck involves load with dirt, deliver the dirt, return to the bulldozer where
it joins a queue for another load of dirt.
Then, determine the most appropriate queuing model for the dirt-moving process and then
use that model to determine how many dump trucks to rent in order to minimize the expected
cost of fulfilling the contract.
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