Question
The cranberry growers formed a cooperative many years ago to achieve economies of scale for the processing and sale of their cranberries. In that way
The cranberry growers formed a cooperative many years ago to achieve economies of scale for the processing and sale of their cranberries. In that way they can concentrate their efforts on growing and harvesting cranberries as efficiently as possible while they leave the processing and selling to professional operations and marketing managers.
During the two-month harvesting season, growers truck their berries to the nearest processing facility. Trucks arrive at the facility, wait their turn to have their berries graded and weighed, and then dump them into holding bins. If all the holding bins are full, the trucks have to wait until space in the bins opens up. After dumping, the trucks return to the farmer.
Once the berries are in bins, the berries proceed through the plant. The plant makes them ready for sale to retail outlets or to juice or sauce producers. The plant can process up to 800 tons of berries per hour assuming there are 800 tons available to process. If there are more than 800 tons, the excess will be "carried over" to the next hour. If there is less than 800 tons, the plant will of course only process what is there.
Trucks arrive at the facility from 8am until 3 pm. Each truck carries 75 tons of berries. Berry processing starts at 9am and continues until 5pm on a normal day. If there are still berries in trucks or in bins, the processing must continue on overtime until all of the day's deliveries are processed. The plant's bins can hold up to 2,400 tons of berries.
Simulate a day of processing berries on an hour by hour basis. Do 1000 Monte Carlo trials using 123 as your random number seed. The number of trucks that arrive each hour can be described by a Poisson distribution. The mean arrival rate varies by the hour of the day. The arrival rates are listed below.
Set up your simulation in the following way. First keep track of how many berries arrive in an hour and add that amount to any unprocessed berries left over from the previous hour. Then subtract the amount processed in that hour. (Either 800 or whatever is available for processing during that hour if the total is less than 800.)
At the end of the normal workday (5pm), overtime begins. Make one calculation for the hours of overtime needed and any other statistics you are keeping.
Calculate the amount of overtime the plant must use to complete of the berries on the average day. From the frequency distribution, the plant will finish the berries 95% of the days with what amount (or less) of overtime? What is the average number of trucks waiting to dump their berries at 5pm?
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