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# Queuing Theory

The wheat harvesting season is short. Farmers deliver their truck loads of wheat to a giant central storage bin within a two-week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned cooperatively and it is to every farmer's benefit to make the unloading/storage process as efficient as possible. Waiting and unloading cost for truck and driver is \$18/per hour. The storage bin is open and operated 16 hours per day, 7 days per week during the harvest season and is capable of unloading 35 trucks per hour according to exponential distribution. Full trucks arrive all day long (during the hours the bin is open) at a rate of about 30 per hour, following a Poisson pattern.

a) average number of trucks in the unloading system
b) average time per truck in the system
c) utilization rate for the bin area
d) probability taht there are more than three trucks in the system at any given time
e) total daily cost to the farmers of having their trucks tied up at any given time
f) If they enlarged the bin it would cut unloading costs by 50%. It will cost \$9,000 to do so. Would it be worth it?

#### Solution Summary

Solutions to Queuing Theory are provided.

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