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Delivery trucks from a supplier arrive at a warehouse at a rate of 2 per hour during business hours. Crews at each dock of the warehouse can unload the truck at a rate of 1 per hour. Each dock is staffed with two workers, i.e., two workers can unload one truckload per hour. While a truck is detained in unloading, a cost of $200/hr is incurred due to lost productive use of the truck and hourly wages of the truck driver and his assistant. Recent changes in wage rates have caused the warehouse manager to reexamine the question of how many crews and docks to use. The costs associated with unloading are dock cost and worker salary. The dock cost is $100/hr and the new rate for each worker in the unloading crew is $25/hr. Assume the arrival and service rates are Poisson.
A) What is the minimum number of docks to be used?
B) Find the optimal number of dock and crews?
C) If the truck arrival rate increases to 3 per hour, what are the new minimum number of docks and optimal number of docks and crews?
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