A worker at the unloading dock of a warehouse takes, on average, 15 minutes to unload a truck. On average, three trucks arrive every hour at the unloading dock. Assume there is enough space to accommodate any number of waiting trucks at the warehouse and the average inter-arrival time and the unloading time are both exponentially distributed.
a. What is the average number of trucks in the waiting line before being unloaded?
b. What is the total time (waiting and unloading) that a truck spends in the system?
Management is considering adding an additional worker as there is sufficient space on the loading dock to allow two trucks to unload at the same time. Each unloading dock worker is paid $200 per hour while the hourly waiting cost (incurred while waiting in line and being unloaded) of a truck is $500.
c. With a crew of two workers what is the average number of trucks in the system?
d. With the crew of two workers, what is the total average cost per hour (including the waiting cost and the wage of the two workers)?
e. Assume that having two workers at the unloading dock costs $720 per hour including the cost of waiting and the wages paid to the workers. (We are making this assumption so that you do not need to know the answer to the previous question to answer this one.) Does adding another worker to have in total of 3 unloading dock workers reduce the total average cost per hour compared to the case with 2 workers?