Problem:
The Atlantic Coast Shipping Company has a warehouse terminal. The capacity of the terminal docks are three trucks. As trucks enter the terminal, the driver receives a number, and when one of the three dock spaces become available, the truck with the lowest number enters the vacant dock. Truck arrivals are Poisson distributed, and the unloading and loading times (service times) are exponentially distributed. The average arrival rate at the terminal is 5 trucks per hour, and the average time to load or unload a truck equals 30 minutes.
The management of the shipping company is considering the following alternatives for improving the system:
Alternative No. 1: Add extra employees to reduce the average time to load or unload a truck to 24 minutes (instead of 30 minutes) at an annual cost of $25,000.
Alternative No. 2: Add a forth dock at an annual cost of $30,000 per year. The average time to load or unload a truck is still 30 minutes.
The management estimates that it will increase its profit by $600 per year for each minute it is able to reduce a truck's time spent in the system. Analyze each alternative and clearly state your recommendation stating its financial and operational implications.