Sea Dock, a private firm, operates an unloading facility in the Gulf of Mexico for supertankers delivering crude oil for refineries in the Port Arthur area of Texas. Records show that, on average, 2 tankers arrive per day, with a Poisson distribution. Supertankers are unloaded one at a time on a first- come, first- served ( FCFS) basis. Unloading requires approximately 8 hours of a 24- hour working day, and unloading times have a negative exponential distribution.
a. Sea Dock has provided mooring space for 3 tankers. Is this sufficient to meet the U. S. Coast Guard requirement that at least 19 of 20 arrivals should find mooring space available?
b. Sea Dock can increase its unloading capacity to a rate of 4 ships per day through additional labor at a cost of $ 480 per day. Considering the $ 1,000- per- day demurrage fee charged to Sea Dock for keeping a supertanker idle ( this includes unloading time as well as time spent waiting in queue), should management con-sider this expansion opportunity?