Ships arrive at a port facility at an average rate of 2 ships every 3 days. On t
ID: 459509 • Letter: S
Question
Ships arrive at a port facility at an average rate of 2 ships every 3 days. On the average, it takes a single crew 1 day to unload a ship. Assume that interarrival and service times are exponential. The shipping company owns the port facility as well as the ships using that facility. It is estimated to cost the company $1,000 per day that each ship spends in port. The crew servicing the ships consist of 100 workers, who are each paid an average of $30 per day. A consultant has reccomended that the shipping company hire an additional 40 workers and split the employees into two equal-sized crews of 70 each. This would give each crew an unloading or loading time average 3/2 days. Which crew arrangement would you reccomend to the company?
Explanation / Answer
Case 1:
arrival rate =2/3
Service rate = 1
Probability that no ship in queue = (1-2/3)
= 1/3
Case 2:
arrival rate =2/3
Service rate = 2/3
Probability that no ship in queue = (1-2/3*3/2)
= 0
Each day cost to company when ship spends in port = $ 1,000
Extra cost to company On hiring additinal 40 workers = $ 1,200
We can make from the analysis of case that it will be good to hire extra 40 crew workers because it give us cost benefit of $ 300 ($1500 - $1200)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.