Ships arrive at a port facility at an average rate of 2 ships every 3 days. On t
ID: 459508 • 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
Ans – Option two by hiring additional worker is more economical,it is explained below.
Arrival time- 2 Ships every 3 days
Port cost per day = $1000
Total worker = 100
Additional Workers = 40
Pay of each worker = $30 per day
Option 1- When no additional Worker is hired
Cost of stay at the port for 3 days- 3*1000 = $3000
Payment to workers for 3 days- 3*30*100 = $9000
Total cost for 3 days stay with loading and uloading = $ 12000
Option 2- When additional 40 workers are hired
Note- When additional workers are hired total number of worker being increased to 140 and as suggested by the consultant they have been splited in 2 teams working simultaneously on each ship, so number of days will remain same but loading and unloading time will be reduced to 2 days and also stay at the port also got reduced to 2 days.
Cost of stay at the port for 2 days- 2*1000 = $2000
Payment to workers for 2 days- 2*30*140 = $8400
Total cost for 3 days stay with loading and unloading = $ 10400
So total saving while using additional workers = $ (12000- 10400) = $1600 so option by hiring additional workers is more convenient and economical.
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