1. Seaports are important in global supply chains. Their management plays an important part in minimizing waiting time for ships that visit seaports for loading and unloading cargo and port utilization. The Oakland seaport is a busy container seaport on the West coast of America, but it is a bit relaxed in the month of December. Based on the past data, it is observed that 6 ships arrive there, on an average, per day, and it takes 3 hours to unload a ship on an average, with a standard deviation of 4 hours. Determine the following: a. Minimum number of unloading facilities. λ=Arrival rate=6 u=Serving rate= 3 hrs (1/3 x 24)-8 ships per day Utilization (p)=2 μ=6/8=0.75 p/c should be less than 1.0 p/c<1 0.75/c<1 0.75/1

Queueing system analyzes the arrival pattern and service time in a system and optimizes the queue in terms of reduced waiting time in the queue as well as the system.

The given information is as follows.

Arrival rate $\lambda$ = 6 Ships/day

Service rate $\mu$ = $\frac{1}{3}\times 24=8$ ships/day

The standard deviation of service time $\sigma$ = 4 hrs.

The calculations in part (d) are incorrect. Correct calculations are as follows.

Probability of 2 ships in the system = $P_0\times {\left(\frac{\lambda }{\mu }\right)}^n=0.25\times {\left(\frac{6}{8}\right)}^2=0.25\times {\left(0.75\right)}^2 = 0.1406$

Probability of 4 ships in the system = $P_0\times {\left(\frac{\lambda }{\mu }\right)}^n=0.25\times {\left(\frac{6}{8}\right)}^4=0.25\times {\left(0.75\right)}^4 = 0.0791$