Bulk port operations. Port Lasfar is an iron ore exporting port that operates 24 hours a day and 365 days a year. The annual export plan calls for nominal deterministic ship arrivals at the rate of one ship every 20 hours. However, ships usually do not arrive on time due to weather conditions, rough seas, or other reasons, and consequently, each ship is given a 7-day lay period. Assume that ships arrive iid uniformly in their lay periods. Ships vary in tonnage according to the following distribution:

Arriving ships queue up FIFO (if necessary) at an offshore anchorage location, from where they are towed into port by a single tug boat as soon as the berth becomes available. The tug boat is stationed at a tug station located at a distance of 30 minutes away from the offshore anchorage. Travel between the offshore anchorage and the berthing area takes 1 hour.

There are two berths and two loaders at the port. An uninterrupted iron ore supply arrives at the port from a nearby mine. Whenever there is only one ship at the berths (only one berth is busy), both loaders load the ship together in half the time. However, as soon as another ship arrives at the empty berth, one of the loaders starts working on the new ship. In this case, the current ship continues its loading with only one loader. The loaders are identical and their rate of loading is 2000 tons per hour. Hence, the loading rate becomes 4000 tons per hour when both loaders work on the same ship. Assume no time is involved in shifting loaders. Once a ship is loaded at a berth, it relinquishes that berth (and the loader), and then requests tug boat service and waits until the tug boat arrives. Since there is only one tug boat, it does not matter whether it waits at the berth and then relinquishes the berth after the tug boat arrives or it releases it first and waits in a different area. The tug boat tows it away to the offshore anchorage, from where the boat departs with its iron ore for its destination. Higher priority is given to departing vessels in seizing the tug boat. Port Lasfar does not experience tidal activity or storms or any other stoppages.

a. Develop a model for Port Lasfar, and simulate it for 1 year (8760 hours).

b. Estimate the following statistics:

Berth and ship loader utilization

Average ship port time

Average number of ships at the anchorage

Average ship delay at the anchorage

Since a loader may have to be separated from a ship in the middle of loading, you may approximate the loading time as consisting of increments of, say, 10 minutes, and load as much as you can in a 10-minute period and then check the status of the other berth. If you need to separate a loader, do it immediately; otherwise, continue for another 10 minutes of loading. Loading will continue until the entire ship is loaded. During this time, the model may experience periods with one loader working on the ship, and other periods with two loaders working on the ship.

Tonnage = 45,000 57,000 65,000 with probability with probability with probability 0.30 0.50 0.20.