A port in Africa loads tankers with crude oil for overwater shipment, and the port has fac...

A port in Africa loads tankers with crude oil for overwater shipment, and the port has facilities for loading as many as three tankers simultaneously. The tankers, which arrive at the port every 11 ± 7 hours, are of three different types. (All times given as a “±” range in this problem are distributed uniformly over the range.) The relative frequency of the various types and their loading-time requirements are:

There is one tug at the port. Tankers of all types require the services of a tug to move from the harbor into a berth and later to move out of a berth into the harbor. When the tug is available, any berthing or deberthing activity takes about an hour. It takes the tug 0.25 hour to travel from the harbor to the berths, or vice versa, when not pulling a tanker. When the tug finishes a berthing activity, it will deberth the first tanker in the deberthing queue if this queue is not empty. If the deberthing queue is empty but the harbor queue is not, the tug will travel to the harbor and begin berthing the first tanker in the harbor queue. (If both queues are empty, the tug will remain idle at the berths.) When the tug finishes a deberthing activity, it will berth the first tanker in the harbor queue if this queue is not empty and a berth is available. Otherwise, the tug will travel to the berths, and if the deberthing queue is not empty, will begin deberthing the first tanker in the queue. If the deberthing queue is empty, the tug will remain idle at the berths.

The situation is further complicated by the fact that the area experiences frequent storms that last 4 ± 2 hours. The time between the end of one storm and the onset of the next is an exponential random variable with mean 48 hours. The tug will not start a new activity when a storm is in progress but will always finish an activity already in progress. (The berths will operate during a storm.) If the tug is traveling from the berths to the harbor without a tanker when a storm begins, it will turn around and head for the berths. Run the simulation model for a 1-year period (8760 hours) and estimate:

(a) The expected proportion of time the tug is idle, is traveling without a tanker, and is engaged in either a berthing or deberthing activity

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(b) The expected proportion of time each berth is unoccupied, is occupied but not loading, and is loading

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(c) The expected time-average number of tankers in the deberthing queue and in the harbor queue

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(d) The expected average in-port residence time of each type of tanker

Use stream 1 for interarrivals, stream 2 to determine the type of a tanker, stream 3 for loading times, stream 4 for the duration of a storm, and stream 5 for the time between the end of one storm and the start of the next.

A shipper considering bidding on a contract to transport oil from the port to the United Kingdom has determined that five tankers of a particular type would have to be committed to this task to meet contract specifications. These tankers would require 21 ± 3 hours to load oil at the port. After loading and deberthing, they would travel to the United Kingdom, offload the oil, return to the port for reloading, etc. The round-trip travel time, including offloading, is estimated to be 240 ± 24 hours. Rerun the simulation and estimate, in addition, the expected average in-port residence time of the proposed additional tankers. Assume that at time 0 the five additional tankers are in the harbor queue. Use the same stream assignments as before, and in addition use stream 6 for the oil-loading times at the port and stream 7 for the round-trip travel times for these new tankers. [This problem is an embellishment of one in Schriber (1974, p. 329).]