Logistics Modelling - Independent Exponential Inter-arrival Time - Engineering Assessment Answer

Engineering Assessment Answer

TASK: Problem 1 Coal trains arrive at an unloading facility with independent exponential interarrival times with a mean of 10 hours. If a train arrives and finds the system idle, the train is unloaded immediately. Unloading times for the train are independent and distributed uniformly between 3.5 and 4.5 hours. If a train arrives at a busy system, it joins a FIFO queue. The situation is complicated by what the railroad calls “hogging out.” In particular, a train crew can work for only 12 hours, inclusive of idle time, and a train cannot be unloaded without a crew present. When a crew’s 12 hours expire, they leave immediately and a replacement crew is called. The amount of time between when a replacement crew is called and when it actually arrives is independent and distributed uniformly between 2.5 and 3.5 hours. Questions to Problem 1 a) Using SIMUL8, perform 100 independent runs to determine the average time a train spends in the system from the “Results Manager” in SIMUL8. A screenshot of your simulation model should be provided in your report. Use the number 1 as your initial random seed. NOTE: To build the computer model in SIMUL8 to model the problem, you will need to research on the suitable feature(s) of a basic object(s) of the software to use. b) Management of the unloading facility decide to decrease the working hours of a crew from 12 hours to 11 hours, and the amount of time between when a replacement crew is called and when it actually arrives to be independent and distributed uniformly between 1.5 and 3 hours, instead of between 2.5 hours and 3.5 hours. By performing statistical analysis using the CRN technique, determine how these changes affect the average time spent by a train in the system. A trial should contain at least 20 runs. Use the number 13 as your initial random seed. Problem 2 In a quarry, trucks deliver ore from three shovels to a single crusher. Trucks are assigned to specific shovels so that a truck will always return to its assigned shovel after dumping a load at the crusher. Two different truck sizes are in use, 20 and 50 tons. The size of the truck affects its loading time at the shovel, travel time to the crusher, dumping time at the crusher, and return trip time from the crusher back to its shovel, as follows (all times are in minutes) Questions to Problem 2 a) Conceptual Model. Develop a conceptual model for the problem, by describing the objectives, inputs, outputs, content (including a logic flow diagram), assumptions and implications of the model, in approximately 500 words. b) Computer Model. Build a simulation computer model in SIMUL8 to model the system as described in the problem. A screenshot of your simulation model should be provided in your report. Without considering additional trucks, run the model 100 times to estimate the expected time-average number in the queue for the crusher and the expected utilisation of all four pieces of equipment from the “Results Manager” in SIMUL8. Use the number 1 as your initial random seed. Problem 3 Consider a single server system with a single queue. Customers arrive with interarrival times that are exponentially distributed with a mean of 5 minutes. All customers that arrive wait for at least 4 minutes before being served by the single server, if the server is available. At the end of the 4 minutes wait, a customer may renege, that is, leave the queue without being served. A customer will actually leave with the following probabilities:

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