Reference no: EM132298584

Logistics Modeling Assignment -

Problem 1 - Coal trains arrive at an unloading facility with independent exponential inter-arrival 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.

If a train is being unloaded when its crew hogs out, unloading is suspended until a replacement crew arrives. If a train is in a queue when its crew hogs out, the train cannot leave the queue unitl a replacement crew arrives. Thus, the unloading equipment can be idle with one or more trains in a queue.

Run the simulation model for 720 hours.

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 suitable feature(s) of 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):

	20-ton truck	50-ton truck
Load	Exponentially distributed with mean 5	Exponentially distributed with mean 10
Travel	Constant 2.5	Constant 3
Dump	Exponentially distributed with mean 2	Exponentially distributed with mean 4
Return	Constant 1.5	Constant 2

To each shovel are assigned two 20-ton trucks and one 50-ton truck. The shovel queues are all FIFO, and the crusher queue is ranked in decreasing order of truck size. Assume that at time 0, all trucks are at their respective shovels, with the 50-ton trucks just about to be loaded. Run the simulation model for 8 hours.

Problem Situation: There is a possibility of purchasing at most two more trucks, which can be 20-ton truck or 50-ton truck, to further improve the utilisation of the four pieces of equipment (the three shovels and the single crusher). A 20-ton truck costs £10,000, while a 50-ton truck costs £20,000. Management of the quarry needs to address the two conflicting objectives of increasing utilisation of equipment, as well as, the additional cost incurred in purchasing additional trucks.

a) Conceptual Model. Develop a conceptual model for the problem, by describing the objectives, inputs, outputs, content (including a logic flow diagram), assumptions and simplications 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.

NOTE:

• Do not model the travel and return time for the truck by adjusting the "travel time" in the linking arrow between basic objects. All "travel times" in arrows should be set to zero.
• Model the trucks to be in queue/storage bin basic objects at time 0, instead of generating them by work entry points.

c) Report to Manager. Write a report of approximately 1500 words to the system manager, explaining your recommendations to the problem situation described above. Include the reasoning behind your choice, and the comparative advantages and disadvantages of your choice. Include graphs/tables to explain and illustrate your recommendations. Remember that this report is presented to a business manager and should hence be of high quality and not overly-technical.

Problem 3 - Consider a single server system with a single queue. Customers arrive with inter-arrival 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:

Position in queue at the end of 4 minutes wait	1	2	3	≥ 4
Probability of reneging	0.00	0.25	0.50	1.00

A customer who does not renege at the end of a 4 minutes wait will wait in the queue until he/she is being served. Service times at the server are exponential with mean 6.8minutes.

Run the simulation model for 8 hours.

Using SIMUL8, perform 100 independent runs to determine the number of customers who renege from the "Results Manager" in SIMUL8. Describe as clearly as possible in about 300 to 500 words how your SIMUL8 model is built. Screenshots and computer outputs should be provided in your description. You need to submit the SIMUL8 file used to solve the problem. Use the number 1 as your initial random seed.