Quantitative Modelling and Decision Making: Simulation and Analysis

Penalties for Late Submissions

• Late submission of any item of coursework for each day or part thereof (or for hard copy submission only, working day or part thereof) for up to five days after the published deadline, coursework relating to modules at Levels 0, 4, 5, 6 submitted late (including deferred coursework, but with the exception of referred coursework), will have the numeric grade reduced by 10 grade points until or unless the numeric grade reaches or is 40. Where the numeric grade awarded for the assessment is less than 40, no lateness penalty will be applied.

• Late submission of referred coursework will automatically be awarded a grade of zero (0).

• Coursework (including deferred coursework) submitted later than five days (five working days in the  case of hard copy submission) after the published deadline will be awarded a grade of zero (0).

• Where genuine serious adverse circumstances apply, you may apply for an extension to the hand-in date, provided the extension is requested a reasonable period in advance of the deadline.

This Assignment assesses the following module Learning Outcomes:

1. Select and apply quantitative modelling concepts for problem solving and decision making.

2. Use classical decision theory as aid to decision making.

3. Acquire a critical awareness of the logical process of modelling complex decision problems.

4. Apply techniques and practice to model real-world problems.

5. Derive solution(s) using a suitable software package when required.

6. Critically analyse and report results.

The number of machine breakdowns per day at Yuwen Chen’s factory is 0, 1, or 2, with probabilities 0.5, 0.3, or 0.2, respectively.

1. Make a Monte-Carlo Hand Simulation to generate the number of breakdowns for 10 consecutive days. The following random numbers have been generated for you to use in the hand simulation 13, 14, 02, 18, 31, 19, 32, 85, 31, and 94. What proportion of these days had at least one breakdown?

Yuwen Chen’s factory has five (5) identical machines and the machines operate in parallel. Jobs arriving the factory are required to be processed only on any ONE of the machines. The jobs are loaded on machines on first come first served basis. Jobs inter-arrival times are exponentially distributed with rate parameter set to 8 minutes. The operation times follow a uniform distribution between 5 and 15 minutes.

2. Using Witness (https://www.lanner.com/en-us/technology/witness-simulation-software.html) OR Flexsim (https://www.flexsim.com/) Simulation Software, conduct a computer simulation of the factory to study the effect of machine breakdowns on operations.

a) Develop a brief for Yuwen Chen’s factory simulation task; describe the process involved in the factory operations and present a process map of the operations. State and discuss your assumptions.

b) Develop a Simulation model for the Yuwen Chen’s factory task.

c) Use the simulation model developed to estimate the average number of jobs completed per day i.e. 1,080 minutes.

d) Discuss your results. Yuwen Chen’s factory is interested in using a virtual engineering platform to explore their simulation models.

3. Critically discuss the benefits the factory could derive from conducting their simulation studies on a virtual engineering platform.