**Assignment Task**

**Task **

**Witness simulation **

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Create the model and optimise the profit for the plant described in the following. You need to simulate ten days operation after an appropriate warm-up period.

**Description **

A manufacturing plant that produces gearboxes has to be designed and optimized. Each gearbox is composed of the following components: two gears, two bearings, and one casting.

**Gears**are manufactured in a separate plant and arrive via a 20 m conveyor belt,- According to a time distribution defined in the excel file or any appropriate distribution of your choice (such as a uniform distribution between 1 to 2.5 minutes).
- The conveyor is of a belt type, and gears have a footprint of 80 by 80 by 100 mm, and can be spaced on the conveyor 100 mm apart.
- The maximum capacity of the conveyor is 180 parts, and the speed is 5 m/min.
**Castings**are drawn from stock and loaded to a CNC workstation for additional machining and boring.- An operator loads each casting to the workstation (loading operation takes 0.5 to 1 minutes) and unloads them to a bin (maximum capacity 50)
- Unloading takes 0.5 to 0.9 minutes and the machining cycle takes 2.3 minutes.
- Every 20th machined casting is not loaded to the bin, but to an inspection station.
- The inspection operation cycle time is triangularly distributed with a minimum of 0.8 minutes, a maximum of 2.2 minute, and a mode of 1.1 minutes.
- The inspection is manually carried out by the operator(s).
- Previous tests have shown that after 20 samples inspected there is a 70% chance that the critical dimensions (bores for bearings) are at the upper tolerance limit.
- When this occurs, the tools in the CNC workstation are replaced and the machine is cleaned. The operation time is triangularly distributed with a minimum of 2.5, maximum of 3.7, and mode of 3.2 minutes.
- The failed gearbox is scrapped.
**The gearbox assembly**process is manually performed by an operator.- Bearings are assumed to be always available. The process takes a mean of 3 minutes with a standard deviation of 0.7 minutes, but no less than 2.2 minutes and no more than 5 minutes
- Each assembled gearbox is put into a buffer for testing.

**A testbenchruns**the gearboxes for 10 minutes and can initially take up to five at a time.- An operator loads and unloads them to the test points.
- Loading and unloading both take from 0.2 to 0.4 minutes for each gearbox.
- There is a 93% chance of passing the gearbox for shipping, while the failed gearboxes are sent directly to a disassembly station where an operator will remove the gears and put them back on the conveyor 5 m from its end.
- The gearbox castings and bearings are instead discarded. Disassembly takes a mean of 2.3 minutes, with a standard deviation of 0.4, but no less than 1.7 minutes and no more than 3.5 minutes.
- The plant is staffed by a number of operators (to be decided) who are trained in all activities.

**Costs and Budget **

The company has already purchased the CNC workstation for £72K. The CNC workstation needs to be repaid in three years. The plant operates on an eight-hour shift. Operators have a 15-minute break in the morning and afternoon, and one hour for lunch.

Additionally, you have a budget of £15K to set up the remainder of the plant. This expenditure must be repaid within one year.

**Costs **

Assembly stations with appropriate tooling: £1800

Bins for machined gearboxes: £200

Text bench space per gearbox: £2200

Fixed cost for hiring an operator (advertising, training, etc.): £1500

Operator hourly rate including on-costs: £15.60

**Task **

Optimise the plant to achieve maximum profit within the allotted budget. You may need to optimise the plant for the priorities of the machines first. The expected profit for each completed and working gearbox is £80.

Investigate what effect a 90-minutes breakdown of the CNC workstation and of the conveyor belt would have on the daily production rate.

Write a report describing your model and present results on a series of tests on the model. In your conclusions, present an evaluation of the model in the light of all the assumptions made and what limitations they place on the model. The report must be in the form of a standard technical report or article and should include:

**Abstract ****Introduction **

This should include some explanation of stochastic modelling and methods and tools available to carry out discrete-event simulation to form a literature review. For example, you might want to discuss software packages other than Witness for discrete event simulation.

You should also introduce the problem by a description of the plant; the use of a block diagram may help.

**Methods **

Describe your modelling technique and the structure of the Witness model. Justify your approaches to building the model and include any relevant references. Describe the approach to optimisation and describe all equations or functions used.

**Results **

Present the results of your optimisation and experiments, the expected daily, hourly production and the profit from the plant.

**Discussion **

Discuss the model, its performance and implications on the real system. Discuss and evaluate the limitations of the model.

**Conclusions **

Provide some conclusions in a form that will advise the company management on the feasibility and expected returns for the plan.

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