EBUS504 Operations Modelling and Simulation Assignment, University of Liverpool

Assignment Questions 

1.  Practical questions: Operations modelling (60 Marks)

A flexible manufacturing cell consists of three machines (M1, M2 and M3), an assembly machine (MA) and an inspection station. The cell processes three types of parts (Part 1, 2 and 3) which are assembled to make product A. Each part requires a specific set of operations as follows:
P1: Machine M1, then Machine M2
P2: Machine M3
P3: Machine M1, then Machine M3
Product A: Assembled on MA from 2*P1 and 2*P2 and 1*P3

5 Products A as a batch will be under inspection after they complete operations on MA. This quality check takes 5 minutes to complete and it will incur a cost of $0.5 per minute. Through this quality inspection, about 1% of products A will be found as faulty and be scrapped. The non-defective products A will be shipped out.

Parts are delivered regularly by suppliers. Suppliers deliver the parts with the following costs:

P1: cost $ 15 for each delivery, $ 1.5 for each part P2: cost $ 10 for each delivery, $ 1 for each part P3: cost $ 20 for each delivery, $ 2 for each part
The delivery cost can account for a batch size up to 100 units of materials but since the three raw materials (i.e. P1, P2, P3) are supplied by different suppliers so they cannot be bundled for delivery. Every part that arrives but gets rejected will incur a 20% penalty of the delivery cost.
The cycle time for each part on each machine is fixed but dependent of the type of part processed. Each machine incurs an operation cost. The table below presents these data.

Each faulty final product will incur a scrapping cost of $50.

Assumptions:

• All time units are in minutes.
• The total floor space is 250 m2. The amount of floor space taken by each machine is 4 m2. This includes space for access and maintenance. 

Parts that are not in a machine require a floor space. Parts have different shapes and hence different storage space requirements. You can find these data in the below table. Please note that the parts CANNOT be stacked.

Your answers to the requirements below will be based on running the model for 30,000 minutes.

1.  Determine the optimal procurement plan of P1, P2 and P3 and discuss why these are the optimum values for maximizing the system output and minimizing the costs at the same time. TIP: Your system needs to be stable. Use a Gantt chart to find the bottleneck of the system and use appropriate calculations to support your arguments and analyses. (20%) (Page limit: 7 pages);
2. Assume that an operator is needed to set up three machines (M1, M2, M3) each time a part
   enters the machine. The setup takes 2 minutes to complete and is not dependent on the type of the parts. Identify the optimal minimum number of operators needed to produce the same output you have obtained in question a and support your answers with appropriate analyses. (10%) (Page limit: 2 pages);
3. This model extends the model built in question b with the optimized system parameters (such as the optimized procurement plan, and number of operators).
   Assume that the suppliers are not that prompt in delivery and their deliver rates vary. There are also variations in the setup time of the three machines (including M1, M2, and M3) and variations in the cycle time of the inspection station.

• Analyze the steady-state of your model (with appropriate time cell size and window size of your choice) regarding the new changes and discuss what are the impacts on the operations? (10%) (Page limit: 3 pages)

1.    If the suppliers’ delivery rates vary at  20% following a uniform distribution, all three machines’ setup time varies at  20% following a triangular distribution, and the inspection station’s cycle time varies at  20% following a triangular distribution;
2. If the suppliers’ delivery rates vary at  30% following a uniform distribution, all three machines’ setup time varies at  30% following a triangular distribution, and the inspection station’s cycle time varies at  30% following a triangular distribution;

• How can you minimize the impact of these variations at 30% variation (Critically discuss your plan with support of expected evidences from your model)? Propose TWO different solutions to double the production of your current model and critically discuss the pros and cons of your proposed solutions with rich reflections on their real-life implications (Your discussions for this question are expected to show good research efforts with broad references to credible academic resources). (20%) (Page limit: 8 pages)

TIP:

The function used to create a uniform distribution for the inter-arrival time is:

UNIFORM(min value, max value)
For example, a 20% variation with average inter-arrival time of 1 minute would be represented as follows:
UNIFORM(0.8,1.2)
The function used to create a triangular distribution for cycle time is:

TRIANGLE(min value, mode value, max value)
For example, a 20% variation with average cycle time of 1 minute would be represented as follows:
TRIANGLE(0.8, 1, 1.2)

2.  Practical questions: System Dynamics (30 Marks)

Assume you are a manager at the national fish and wildlife service. Your job is to recommend policies about managing a fishery near your national borders. Since fishing contributes significantly to your country's economy, your choices must ensure the wellbeing of the fish population and the fishing industry. For simplicity, all the individual fishing companies are combined into one aggregate company.

You'll be fishing in an aqua area covering 100 square miles. In this area, the ideal fish population is 1,200. On average, every female fish can regenerate 12 offspring every year. Nature has a mechanism that slows down fish reproduction to prevent overcrowding, when this number is reached. Table 1 gives details on the effect of this natural restriction on the fish population.

Table 1 Effect of natural restriction on fish population

However, this fish's environment is disrupted by the fishing industry. If the industry only fishes a
small amount, the fish will be able to quickly bounce back to their ideal population of 1,200. If small depletions from the industry keep happening, the fish will establish a new ideal population below 1,200. However, if the fish number drops steeply from heavy fishing, there will be so few fish left to reproduce. In this case, it will take a long time to recover, even without the presence of the fishing industry.

Modern fishing ships are equipped with sonar tracking and other high-tech equipment to aid in finding and catching fish. Thus, the ships can come back almost fully loaded even when the fish numbers start to decrease. Company only notices a substantial decrease in their catch when the fish population has already fallen to dangerously low levels.

Table 2 shows the catch per ship varying with fish density. Fish density is defined as the number of fish found per square mile where the fish population lives.

Table 2 Effect of density on catch per ship

Fish meat is a popular ingredient in local’s cuisine and hence each fish can be sold at $20. Every year, your company harvests the fish and uses 20% of annual profits to purchase more ships at $300 apiece. Profits are determined by the revenues from selling fish meats and the company’s operating costs. The operating costs are based on how many ships the company owns, with each ship costing $250 a year to maintain and run. Simulation begins with zero net profit in your company. Initially, your company owns 10 ships and the fishing area contains 1,000 fish.

Please note that the numbers used in the problem description aren't realistic. However, they are consistent and don't impact the model's behavior. You could think of these numbers as representing thousands to make it easier.

You are expected to create a model of your nation's fish population and fishing industry. You then will use it to see how different regulations would affect both the fish population and the fishing economy, while addressing the below questions.

Q1. Draw the casual loop diagram with respect to the above description. Build the baseline model, observe the system behavior over 10 years, and explain why the system generated the exhibited behavior. Try to tell the story of what happened in the simulation by making references to the feedback loops describing the system. (10%) (Page limit: 3 pages)

Q2 Clearly, we don’t want to exhaust our fish supply and want to the system produce a stable fish population, while pursuing outstanding financial data. The reason is obvious. If the fish population is greatly reduced, that would eventually lead to the fishing industry's collapse and job losses. After heated discussions, there are several potential regulatory solutions to consider.

a)   A possible policy alternative is to impose a high tax (say $200 per ship) on new ships, making them more expensive and limiting their purchases.
b)   Another policy alternative is to prohibit specific fishing methods, making it harder for ships to catch fish. Fewer fish caught means that the fish population has a better chance for survival. Table 3 gives detailed effects of density on catch per ship under the new policy. 

Table 3 Effect of density on catch per ship with new policy

c)   Another policy might be to force all boats over a certain age have to be dry docked for safety reasons, assuming the average lifetime of a ship is 12 years.
d)  Suppose that we design an environmental tax which will charge the fishermen on a per fish basis, based on the total number of fish caught each year. Table 4 gives taxing details.

Table 4 Fish Tax

For each alternative policy, discuss if the proposed policy is successful in addressing the issue, explain any differences in system behavior between the one generated by the policy and that of the baseline model. Try to tell the story of the differences between the two simulations by making reference to the feedback loops describing the system. (20%) (Page limit: 9 pages)