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Oil and Petroleum Products Explained Refining Crude Oil Assignment
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Assignment Task
Brief
The Big Oil Company are in the process of setting up a new oil field to drill for crude oil, refine the oil into different blends of petrol, and ship the blends to their different warehouses. They have hired you to help them choose the most efficient way to organize their resources.
The first thing they need to do is extract crude oil from the earth. To do this, they need to buy pumps so that they can pump the oil out. A small pump can produce 500 barrels of crude oil. A large pump can produce 1,000 barrels of crude oil. The firm wants to produce at least 100,000 barrels. Also, the area of the oil field is 4,000m2. Each small pump takes up 10m2 and each large pump takes up 50m2. A small pump costs $20,000 and a large pump costs $25,000. What is the optimum combination of large and small pumps that minimizes costs for the firm?
Once they have extracted the crude oil, they then send it to the refinery. The extracted crude oil can be divided into three separate categories. The amount of each category available is given below.
|
Category |
Barrels Available |
|
1 |
50,000 |
|
2 |
30,000 |
|
3 |
20,000 |
They wish to make three different petrol blends from the crude oil: High Quality, Medium Quality, and Low Quality. The combinations of the categories of crude which are required to make a barrel of each of the blends are given below.
|
Quality |
Specifications |
Selling Price Per Barrel |
|
Low |
At least 50% of 1 At least 30% of 2 |
10 |
|
Medium |
At least 40% of 2 At least 10% of 3 |
15 |
|
High |
At least 50% of 3 No more than 25% of 1 |
25 |
The firm wishes to produce at least 30,000 barrels of each type of petrol. What combination should they choose in order to maximize the revenue from selling the barrels?
Assume that the firm has produced 90,000 barrels of petrol. With the petrol prepared, it then needs to be shifted to different storage facilities. There are a variety of different transportation options available to the firm. The barrels can be transferred by train, by truck, by plane, or by ship, which need to be rented by the firm for a fee. There are three different storage facilities: A, B, and C. Not all transport modes can deliver to all warehouses. The cost of transportation varies by which facility it is being transferred to. All this information is presented in the table below.
|
Transport |
Delivers to ($ per barrel) |
Rental Charge |
Capacity |
|
Train |
A (2); B (2) |
$15,000 |
30,000 |
|
Truck |
A (2); B (3); C (2) |
$5,000 |
20,000 |
|
Aircraft |
A (3); B (3); C (2) |
$30,000 |
40,000 |
|
Ship |
B (1); C (2) |
$50,000 |
60,000 |
Facility A demands 20,000 barrels of petrol, Facility B demands 30,000 barrels, and Facility C demands 40,000 barrels. Find the optimum transportation schedule for the firm which minimizes the cost of meeting this demand. Remember, if the firm does not choose to use a particular transportation method, then it does not have to pay the rental fee!
Instructions
To write up the report, you must follow these steps:
1. Write out the mathematical models for the three linear programming problems. Make sure to clearly identify the decision variables, the objective function, and the constraints. Provide a written description in the report for each model explaining what the model is trying to do.
2. Programme the models in Excel and solve them using Solver for the correct answer. Make sure that the Excel sheets are clearly labelled so that the decision variables, objective function, and constraints are easy to find and follow.
3. Analyse the “Answer Report” which is provided by the Solver feature. For each model, what is the optimum value? What are the values of the decision variables? Which constraints bind? Which constraints have slack/surplus?
4. Analyse the “Sensitivity Report” which is provided by the Solver feature. For the first and second problems, which constraints should the firm relax, if they had the option to? How would the relaxation of these constraints affect the results? For the third problem, find a value for one of the $ per barrels where a marginal (e.g. one unit) increase in the parameter results in the firm stopping using that method of transport. Also, if there was a ship which had a capacity of 70,000 barrels, how much would the firm be willing to pay to rent that ship? In all cases, provide explanations for your answers.
5. Oil drilling, oil blending, and transportation problems are very common subjects in the field of linear programming. From your reading of the relevant literature, is there any other relevant information that Big Oil Company should be considering in relation to the three problems?
Structure
When writing the report, you may wish to address a single step for each model before moving on to the next step, or you may choose to address each step for a single model and then move on to the next model. Either way is acceptable as long as the structure is coherent.
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