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Petroleum Industry Management


Your team provides consulting services to a petroleum company. The task i s to advise them on how to meet the demands of their customers for motor oil, diesel oil and gasoline. They have, at the moment, three refineries. They have decided not to store any excess production for a variety of reasons, including added insurance costs, environmental factors, and deterioration of gasoline over time.


From a barrel of crude oil, each refinery produces three different products: motor oil, diesel oil, and gasoline. Each refinery also produces a waste product, called parrafin. The table below shows production figures for each of the three refineries. The numbers in the table are gallons of product or waste produced from each barrel of crude oil. (A barrel is a unit of measurement, equal to 42 gallons, used mainly for historical reasons.)

Product Refinery 1 Refinery 2 Refinery 3
motor oil 15 3 3
diesel oil 10 14 5
gasoline 5 5 12
paraffin 3 5 2

Suppose that the current daily demand from your distributor for products is 1950 gallons of motor oil, 3100 gallons of diesel oil, and 5100 gallons of gasoline.


Set up a system of equations that describes the situation above.
Solve your equations to determine the number of barrels of crude oil each refinery should get so that the refineries, as a group, meet the demand for the three products.
Suppose that the demand for each product doubled simultaneously. How would your answer to the previous problem change? Explain your result mathematically.
Now suppose that another distributor has come forward and says that it would require 750 gallons of motor oil, 2000 gallons of diesel and 2000 gallons of gasoline per day. How would you set up production to satisfy this distributor only? That is, suppose this is the only distributor to which the company is selling. Is there only one way of doing this?
Now calculate the needs of each refinery, in barrels of crude oil per day, if both distributors are to be satisfied. How does this compare to your two previous answers? What mathematical conclusion can you draw? (Use the original demand from the first distributor of 1950 gallons of motor oil, 3100 gallons of diesel oil, and 5100 gallons of gasoline.)
In real life applications, constants are rarely ever exactly equal to their stated value; certain amounts of uncertainty are always present. This is part of the reason for the science of statistics. In the above model, the daily productions for the refineries would be averages over a period of time. Your job here is to explore what effect small changes in the parameters have on the output.

To do this, pick any 3 coefficients, one at a time, and vary them one way and the other by 3%. For each case , note what effect this has on the solution, as a percentage change. Can you draw any overall conclusion?

The activity just described is called a sensitivity analysis. A model which does not change much for modest changes in its parameters is said to be robust.

Suppose refinery 3 is shut down temporarily by the EPA for excessive emissions. If the demand is still 1950 gallons of motor oil, 3100 gallons of diesel oil, and 5100 gallons of gasoline, what would you now say about the company's ability to meet it? What production schedule do you recommend? (Hint - set the coefficients for refinery 3 to zero and try to solve the resulting problem.)

The situation in the problem above has caused enough concern that the company is considering buying another refinery, identical to refinery 3, and using it permanently. Assuming that all 4 refineries are on line, what production schedule do you recommend to meet the demand given in the previous exercise? In general, what can you say about any increased flexibility that the fourth refinery might provide?

The company has just found a candle maker that will buy the parrafin waste product. Assuming three refineries and the same demand of 1950 gallons of motor oil, 3100 gallons of diesel oil, and 5100 gallons of gasoline how much parrafin can be supplied?

The company is considering selling refinery 1, due to aging and inefficient equipment and high workmans compensation costs in the state where refinery 1 is located. They would like to know what this would do to their production capacity. Specifically, they would like examples of demands they could and could not meet with only refineries 2 and 3 in operation. Also, they would like you to comment on the effect of having refineries 2, 3 and 4. Any general statements you could make here would be helpful. (Hint - your comments should include a discussion of the terms unique, no solution, overdetermined, and underdetermined as they apply in the context of the petroleum refineries.)

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William W. Farr