The first industrial application of LP was to an oil refinery scheduling problem in 1951. Chemical Engineering has been an important area of application of OR ever since and some significant advances in optimization have come from Chemical Engineers. The following diagram was taken from the "Learning Centre" that used to be on the website of Shell Lubricants.
This assignment develops a very simple model of an oil refinery with three distillation columns and a blender. [This is also because some refinery operations have nonlinear relationships between input and output quantities.] If this scares you, don't worry, the background required is only high school science and/or general knowledge.
Scottish Petroleum has a refinery consisting of three distillation columns, labelled A, B and C, and a blender. The distillation columns take crude oil and split it into butane, fraction 1, fraction 2, fraction 3 and tar (asphalt), with some waste. Each of the distillation columns can be operated independently and for up to 24 hours per day (ie continuously). [Note that the output of fraction 1, fraction 2 and fraction 3 from each distillation column goes directly into the blender, not into the next distillation column. The output of tar from each distillation column is considered to be a finished product.]
The butane and tar can be sold as products. Fraction 1, fraction 2 and fraction 3 are blended to produce petrol (gasoline), kerosene (jet fuel) and diesel. At present it is company policy not to try to sell more than the demand for each product: any excess output of butane, tar or unblended fractions must be disposed of at a cost. All waste must also be disposed of at a cost.
With a view to analysing the economics of increased produciton, Scottish Petroleum needs a model of its refinery in order to determine the optimal distillation column operating policy. Derive a model in Xpress-IVE using the data below.
The output of the three distillation columns (tonnes/hour) and running costs (£/hour) is given in the following table.
| Output | Column A | Column B | Column C | |
|---|---|---|---|---|
| Butane | 45 | 63 | 95 | |
| Fraction 1 | 28 | 35 | 58 | |
| Fraction 2 | 23 | 38 | 60 | |
| Fraction 3 | 35 | 40 | 50 | |
| Tar | 20 | 25 | 25 | |
| Waste | 50 | 50 | 25 | |
| Running cost | 8000 | 12500 | 21000 | |
The proportions of the three fractions that are blended to produce the three products are given in the following table. For example, one tonne of Petrol is made from 500kg of Fraction 1, 350kg of Fraction 2 and 150kg of Fraction 3.
| Petrol | Kerosene | Diesel | ||
|---|---|---|---|---|
| Fraction 1 | 0.50 | 0.30 | 0.20 | |
| Fraction 2 | 0.35 | 0.50 | 0.25 | |
| Fraction 3 | 0.15 | 0.20 | 0.55 | |
The products of the refinery have selling prices (£/tonne) and demands (tonnes/day) are given in the following table.
| Product | Price | Demand | |
|---|---|---|---|
| Butane | 200 | 3000 | |
| Petrol | 160 | 2000 | |
| Kerosene | 140 | 1500 | |
| Diesel | 150 | 1750 | |
| Tar | 10 | 500 | |
Any output from the distillation columns that is not sold as products or blended must be disposed of. The disposal costs (£/tonne) are given in the following table.
| Output | Disposal cost | |||
|---|---|---|---|---|
| Butane | 0.5 | |||
| Fraction 1 | 0.5 | |||
| Fraction 2 | 0.5 | |||
| Fraction 3 | 0.5 | |||
| Tar | 1.0 | |||
| Waste | 1.0 | |||
The company wishes to increase production, assuming that any production in excess of the demand can be sold at a price that is a multiple of the price up to the demand. Assuming that this multiple is the same for all products, analyse the trends in production as the discount multiplier is increased and identify the minimum value of the multiplier (to within two decimal places) for which each distillation column operates for 24 hours per day. Any further relevant interpretation and observations will add quality to your report.
Ideally, you will write a single Mosel file that generates the results for both parts of the assignment. If it is necessary to run the model twice to get both sets of results, give a clear explanation of what has to be done to generate all the results.
You should write up your work (giving results for Part 1 as well as those for Part 2) as a report of 3-5 sides and submit it by 14:00 on Wednesday 18th February. Your report should not contain the Mosel file and need not contain all the problem data above. An electronic copy of your report (.doc .ps or .pdf), your Mosel file (together with any necessary data files) should be submitted using WebCT by the same deadline. Further guidance on the form of your report is given here.