Hey everyone! It's me Shouq. This is the first lab report for an Industrial Engineering class called Operational research / optimization - OR1 - IE335 which I took in Fall 2017 in the American University of the Middle East (AUM) in Kuwait.
Abstract
The objective of this report is to show our
work in how to solve a crude oil refining and gasoline blending problem using
the operational research method. First, a clear description of the problem is
provided with every detail regarding it. Then the decision variables are
identified as well as the objective functions and the constraints of the
problem. After that we will have to formulate the final linear programming formulation.
Also, the problem will be solved using Lingo and Excel solver to find the
answer of the linear programming problem.
Keywords: Oil, refining,
blending, problem, operational, research.
Introduction
Crude oil refining and gasoline blending is a very huge problem where
companies are trying to select the best combination of components to make a
gasoline product that is needed ("Petroleum
refining - Gasoline blending", 2016). It happens converting the crude oils and other types
of liquid into several petroleum products that we use in our everyday life ("Refining Crude Oil", 2017). The
problem has a great economic importance and impact.
Crude oil refining and gasoline blending problem is very interesting
as it is a complicated problem. It is not easy to find the linear programming
formulation from first glance as well as the fact that we are not well trained
in how to use Lingo and Excel solver. We have two types of crude which are Econe
and Ratawi. We have access to both types of crude with a specific amount that
is available to us in everyday basis. It means that we have limited amounts.
Not to mention that Ratawi costs us less compared to Econe, and our first
instinct will make us choose the cheaper one witch is not always the case or
the right way to see problems.
Crude oil refining and gasoline blending problem is very relevant
problem that need to be solved especially for oil companies and economy. In crude
oil refining and gasoline blending problem we try to maximize the profit which
is the revenue - cost.
Problem description
There is an American Oil of Middle East refinery inside
Kuwait. Ratawi and Econe Crude are the
two types of crudes that this refinery has access to. The daily availability of
Ratawi crude is 150,0000 bbl per day while the daily availability for Econe
crude is 100,000 bbl. For each single bbl of Ratawi crude, the cost will be $20.
On the other hand, the Econe crude will cost the company $25 for every bbl.
The American Oil of Middle East refinery purifies the crude oil and
ends up producing two products. Naphtha and light oil are the two products that
came from the distillation of the crude oils. Every single bbl of Ratawi Crude
produces 0.3 bbl of naphtha as well as 0.65 bbl of light oil. In the other
hand, a single bbl of Eocene Crude producs 0.4 bbl of light oil and 0.55 bbl of
naphtha.
Light oil and naphtha are blended together in order to make 3 finalized
gasoline products and outcomes which are regular gasoline, jet fuel and premium
gasoline. Regular gasoline gas has a ratio of blend of 2:1 from naphtha to
light oil, while the premium gasoline has a ratio of blend of 1:1. When it
comes to the jet fuel, it has a blended ratio of 1:2.
4The regular gasoline has an income of $60 while for premium
gasoline has a profit of $60 comparing it to the premium gasoline which has the
highest revenue which is equal to $100. The demand of the regular gasoline that
we are supposed to satisfy every single day is 100,000 bbl. On the other hand,
the daily demand for the premium gasoline is 80,000 bbl while the demand for
jet fuel is 30,000 bbl for every day.
When the daily demand of anything is not being satisfied, the
company has to be paid by extra cost. The extra cost is $6 for everything
single bbl for a regular gasoline. Moreover, the extra cost for jet fuel is $12
per bbl, while for the premium gasoline is $7 for every single bbl.
Problem formulation
Figure 1
Crude oil refining and gasoline blending
procedure.
From figure 1, crude oil refining and
gasoline blending procedure is made through two main procedures. So first two
types of crude oil enter the refinery distill: Ratawi and Eocene with daily
availability of 150,00 and 100,000. Moreover, the cost for Ratawi will be 20$
per bbl and 25$ for Eocene. After the refinery distills process it will produce
two main oil products; Naphtha oil and Light oil. X1 as
Naphtha oil and X2 as Light oil. In addition, both X1 and X2 start the blend
process and end up with three types of gasoline: Y1 as Regular , Y2 as Premium
and Y3 as Jet fuel. To add
more, the ratio from Naphtha to light oil for each type of gasoline was 2:1 for
Regular, 1:1 for Premium and 1:2 for Jet fuel. To clarify more these are the
decision variables:
Decision variables
· X1: produced intermediate Naphtha
oil.
· X2 :
produced intermediate Light oil.
· Y1: produced gasoline Regular fuel.
· Y2 : produced gasoline Premium fuel.
· Y3 : produced gasoline Jet fuel.
· S1 : the shortage in Regular fuel.
· S2 : the shortage in Premium fuel.
· S3 : the shortage in Jet fuel.
The blending ratio above will be presented in equations
as follows:
·
2X1 + X2 = Y1; Regular fuel
Equation 1
- X1 + X2 = Y2 ; Premium fuel
Equation 2
·
X1 +2X2 = Y3 ; Jet fuel
Equation 3
Given that the revenue for Regular
fuel Y1 is 40$ ,
Premium fuel Y2 is 60$ and Jet
fuel Y3 is 100$ .
The previous bullets explain what the
decision variables are. As shown, X1 and X2 are production
of refinery distill, where Y1, Y2, Y3 are the
production from the blending process. Through this procedure there is some
shortage from blending and they are defined as S1 for Regular fuel, S2 for Premium
fuel and S3 for the Jet
fuel.
Objective function
Maximize.
Z= ( 40 Y1 + 60 Y2 + 100 Y3)
- (6 S1 + 7 S2 + 12 S3 )
- 20 ( 0.3 X1 + 0.65 X2)
- 25 ( 0.55 X1 + 0.4 X2)
Equation 4
For the objective function it is
maximization. And for Z it is the (revenue – cost). So for ( 40 Y1 + 60 Y2 + 100 Y3) the 40$, 60$,
100$ the revenue from the procedure for Y1, Y2, Y3 respectively. Secondly, (6 S1+ 7 S2 + 12 S3 ) the 6$, 7$, 12$ are the extra costs for the
shortage in Regular, Premium and Jet fuel. Third, 20 (0.3 X1+ 0.65 X2) the 20$ present the Ratawi cost and one Ratawi bbl
revenue 0.3 from Naphtha oil and 0.65 from light oil. Finally, as we did for
Ratawi it is the same for Eocene except the revenue and the cost so the
following equation 25 (0.55 X1 + 0.4 X2), represent 25$ cost , and one bbl from Eocene
revenue 0.55 from Naphtha oil and 0.4 Light oil.
Subject to
1. 0.3 X1 + 0.65 X2 =< 150,000
Equation 5
Which means the quantity from both Naphtha
oil which is 45,000 bbl and Light oil which is 97,500 bbl should be less or
equal the daily availability of Ratawi (150,000).
2. 0.55 X1 + 0.4 X2 =< 100,000
Equation 6
Which means the quantity from both Naphtha
oil which is 55,000 and for light oil 40,000 should be less or equal the daily
availability of Eocene (100,000).
3. 2 X1 + X2 = Y1
Equation 7
This is the blending ratio from Naphtha oil
and light oil to regular fuel.
4. X1 + X2 = Y2
Equation 8
This is the blending ratio from Naphtha oil
and light oil to premium fuel.
5. X1 + 2X2 = Y3
Equation 9
This is the blending ratio from Naphtha oil
and light oil to Jet fuel.
6. Y1 + S1 = 100,000 ; 2 X1 + X2 + S1 = 100,000
Equation 10
The shortage plus the production for
regular fuel shouldn’t exceed the demand.
7. Y2 + S2 = 80,000 ; X1 + X2 + S2 = 80,000
Equation 11
The shortage plus the production for premium
fuel shouldn’t exceed the demand.
8. Y3 + S3 = 30,000 ; X1 + 2 X2 + S3 =
30,000
Equation 12
The shortage plus the production for jet
fuel shouldn’t exceed the demand.
9. Y1, Y2, Y3, S1, S2, S3, X1, X2 >= 0
Equation 13
Non-negativity constrains.
Conclusion
]H
The final Linear
Programming Formulation is
Methodology
First, we will start by providing the Lingo solution of
the previously mentioned LP formulation. Then we will continue by proving the
Excel Solver answer as well. In both solutions we will provide an explanation
of what we did and how did we get that specific answer.
Lingo
Figure 3: The Lingo coding
Figure 4: The result of solving the problem using Lingo
Figure 5: The continuous result of solving the problem using Lingo
Figure 6
Figure 7
In this part, we tried solving the
problem using lingo. At first, we defined the variables of this problem and
wrote it in Lingo which is the quantity, constrains and objective as well. We
wrote all of this using Lingo coding. Then we used the feature "solver
status" to get the final result and let us see values.
Excel
Figure 8: The
table of the solution in Excel
We notice that
in the third row we added the coefficient of the final linear programming
formulation that we mentioned before. We also know that we have five
constraints and all the coefficients of x1, x2, s1, s2, and s3. Also, the
limits of the total of each constraint are mentioned in column j. Also, there
is a non-negativity constraint that must be satisfied.
Results
By solving the problem multiple times in excel and using the lingo
program as well, we got the idea of quantity naphtha from regular gasoline. We
want some quantity from naphtha we need 0.3. Also, we want 1:1 from naphtha in
manufacturing premium. The ratio is 1:2 from naphtha in manufacturing jet fuel
while the ratio is 0.65 from light as some as quantity.
The light refers to light inside the regular light inside premium
and light inside jet fuel. The company do their best to achieve their goal
which is achieve the maximum gains and doing all tasks that demand specially
from quantity of regular gasoline or premium gasoline or jet fuel gasoline
without buying any quantities which refers to (s1, s2, s3).
Conclusion
In conclusion, we used excel and lingo to solve the problem in a
perfect way. The problem is about maximization, and maximizing the profit of
the American Oil Company in Kuwait. We have 10 variables and 14 constraints in
this problem. The total profit is 7083333$, and the values of the products in
the Middle East Manufacturing are x11=76666.607 to produce regular gasoline
from required naphtha, x12= 0 to produce regular gasoline from required Eocene,
x13= 30000 to produce premium gasoline from required Naphtha, x21=2333.33 to
produce premium gasoline from required Eocene, x22= 80000 to produce jet fuel
gasoline from required naphtha, x23: 0 to produce jet fuel gasoline from required
Eocene, from this results we figure out that the company does not need to get
penalty from any company so we have s1,s2,s3=0. The optimal solution is 8000
and it is the max value.
References
Refining Crude Oil. (2017). Eia
U.S. Energy Information Administrain. Retrieved 1 November 2017, from https://www.eia.gov/energyexplained/index.cfm?page=oil_refining
Petroleum
refining - Gasoline blending. (2016). Encyclopedia Britannica.
Retrieved 1 November 2017, from https://www.britannica.com/technology/petroleum-refining/Gasoline-blending
The students who worked in this lab report are
- Shouq Alansari
- Hanan Akbar
- Manal Al-Mutairi
- Nour Almuwai
- Reem Almertiji
Knowing that not all students in the group have put equal efforts on this lab report. Some students worked harder than others, and it is normal when it comes to working on groups.
Things to learn from this lab report:
- Spaces are very important. You may lose points because of that.
- Notice that we wrote X1, but it has to be put in specific place as an equation and not typed. We did that, but it does not work in the blog. Below you can see how it should really look like
- Use citation