UNIVERSIDAD DE LA SABANA
OPTIMIZACIÓN EN INGENIERÍA QUÍMICA
Ana María Linares Hoyos – Daniela Conde Bustos – Sara Castro Olaya
Taller I – Corte III – mayo 10/2021
Shale oil, located on the island of Aruba, has a capacity of 1’500.000 bbl of crude oil per day.
The final products from the refinery include three types of unleaded gasoline with different
octane numbers (ON): regular with ON = 87, premium ON = 89, and super with ON = 92.
The refining process encompasses three stages: (1) a distillation tower that produces
feedstock (ON = 82) at the rate of 0.2 bbl per bbl of crude oil, (2) a cracker unit that produces
gasoline stock (ON = 98) by using a portion of the feedstock produced from the distillation
tower at the rate of 0.5 bbl per bbl of feedstock, and (3) a blender unit that blends the gasoline
stock from the cracker unit and the feedstock from the distillation tower. The company
estimates the net profit per barrel of the three types of gasoline to be $6.70, $7.20, and $8.10,
respectively. The input capacity of the cracker unit is 200,000 barrels of feedstock a day. The
demand limits for regular, premium, and super gasoline are 50.000, 30.000, and 40.000
barrels per day. Develop a model for determining the optimum production schedule for the
refinery.
Zmax = gasmoney1 (f11 + f21) + gasmoney2 (f12 + f22) + gasmoney3 (f13 + f23)
Zmax = 6,70 (f11 + f21) + 7,20(f12 + f22) + 8,10(f13 + f23)
Maximize the profit produced by the sale of gasoline.
Restrictions:
1. Daily supply of crude oil
5(f11 + f12 + f13) + 10(f21 + f22 + f23) ≤ 1.500.000
2. Cracker input capacity
2(f21 + f22 + f23) ≤ 200.000
3. Daily demand for regular gasoline
f11 + f21 ≤ 50.000
4. Daily demand for premium gasoline
f12 + f22 ≤ 30.000
5. Daily demand for super gasoline
f13 + f23 ≤ 40.000
6. Regular gasoline
f11 ∗ 82 + f21 ∗ 98 = (f11 + f21) ∗ 87
7. Premium gasoline
f12 ∗ 82 + f22 ∗ 98 = (f12 + f22) ∗ 89
8. Super gasoline
f13 ∗ 82 + f23 ∗ 98 = (f13 + f23) ∗ 92
From equation 6 we can simplify
87 ∗ f11 + 87 ∗ f21 − 82 ∗ f11 − 98 ∗ f21 = 0
5 ∗ f11 − 11 ∗ f21 = 0
From equation 7 we can simplify
82 ∗ f12 + 89 ∗ f22 − 82 ∗ f12 − 98 ∗ f22 = 0
−9 ∗ f22 = 0
From equation 7 we can simplify
92 ∗ f13 + 92 ∗ f23 − 82 ∗ f13 − 98 ∗ f23 = 0
10 ∗ f13 − 6 ∗ f23 = 0
Results
A maximum value is a value known as the extreme of the function. They are the largest
values that a function takes at a point located either within a particular region of the curve.
The maximum that was found of the objective function for this problem was 875000, this
refers to the total sales that the plant has made, to reach this value the following conditions
are met:
f11 = 34375
f12 = 16875
f13 = 15000
f21 = 15625
f22 = 13125
f23 = 25000
The variables can be defined as a function of two input streams to the disintegration unit that
are feed load and disintegrated gasoline, as well as the three final products, f12 refers to the
number of barrels per day to be produced with raw material obtained from process 1 used to
mix the final product 2.
Checking the restrictions, the input capacity of the cracker had a value of 107500, which
reflects that it does not occupy 100% of its capacity but complies with the restriction. In the
same way, verifying the daily supply of crude oil, the result is 868,750, this means that the
production capacity of the plant is not exceeded since this value is below 1,500,000. In
addition, the daily demands of the three types of gasoline were verified: Regular, Premium
and Super, where it was also possible to verify that it fully complies with its maximum
capacity.
Compromiso: A través de esta carta firmada por cada uno de los integrantes del grupo de clase,
manifestamos que conocemos la totalidad del contenido del trabajo que se adjunta con este
formato y que se envía al docente por correo, incluyendo todos los cálculos, anexos, planos o
cualquier otro material necesario para su realización. Así mismo, manifestamos que cada uno de
nosotros revisó detenidamente el contenido del documento y estamos de acuerdo con la entrega.
Por lo tanto, cada uno de nosotros se hace responsable de la integridad académica en el 100% del
trabajo entregado.
Nombre ID Firma
Sara Castro Olaya 0000199941
Ana María Linares Hoyos 0000200906
Daniela Conde Bustos 0000197889
