Refinery Optimization Using LPP

This assignment focuses on optimizing refinery operations for maximum profitability using Linear Programming (LPP). It presents a case study analyzing the profitability of various products like jet fuel, premium petrol, etc., and how LPP can be used to determine the optimal production mix. The report includes calculations, interpretations of results, and a conclusion highlighting the effectiveness of LPP in decision-making for refinery management.

Management Science for Decision Support

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
1. Constructing diagram that shows different products as well as the different processing
stages\..........................................................................................................................................1
2...................................................................................................................................................2
3 and 4 Discussing optimal solution on the basis of outcome assessed through solver..............7
CONCLUSION..............................................................................................................................12
REFERENCES..............................................................................................................................13
APPENDIX....................................................................................................................................14
Appendix 1: Abbreviations of above depicted elements are as follows:...................................14
Appendix 2:...............................................................................................................................16

INTRODUCTION
Linear programming may be served as a tool or method which in turn helps in deriving
best outcome in terms of profit maximization and lower cost. It is a mathematical model which
describes and exhibit linear relationship between the variables (Balakrishnan, Render and Stair,
2011). Such model or tool is highly significant which in turn helps business unit in making
suitable decisions. The present report is based on the case situation of refinery optimization
which will provide deeper insight about the way through which profit can be maximized by the
firm. Hence, LPP entails the manner through which business unit can make optimal use of
resources and thereby maximizes profit.
1. Constructing diagram that shows different products as well as the different processing stages\
On the basis of given case situation, oil refinery purchases of two crude oil go through
from different processes such as distillation, reforming, cracking and blending. Hence, given
case presents that Distillation process divides each crude oil into fractions such as naphthas
(light, medium and heavy), oil (light and heavy) and residuum. Along with this, such naphthas
have octane number of 90, 80 & 70 respectively. Along with this, case study presents that
reforming process produces reformed gasoline and has an octane number of 115. Further, in
cracking light and heavy oil is used by the company for blending either jet fuel or fuel oil. On the
other side, cracked oil is used for blending petrol. Apart from this, residuum can be used by the
company to produce lube oil. Besides this, residuum can also be undertaken to blend into jet fuel
or fuel oil. Thus, by considering all such aspects diagram including input, intermediate and
output products have drawn.
Variables undertaken for refinery optimization problem are enumerated below:

Low Naphtha Blending 1
Crude oil 1 Refining refined gasoline
Medium Naphtha
Crude oil 2 Cracking Cracked gas
Cracked oil
2.
Abbreviations of below depicted elements are mentioned in appendix:
The main objective is to maximize the following functions:
Variables formulation
cr1, cr2, ln, mn, hn, lo, ho, r, lnrg, mnrg, hnrg, rg, locgo, hocgo ≥ 0 ……………..(i)
cg, co, lnpmf, lnrmf, mnpmf, mnrmf, hnpmf, hnrmf, rgpmf, rgrmf ≥ 0 ………………(ii)
cgpmf, cgrmf, lojf, hojf, rjf, cojf, lofo, hofo, rfo, cofo ≥ 0 ………………….
(iii)
D
is
til
la
ti
o
n
Regular petrol
Premium
petrol
Re
sid
uu
m
Heavy
oil
Lig
ht
oil
Heavy
Naphtha
Pro
duc
ing
Lube oil
Blendin
g 2 Jet fuel
Blendi
ng 3
Fuel
oil

rlbo, pmf, rmf, jf, fo, lbo ≥ 0……………………………………………….(iv)
Upper bounding constraints on the basis of limited availability of crude oil
cr1 <_ 20000 …………….(v)
cr2 <_ 30000’………………..(vi)
Distillation capacity constraint
cr1 + cr2 <_ 45000’…………………….(vii)
Reforming capacity constraint
lnrg + mnrg + hnrg <_ 10000……………….(viii)
Cracking capacity constraint
locgo + hocgo <_ 8000………………..(ix)
Stipulation
500 ≤ lbo≤ 1000……………………(x)
Production of light naphtha is highly based on the quantity of crude oil used. Thus, on the basis
of such aspect crude oil splits in distillation process in the following way:
0.1 * cr1 + 0.15 * cr2 = ln………………(xi)
Other constraints
0.2 cr1+0.25 cr2=mn(12)(12)0.2 cr1+0.25 cr2=mn…………(12)∗ ∗ ∗ ∗
0.2 cr1+0.18 cr2=hn(13)(13)0.2 cr1+0.18 cr2=hn……………(13)∗ ∗ ∗ ∗
0.12 cr1+0.08 cr2=lo(14)(14)0.12 cr1+0.08 cr2=lo…………(14)∗ ∗ ∗ ∗
0.2 cr1+0.19 cr2=ho(15)(15)0.2 cr1+0.19 cr2=ho……………(15)∗ ∗ ∗ ∗
0.13 cr1+0.12 cr2=r……………..(16)∗ ∗
Quantity of reformed gasoline produced
0.6∗lnrg+0.52∗mnrg+0.45∗hnrg=rg………………………(17)

Quantities of cracked oil and cracked gasoline produced
0.68∗locgo+0.75∗hocgo=co…………(18)
0.28∗locgo+0.2∗hocgo=cg……………(19)
Quantities of light naphtha used for reforming and blending = quantities available
Lnrg + lnpmf + lnrmf = ln……………(20)
Similar constraints
Mnrg + mnpmf + mnrmf = mn…………..(21)
hnrg + hnpmf + hnrmf = hn..................(22)
locgo+lojf+0.55∗fo=lo ...(23)
hocgo+hojf+0.17∗fo=ho …… (24)
cojf+0.22∗fo=co …… (25)
rlbo+rjf+0.055∗fo=r ….. (26)
cgpmf+cgrmf=cg …. (27)
rgrmf+rgpmf=rg …. (28)
lnpmf+mnpmf+hnpmf+rgpmf+cgpmf = pmf (29)
nrmf+mnrmf+hnrmf+rgrmf+cgrmf = rmf (30)
lojf+hojf+cojf+rjf=jf …. (31)
0.5∗rlbo=lbo ... (32)
pmf≥0.4∗rmf ... (33)
90∗lnpmf+80∗mnpmf+70∗hnpmf+115∗rgpmf+105∗cgpmf≥94∗pmf ... (34)

Reformed motor fuel
90∗lnrmf+80∗mnrmf+70∗hnrmf+115∗rgrmf+105∗cgrmf≥84∗rmf ...(35)
Constraint for jet fuel
lojf+0.6∗hojf+1.5∗cojf+0.05∗rjf≤jf ...,.(36)
Objective for maximization
max7∗pmf+6∗rmf+4∗jf+3.5∗fo+1.5∗lbo ... (37)
Constraints on the basis of second objective are enumerated below:
max7∗pmf+6∗rmf+4∗jf+3.5∗fo+1.5∗lbo …… (38)
cr1≤20000 …… (39)
cr2≤30000 …..(40)
cr1+cr2≤45000 ….. (41)
lnrg+mnrg+hnrg≤10000 ……(42)
locgo+hocgo≤8000 …….(43)
500≤lbo≤1000 ……. (44)
0.1∗cr1+0.15∗cr2=ln …….(45)
0.2∗cr1+0.25∗cr2=mn …… (46)
0.2∗cr1+0.18∗cr2=hn …..(47)
0.12∗cr1+0.08∗cr2=lo …..(48)
0.2∗cr1+0.19∗cr2=ho …. (49)
0.13∗cr1+0.12∗cr2=r …..(50)

.6 lnrg+0.52 mnrg+0.45 hnrg=rg ……(51)∗ ∗ ∗
0.68 locgo+0.75 hocgo=co ……..(52)∗ ∗
0.28 locgo+0.2 hocgo=cg …..(53)∗ ∗
lnrg+lnpmf+lnrmf=ln ……(54)
mnrg+mnpmf+mnrmf=mn …….(55)
hnrg+hnpmf+hnrmf=hn ……..(56)
locgo+lojf+0.55 fo=lo …….(57)∗
hocgo+hojf+0.17 fo=ho …….(58)∗
ojf+0.22∗fo=co ….. (59)
rlbo+rjf+0.055∗fo=r ……(60)
cgpmf + cgrmf=cg ……(61)
rgrmf + rgpmf = rg ……(62)
lnpmf + mnpmf + hnpmf + rgpmf + cgpmf = pmf ……..(63)
lnrmf+mnrmf+hnrmf+rgrmf+cgrmf=rmf….(64)
lojf+hojf+cojf+rjf=jf …(65)
0.5∗rlbo=lbo … (66)
pmf≥0.4∗rmf …… (67)
90∗lnpmf+80∗mnpmf+70∗hnpmf+115∗rgpmf+105∗cgpmf≥94∗pmf…….. (68)
90∗lnrmf+80∗mnrmf+70∗hnrmf+115∗rgrmf+105∗cgrmf≥84∗rmf.... (69)
lojf+0.6∗hojf+1.5∗cojf+0.05∗rjf≤jf ....(70)

cr1,cr2,ln,mn,hn,lo,ho,r,lnrg,mnrg,hnrg,rg,locgo,hocgo≥0 .....(71)
cg,co,lnpmf,lnrmf,mnpmf,mnrmf,hnpmf,hnrmf,rgpmf,rgrmf≥0 ......(72)
cgpmf,cgrmf,lojf,hojf,rjf,cojf,lofo,hofo,rfo,cofo≥0 ......(73)
rlbo,pmf,rmf,jf,fo,lbo≥0 ..........(74)
Hence, objective function pertaining to maximization on the basis of variables that include
profit or cost of final products is as follows:
max7 ∗ premium motor fuel + 6 ∗ regular motor fuel + 4 ∗ jet fuel + 3.5 ∗ fuel oil + 1.5 ∗
lube oil
3 and 4 Discussing optimal solution on the basis of outcome assessed through solver
Distillation
Typ
e
Light
Napht
a
Mediu
m
Naphta
Heavy
Napht
a
Ligh
t Oil
Heav
y Oil
Residuu
m
Wast
e
Tota
l
Crud
e Oil
To
Distill
Availabilit
y
Crud
e 1
0.1 0.2 0.2 0.12 0.2 0.13 0.05 1 15000 20000
Crud
e 2
0.15 0.25 0.18 0.08 0.19 0.12 0.03 1 30000 30000
45000 45000
Naptha Usage
Reform
ed
Gasolin
e
Nap
hta
to
Ref
orm
Reg
ular
Petr
ol
Pre
miu
m
Petr
ol
Total
of
Naph
ta
Used
Ava
ilabl
e
Nap

hta
Light Naphta 0.6 0 0 6000 6000 600
0
Medium Naphta 0.52 0 0 1050
0
1050
0
105
00
Heavy Naphta 0.45 0 0 8400 8400 840
0
Reformed 0
Limit 100
00
Oil usage
Crack
ed oil
Cracked
gasoline Oil to
reform
Oil
used
for
Jet
fuel
Oil
use
d
for
Fu
el
Tot
al of
oil
used
Ava
ilabl
e
Light oil 0.68 0.28 42000 0 0 420
0
420
0
Heavy oil 0.75 0.2 8255.16 474.
84
0 870
0
870
0
Cracked 12425.16
Limit 8000
Residuum usage
Lube Oil Lube Jet Fuel Fuel Oil Total Available

Coefficient Oil
Residuum 0.5 1000 4550 0 5550 5550
Cracked oil usage
Fuel Oil
t
Jet Fuel Total Available
Cracked
oil
0 9024.87 9024.87 9024.87
Gasoline usage
Fuel Oil Jet Fuel Total Available
Cracked
Gasoline
0 2821.03 2821.03 2821.03
Reformed
Gasoline
0 0 0 0
Octane contents
Light
Naphta
Medium
Naphta
Heavy
Naphta
Reformed
Gasoline
Cracked
Gasoline
Octane
Number
90 80 70 115 105

Vapour pressure
Light Oil Heavy
Oil
Cracked
Oil
Residuum
Pressure 1 0.6 1.5 0.05
Fuel Oil Mix Coefficients
Light Oil Heavy
Oil
Cracked
Oil
Residuum
Coefficient 10 3 4 1
Blending
Created Octane
Contents
Octane
minimum
Profit Minimum
Production
Regular
Petrol
0 0 0 0
Premium
Petrol
24087.32 2264208 94 * 24087.32
= 2264208
700 *
24087.32 =
£16,861,126
0
Created Pressure Pressure Profit

Maximum
Jet Fuel 14049.71 14049.71 14049.71 400 * 14049.71 =
£5619884
Available 14049.71
Created Mix
Requirement
Profit
Fuel Oil 0 0 0
Created Minimum Maximum Profit
Lube oil 500 500 1000 75000
Available 500 0 0
Total profitability = £22,556,010
Interpretation: The above depicted evaluation shows that in the case of Jet fuel, fuel and
lube oil profitability aspect accounts for £5619884, £0 & £75000 respectively. In addition to this,
profitability aspect in premium petrol implies for £19028985 significantly. Thus, by taking into
account all such aspects, it can be stated that total profitability in the case of refinery
optimization accounts for £24723869.

CONCLUSION
From the above report, it has been concluded that technique of LPP is highly effectual
which in turn helps in resolving issues more effectually. Besides this, it can be inferred that by
using LPP technique firms can determine optimal solution for decision making. Further, it has
been articulated that by optimizing the refinery profit of £24723869 will be generated by the
concerned authority.

REFERENCES
Books and Journals
Balakrishnan, N., Render, B. and Stair, M. R, 2011. 3rd Edition. Prentice Hall.

APPENDIX
Appendix 1: Abbreviations of above depicted elements are as follows:
CR1 = crude 1
CR2 = crude 2
LN = Light Naphtha
MN = Medium Naphtha
HN = Heavy Naphtha
LO = Light oil
HO = Heavy oil
R = Residuum
LNRG = Light naphtha used to produce reformed gasoline
MNRG = Medium naphtha usage in the production of reformed gasoline
HNRG: Heavy naphtha in reformed gasoline
RG: reformed gasoline
LOCGO: Light oil used to produce cracked oil and cracked gasoline
HOCGO: heavy oil used to produce cracked oil and cracked gasoline
CG: cracked gasoline
CO: cracked oil
LNPMF: light naphtha used to produce premium motor fuel
LNRMF: light naphtha used to produce regular motor fuel
MNPMF: medium naphtha used to produce premium motor fuel

MNRMF: medium naphtha used to produce regular motor fuel
HNRMF: heavy naphtha used to produce premium motor fuel
HNRMF: heavy naphtha used to produce regular motor fuel
RGPMF: reformed gasoline used to produce premium motor fuel
RGRMF: reformed gasoline used to produce regular motor fuel
CGPMF: cracked gasoline used to produce premium motor fuel
CGRMF: cracked gasoline used to produce regular motor fuel
LOJF: light oil used to produce jet fuel
HOJF: heavy oil used to produce jet fuel
RJF: residuum used to produce jet fuel
COJF: cracked oil used to produce jet fuel
RLBO: residuum used to produce lube-oil
PMF: premium motor fuel
RMF: regular motor fuel
JF: jet fuel
FO: fuel oil
LBO: lube-oil

Appendix 2: