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Optimal scheduling of refinery crude oil operations

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Theses and Dissertations

12-1-2010

Optimal Scheduling of Refinery Crude-Oil
Operations
Sylvain Mouret
Carnegie Mellon University

Follow this and additional works at: http://repository.cmu.edu/dissertations
Recommended Citation
Mouret, Sylvain, "Optimal Scheduling of Refinery Crude-Oil Operations" (2010). Dissertations. Paper 23.

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Optimal Scheduling of Refinery
Crude-Oil Operations
A DISSERTATION
Submitted to the Graduate School
in Partial Fulfillment of the Requirements

for the degree of

Doctor of Philosophy
in
Chemical Engineering
by
Sylvain Mouret

Carnegie Mellon University
Pittsburgh, Pennsylvania
December, 2010


Acknowledgments
First of all, I would like to express my most sincere gratitude to my advisor Professor Ignacio
E. Grossmann for his inestimable guidance and support over the course of my Ph.D. He has
managed to create a productive yet friendly environment and proved to be an abundant
source of knowledge for myself. I cannot thank him enough for his confidence in me and his
deep implication in my studies and in my life.
Besides my advisor, I would like to thank my thesis committee members – Professors
Lorenz Biegler, Nikolaos Sahinidis, John Hooker, and Willem-Jan van Hoeve for their time
and valuable comments.
I would like to thank Pierre Pestiaux, my supervisor at Total, whose strong commitment
to the project and never-ending enthusiasm has made this thesis possible.
I would also like to thank Philippe Bonnelle for bringing his experience and his insightful
suggestions into the project as well as other collaborators at SOG and CReG, for their useful
feedback on my work and friendly support. Furthermore, I am grateful to Total Refining &
Marketing for financial support of this project.
I wish to express my thankfulness for all my past and present workmates in the PSE group
for setting a productive mood in the office and a diverting atmosphere out of work. Among
them I would like to specifically mention Rosanna Franco, Gonzalo Guill´en Gos´albez, Ricardo Lima, Rodrigo L´
opez-Negrete de la Fuente, Mariano Martin, Roger Rocha, Sebastian
Terrazas, and Victor Zavala with whom I share many unforgettable memories.


I would also like to thank my fellow football and tennis teammates, Tarot card players,
French speaking lunchers, barbecue grillers, etc... who made my Pittsburgh experience a
very enjoyable one.
I want to express my gratitude to my family who has always been there when I needed
them, and to my 18-month-old niece Anna for being so cute and joyful.

Acknowledgments

ii


Last but not least, I cannot thank enough my beloved fianc´ee Charlotte for her patience
and for standing by me during the past three and a half years. Her unconditional love is
never to be forgotten.

Acknowledgments

iii


Abstract
This thesis deals with the development of mathematical models and algorithms for optimizing refinery crude-oil operations schedules. The problem can be posed as a mixed-integer
nonlinear program (MINLP), thus combining two major challenges of operations research:
combinatorial search and global optimization.
First, we propose a unified modeling approach for scheduling problems that aims at
bridging the gaps between four different time representations using the general concept of
priority-slots. For each time representation, an MILP formulation is derived and strengthened using the maximal cliques and bicliques of the non-overlapping graph. Additionally,
we present three solution methods to obtain global optimal or near-optimal solutions. The
scheduling approach is applied to single-stage and multi-stage batch scheduling problems
as well as a crude-oil operations scheduling problem maximizing the gross margin of the
distilled crude-oils.
In order to solve the crude-oil scheduling MINLP, we introduce a two-step MILP-NLP
procedure. The solution approach benefits from a very tight upper bound provided by the
first stage MILP while the second stage NLP is used to obtain a feasible solution.
Next, we detail the application of the single-operation sequencing time representation
to the crude-oil operations scheduling problem. As this time representation displays many
symmetric solutions, we introduce a symmetry-breaking sequencing rule expressed as a
deterministic finite automaton in order to efficiently restrict the set of feasible solutions.
Furthermore, we propose to integrate constraint programming (CP) techniques to the
branch & cut search to dynamically improve the linear relaxation of a crude-oil operations
scheduling problem minimizing the total logistics costs expressed as a bilinear objective.
CP is used to derived tight McCormick convex envelopes for each node subproblem thus
reducing the optimality gap for the MINLP.

Abstract

iv


Finally, the refinery planning and crude-oil scheduling problems are simultaneously solved
using a Lagrangian decomposition procedure based on dualizing the constraint linking crude
distillation feedstocks in each subproblem. A new hybrid dual problem is proposed to update
the Lagrange multipliers, while a simple heuristic strategy is presented in order to obtain
feasible solutions to the full-space MINLP. The approach is successfully applied to a small
case study and a larger refinery problem.

Abstract

v


Contents
Acknowledgments

ii

Abstract

iv

Contents

vi

List of Tables

x

List of Figures
1 Introduction
1.1 Single-Stage and Multi-Stage Batch Scheduling
1.2 Optimization of Oil Refineries . . . . . . . . . .
1.2.1 Refinery Planning . . . . . . . . . . . .
1.2.2 Crude-Oil Operations Scheduling . . . .
1.3 Mixed-Integer Optimization Tools . . . . . . .
1.3.1 Mixed-Integer Linear Programming . . .
1.3.2 Mixed-Integer Nonlinear Programming .
1.3.3 Constraint Programming . . . . . . . .
1.3.4 Lagrangian Relaxation . . . . . . . . . .
1.3.5 Symmetry-Breaking Approaches . . . .
1.4 Overview of Thesis . . . . . . . . . . . . . . . .
1.4.1 Chapter 2 . . . . . . . . . . . . . . . . .
1.4.2 Chapter 3 . . . . . . . . . . . . . . . . .
1.4.3 Chapter 4 . . . . . . . . . . . . . . . . .
1.4.4 Chapter 5 . . . . . . . . . . . . . . . . .
1.4.5 Chapter 6 . . . . . . . . . . . . . . . . .
1.4.6 Chapter 7 . . . . . . . . . . . . . . . . .

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2 Time Representations and Mathematical Models
Problems
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
2.2 Case Study . . . . . . . . . . . . . . . . . . . . . .
2.3 Time Representations . . . . . . . . . . . . . . . .
2.4 Mathematical Models . . . . . . . . . . . . . . . .
2.4.1 Sets and Parameters . . . . . . . . . . . . .
2.4.2 Variables . . . . . . . . . . . . . . . . . . .
2.4.3 MOS Model . . . . . . . . . . . . . . . . . .
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3 Short-Term Scheduling of Crude-Oil Operations
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Problem Statement . . . . . . . . . . . . . . . . . . . . .
3.2.1 General Description . . . . . . . . . . . . . . . .
3.2.2 Case Study . . . . . . . . . . . . . . . . . . . . .
3.3 Mathematical Models . . . . . . . . . . . . . . . . . . .
3.3.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Parameters . . . . . . . . . . . . . . . . . . . . .
3.3.3 Variables . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Objective Function . . . . . . . . . . . . . . . . .
3.3.5 General Constraints . . . . . . . . . . . . . . . .
3.3.6 Strengthened Constraints . . . . . . . . . . . . .
3.3.7 Symmetry-Breaking Constraint for MOS Models
3.3.8 Full Models . . . . . . . . . . . . . . . . . . . . .
3.4 Solution Method . . . . . . . . . . . . . . . . . . . . . .
3.5 Computational Results . . . . . . . . . . . . . . . . . . .
3.5.1 Scheduling Results . . . . . . . . . . . . . . . . .

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2.5

2.6

2.7

2.8

2.9

2.4.4 MOS-SST Model . . . . . . . . . .
2.4.5 MOS-FST Model . . . . . . . . . .
2.4.6 SOS Model . . . . . . . . . . . . .
Strengthened Reformulations . . . . . . .
2.5.1 Non-overlapping Graph Properties
2.5.2 MOS Model . . . . . . . . . . . . .
2.5.3 MOS-SST Model . . . . . . . . . .
2.5.4 MOS-FST Model . . . . . . . . . .
2.5.5 SOS Model . . . . . . . . . . . . .
Solution Methods . . . . . . . . . . . . . .
2.6.1 Additive Approach . . . . . . . . .
2.6.2 Multiplicative Approach . . . . . .
2.6.3 Direct Approach . . . . . . . . . .
Single-Stage Batch Scheduling Problem .
2.7.1 MOS Model . . . . . . . . . . . . .
2.7.2 MOS-SST Model . . . . . . . . . .
2.7.3 MOS-FST Model . . . . . . . . . .
2.7.4 SOS Model . . . . . . . . . . . . .
2.7.5 Models Comparison . . . . . . . .
Multi-Stage Batch Scheduling Problem . .
2.8.1 MOS Model . . . . . . . . . . . . .
2.8.2 MOS-SST Model . . . . . . . . . .
2.8.3 MOS-FST Model . . . . . . . . . .
2.8.4 Models Comparison . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . .

Contents

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vii


3.6

3.5.2 Performance of the
3.5.3 Performance of the
3.5.4 Performance of the
3.5.5 Performance of the
Conclusion . . . . . . . .

MOS Model . . . . . . . . . . . . . .
MOS-SST Model . . . . . . . . . . .
MOS-FST Model . . . . . . . . . . .
MILP-NLP Decomposition Strategy
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4 Single-Operation Sequencing Model for Crude-Oil Operations Scheduling 92
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.2 Strengthened Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.3 Symmetry-Breaking Constraints . . . . . . . . . . . . . . . . . . . . . . . .
95
4.3.1 Symmetric Sequences of Operations . . . . . . . . . . . . . . . . . .
95
4.3.2 A Sequencing Rule Based on a Regular Language . . . . . . . . . . .
95
4.3.3 Rule Derivation for COSP1 . . . . . . . . . . . . . . . . . . . . . . .
97
4.3.4 Regular Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
4.4 Computational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.4.1 Performance of the SOS Model . . . . . . . . . . . . . . . . . . . . . 101
4.4.2 Effect of the Number of Priority-Slots . . . . . . . . . . . . . . . . . 102
4.4.3 Remark on the Optimality of the Solution . . . . . . . . . . . . . . . 103
4.4.4 Effect of Symmetry-Breaking Constraints . . . . . . . . . . . . . . . 105
4.5 Comparison of Crude-Oil Scheduling Models . . . . . . . . . . . . . . . . . . 106
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5 Tightening the Linear Relaxation of a Crude-Oil
MINLP Using Constraint Programming
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
5.2 MINLP Model . . . . . . . . . . . . . . . . . . . .
5.3 Reformulation and Linear Relaxation . . . . . . . .
5.4 McCormick Cuts . . . . . . . . . . . . . . . . . . .
5.5 Computational Results . . . . . . . . . . . . . . . .
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . .

Operations Scheduling
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. . . . . . . . . . . . . . 118

6 Integration of Refinery Planning and Crude-Oil Scheduling
grangian Decomposition
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Refinery Planning Problem . . . . . . . . . . . . . . . . .
6.2.2 Crude-Oil Scheduling Problem . . . . . . . . . . . . . . .
6.2.3 Full-Space Problem . . . . . . . . . . . . . . . . . . . . . .
6.3 Lagrangian Decomposition Scheme . . . . . . . . . . . . . . . . .
6.4 Solution of the Dual Problem . . . . . . . . . . . . . . . . . . . .
6.5 Heuristic Solutions . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 CDU Feedstocks and Lagrange Multipliers . . . . . . . . .

Contents

using La120
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viii


6.7
6.8
6.9

6.6.2 Multi-Period Refinery Planning . . . . . . . . . . . . . .
6.6.3 CDU Feedstocks Aggregation . . . . . . . . . . . . . . .
6.6.4 Handling Nonlinearities in Crude-Oil Scheduling Model
6.6.5 Handling Nonlinearities in the Refinery Planning Model
6.6.6 Detailed Implementation . . . . . . . . . . . . . . . . . .
Numerical Illustration . . . . . . . . . . . . . . . . . . . . . . .
Larger Refinery Problem . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Conclusion
7.1 Time Representations and Mathematical Models . . . . . . . . . . . . . .
7.2 Short-Term Scheduling of Crude-Oil Operations . . . . . . . . . . . . . . .
7.3 Single-Operation Sequencing Model for Crude-Oil Operations Scheduling
7.4 Tightening the Linear Relaxation of an MINLP Using CP . . . . . . . . .
7.5 Integration of Refinery Planning and Crude-Oil Scheduling . . . . . . . .
7.6 Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . .

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.
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.
.

137
138
139
140
140
142
148
154

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.
.
.
.
.
.

156
156
159
160
161
163
164
165

8 Bibliography

168

Appendices

177

A On Tightness of Strengthened Constraints

179

B Crude-Oil Operations Scheduling Examples

181

C Mathematical Models for Crude-Oil Operations
C.1 MOS Model . . . . . . . . . . . . . . . . . . . . .
C.2 MOS-SST Model . . . . . . . . . . . . . . . . . .
C.3 MOS-FST Model . . . . . . . . . . . . . . . . . .
C.4 SOS Model . . . ..025, 0.035]
[0.045, 0.065]
[0.075, 0.085]
[0, 500]
Transfer flowrate
[50, 500]
Number of distillations

Crude Vessels

12 days
Amount of crude (Mbbl)
500
500
500
Initial amount of crude (Mbbl)
200
200
200
Initial amount of crude (Mbbl)
300
500
300
Gross margin ($/bbl)
1
6
8.5
2
5
8
3
Demand (Mbbl)
[500, 500]
[500, 500]
[500, 500]
[0, 500]
5

Storage Tanks Charging Tanks CDUs
4
1

5
6

2
3

8
9

7
10
11
12

14
15
16
17
18
19

13

Figure B.3: Refinery crude-oil scheduling system for COSP4.

Appendix B. Crude-Oil Operations Scheduling Examples

183


Table B.4: Data for COSP4.
Vessels
Vessel 1
Vessel 2
Vessel 3
Storage tanks
Tank 1
Tank 2
Tank 3
Tank 4
Tank 5
Tank 6
Charging tanks
Tank 1 (mix X)
Tank 2 (mix Y)
Tank 3 (mix Z)
Tank 4 (mix W)
Crudes
Crude A
Crude B
Crude C
Crude D
Crude E
Crude F
Crude G
Crude H
Crude mixtures
Crude mix X
Crude mix Y
Crude mix Z
Crude mix W
Unloading flowrate
Distillation flowrate

Scheduling horizon
Arrival time
Composition
0
100% A
5
100% B
10
100% C
Capacity (Mbbl)
Initial composition
[100, 900]
100% D
[100, 1,100]
100% A
[100, 1,100]
100% B
[100, 1,100]
100% C
[100, 900]
100% E
[100, 900]
100% E
Capacity (Mbbl)
Initial composition
[0, 800]
100% F
[0, 800]
100% G
[0, 800]
100% H
[0, 800]
100% E
Property 1
0.03
0.05
0.065
0.031
0.075
0.0317
0.0483
0.0633
Property 1
[0.03, 0.035]
[0.043, 0.05]
[0.06, 0.065]
[0.071, 0.08]
[0, 500]
Transfer flowrate
[20, 500]
Number of distillations

Appendix B. Crude-Oil Operations Scheduling Examples

15 days
Amount of crude (Mbbl)
600
600
600
Initial amount of crude (Mbbl)
600
100
500
400
300
600
Initial amount of crude (Mbbl)
50
300
300
300
Gross margin ($/bbl)
3
5
6.5
3.1
7.5
3.17
4.83
6.33
Demand (Mbbl)
[600, 600]
[600, 600]
[600, 600]
[600, 600]
[0, 500]
7

184


Appendix C
Mathematical Models for Crude-Oil
Operations Scheduling Problems
C.1

MOS Model

Gc · Vivc

max
i∈T r∈RD v∈Ir c∈C

s.t.

Variable bound and time constraints (3.1)
Cardinality constraints (3.2)
Precedence constraints (3.3)
Continuous distillation constraints (3.4)
Variable constraints (3.5)
Operation constraints (3.6)
Resource constraints (3.8)
Demand constraint (3.9)
Clique-based assignment constraint (3.10)
Clique-based non-overlapping constraint (3.11)
Ziv ≤

Z(i−1)v

i ∈ T, i = 1, v ∈ W

v ∈W
N Ovv =1

Ziv ≥ 1

i∈T

v∈W

Siv , Div , Eiv , Vivt , Vivc , Ltir , Lirc ≥ 0
Ziv ∈ {0, 1}

i ∈ T, v ∈ W, c ∈ C, r ∈ R
i ∈ T, v ∈ W

Appendix C. Mathematical Models for Crude-Oil Scheduling Problems

185


C.2 MOS-SST Model

C.2

MOS-SST Model

Gc · Vivc

max
i∈T r∈RD v∈Ir c∈C

s.t.

Variable bound and time constraints (3.1)
Cardinality constraints (3.2)
Precedence constraints (3.3)
Continuous distillation constraints (3.4)
Variable constraints (3.5)
Operation constraints (3.6)
Resource constraints (3.8)
Demand constraint (3.9)
Clique-based assignment constraint (3.10)
Clique-based non-overlapping constraint (3.11)
ti−1 ≤ ti

i ∈ T, i = 1

Siv ≤ ti

i ∈ T, W ∈ clique(GN O )

v∈W

Siv ≥ ti − H · (1 −
v∈W

Ziv )

i ∈ T, W ∈ clique(GN O )

v∈W

Ziv ≥ 1

i∈T

v∈W

Siv , Div , Eiv , Vivt , Vivc , Ltir , Lirc ≥ 0
Ziv ∈ {0, 1}

i ∈ T, v ∈ W, c ∈ C, r ∈ R
i ∈ T, v ∈ W

ti ∈ [0, H]

Appendix C. Mathematical Models for Crude-Oil Scheduling Problems

i∈T

186


C.3 MOS-FST Model

C.3

MOS-FST Model

Gc · Vivc

max
i∈T r∈RD v∈Ir c∈C

s.t.

Variable bound and time constraints (3.1)
Cardinality constraints (3.2)
Precedence constraints (3.3)
Continuous distillation constraints (3.4)
Variable constraints (3.5)
Operation constraints (3.6)
Resource constraints (3.8)
Demand constraint (3.9)
Clique-based assignment constraint (3.10)
Clique-based non-overlapping constraint (3.11)
Siv = ti · Ziv
Siv , Div , Eiv , Vivt , Vivc , Ltir , Lirc ≥ 0
Ziv ∈ {0, 1}
ti =

i ∈ T, v ∈ W
i ∈ T, v ∈ W, c ∈ C, r ∈ R
i ∈ T, v ∈ W

i−1
·H
n

Appendix C. Mathematical Models for Crude-Oil Scheduling Problems

i∈T

187


C.4 SOS Model

C.4

SOS Model

Gc · Vivc

max
i∈T r∈RD v∈Ir c∈C

s.t.

Variable bound and time constraints (3.1)
Cardinality constraints (3.2)
Precedence constraints (3.3)
Continuous distillation constraints (3.4)
Variable constraints (3.5)
Operation constraints (3.6)
Resource constraints (3.8)
Demand constraint (3.9)
Clique-based assignment constraint (3.10)
Clique-based non-overlapping constraints (4.1)
Biclique-based non-overlapping constraints (4.2)
Symmetry-breaking constraints (4.3)
Ziv ≥ 1

i∈T

v∈W

Siv , Div , Eiv , Vivt , Vivc , Ltir , Lirc ≥ 0
Ziv ∈ {0, 1}

i ∈ T, v ∈ W, c ∈ C, r ∈ R
i ∈ T, v ∈ W

Appendix C. Mathematical Models for Crude-Oil Scheduling Problems

188


Appendix D
Mathematical Model for the Refinery
Planning Problem
In this section, the ANN model developed in Gueddar and Dua (2010) for CDU simulations
is presented. It is based on a layered directed graph which represents the model calculations
(see Fig. D.1). Each node in the input/output layers correspond to one input/output
variable. Each node j = 1, . . . , Nn in the intermediate layer l = 1, . . . , Nl corresponds to an
activation variable alj and a transformed variable hlj . The activation variables are calculated
from the transformed variables of the previous layer using an affine expression while the
transformed variables are calculated by applying the hyperbolic tangent to their associated
activation variable. The ANN equations are expressed as follows.

Nx

a1j

1
wji
xi + b1j

=

j = 1, . . . , Nn

(D.1)

l = 1, . . . , Nh , j = 1, . . . , Nn

(D.2)

l = 2, . . . , Nh , j = 1, . . . , Nn

(D.3)

k = 1, . . . , No

(D.4)

i=1

hlj = tanh alj
Nn

alj

l l−1
wji
hi + blj

=
i=1
Nn

h
Wki hN
i + Bk

uk =
i=1

The model uses the following parameters:
• Nx is the number of inputs
• No is the number of outputs
• Nh is the number of intermediate layers
Appendix D. Mathematical Model for the Refinery Planning Problem

189


x1
x2

u1

x3

u2

x4

Output layer
Intermediate layers

Input layer
Figure D.1: Layered artificial neural network.
• Nn is the number of nodes in each intermediate layer
• wjil , blj , Wki , Bk are parameters specific to the ANN
Dua (2010) demonstrates how to tune the ANN parameters by minimizing the total prediction error as well as the ANN complexity. This tuning step is performed by solving
a training MINLP. We denote CDUANN(x, u) the set of constraints defining the relation
between the ANN inputs x and outputs u. In particular, the model inputs include crude
ip
and CDU cut points τ k (k ∈ {naphta, kerosene, diesel}), and the model outproperties qC

puts include cut yields αijk and crude cut properties q1ijkp . All crude property inputs are
fixed while CDU cut points are variable. The cut point between diesel and residue cuts can
take three discrete values defining the three CDU operating modes. All the outputs are
variable. The full refinery planning model is expressed as follows.

Appendix D. Mathematical Model for the Refinery Planning Problem

190


pl xlS

max

(sales revenue maximization)

l∈L

s.t.

i
xij
F ≤C

0≤

i∈I

(crude availability)

k∈K

(CDU cut point limits)

j∈J

τk ≤ τk ≤ τk
CDUANN

ip k
qC
, τ , αijk , q1ijkp

(CDU model)

xij
F ≤ FR · H

FR · H ≤

(CDU flowrate limitations)

i∈I j∈J
ijk
xijk
· xij
1 =α
F

xijk
1 =
i∈I

xjkl
2

(i, j, k) ∈ I × J × K

(CDU yield calculation)

(j, k) ∈ J × K

(pool mass balance)

l∈L
jkp
q1ijkp xijk
1 = q2

i∈I

xjkl
2

(pool quality balance)
(j, k, p) ∈ J × K × P
nonlinear

l∈L
l
xjkl
2 = xS

l∈L

(product mass balance)

l∈L

(maximum product demand)

j∈J k∈K

xlS ≤ Dl
lp l
q2jkp xjkl
2 ≤ Z xS

(product quality requirement)
(l, p) ∈ L × P

j∈J k∈K

nonlinear

ijk
jkl
l
ijk
xij
≥0
F , x1 , x2 , xS , α

q1ijkp , q2jkp , τ k ∈ R

Appendix D. Mathematical Model for the Refinery Planning Problem

191



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