Scheduling, Logistics, Planning, and Supply Chain ... · TK-44114 (q=2) Schedule of diluents in the...

José M. Pinto

Feb 07, 2008

Scheduling, Logistics, Planning, and Supply Chain Management for Oil

Refineries

OUTLINE

• Introduction • Scheduling models

– crude oil scheduling– fuel oil / asphalt scheduling

• Logistics– oil supply model– pipeline distribution

• Planning Models– refinery diesel production

• Supply Chain Management Models• Conclusions

MOTIVATION

Economical TargetsProfitability Maximization (Pelham and Pharris, 1996; Ramage, 1998)

Minimization of Operational Costs (Bodington and Shobrys, 1996)

Maximization of supply chain value (Chopra and Meindl, 2003)

Decision Support Tools

Maximization of integrated margins (Thijssen and Lasschuit, 2003)

ADVANCESAvailability of more powerful and less expensive computers;Mathematical Developments:

Time representation; (Moro and Pinto, 1998)

Combinatorics in MIP;(Raman and Grossmann, 1994)

Non-convexities in MINLP;(Viswanathan and Grossmann, 1990)

Consequences for the Petroleum and Chemical Industry: (Ramage, 1998)

Unit LevelOptimization

Plant-wideOptimization

1980’s 2000’s

Supply ChainOptimization

1990’s

ROADMAP OIL OPERATIONS

Planning of oil exploration(Carvalho)

Oil supply scheduling(Más)

Refinery planning(Moro)

Refinery SchedulingDistillation (Smania)

Fuel Oil / Asphalt area (Joly)LPG scheduling (Moro)

Utility systems (Micheletto)Paraffins (Casas-Liza)

Pipeline scheduling(Rejowski Jr.,Hassimotto)

Pipeline network planning (Assis)

Supply chain management (Neiro, Chen)

OUTLINE

• Introduction • Scheduling Models





SHORT TERM CRUDE OIL SCHEDULING Crude Oil System

OBJECTIVES

Maximize operating profitrevenue provided by oil processing cost of operating the tanks

Generate a schedule for crude oil operations receiving oil from pipelinewaiting for brine settlingfeeding the distillation units

TIME SLOT REPRESENTATION

MILP OPTIMIZATION MODEL

Max total operating profitsubject to:

Timing constraintsPipeline material balance equationsPipeline operating rules

Pipeline always connected to a tank

Material balance equations for the tanksVolumetric equationsComponent volumetric balance

Tank operating rulesMinimum settling time

Rules for feeding the distillation unit

DECISION VARIABLES

slot k

Ypj,kYdf,j,k

fraction f

REAL-WORLD EXAMPLE

Oil parcel Volume

(m3)

Start time

(h)

End Time

(h)

Composition

1 60,000 8 20 100% Bonito

2 50,000 48 58 100% Marlin

3 1,000 58 58.2 100% Marlin

4 60,000 100 112 100% RGN

Tank initial conditions

Distillation target flowrate = 1500 m3/h

RESULTS

MODEL SOLUTION

• GAMS / OSL

• CPU time2.80 hrs (Pentium II 266 MHz 128 MB RAM)

• Variable size time slot model912 discrete variables

3237 continuous variables

5599 equations

• Fixed size time slot model

21504 discrete variables !

OUTLINE






FUEL OIL/ASPHALT PRODUCTION SCHEDULING PROBLEM

•The plant produces ≅ 80% of Brazilian fuel oil;

•The plant has significant storage limitations;

•Complex distribution operations;

Product Base Diluent usedFO1FO2FO3FO4UVO1UVO2CAP07CAP20

OCC+LCO or OCC or LCOOCC+LCO or OCC or LCOOCC+LCO or OCC or LCOOCC+LCO or OCC or LCOpure LCOpure LCOpure HGpure HG

RASF RASF RASF RASF RASF RASF RASF RASF

major specification:viscosity

MATHEMATICAL MODELS

non-convex MINLP (viscosity constraints);

Uniform Discretization of Scheduling Horizon;

Objective Function: Minimize Operational Cost.

First Approach:

MILP;

Second Approach:

Linear Transformation

COST = Raw-Material Costs + Inventory Costs + + Pumping Costs + Transition Costs

MINLP MODELMinimize:

Material Balance Constraints

Subject to:

Plant Operating Rules

Demand Supply of Plant Products

at each t, the plant production must be stored in one single tank

simultaneous tank loading and unloading is not allowed (exception: HG storage tank)

UVO / Asphalt may be sent to truck terminals only between 6:00 a.m. and 6:00 p.m.

while asphalt is produced, the RASF diluent must be HG

while asphalt is produced, the OCC stream from UFCC must be directed to storage in TK-42208

Material Flow Constraintsflowrates to oil-pipelines must obey pump limitations flowrates to truck terminals must obey pump limitations

Viscosity Specification Constraints

REAL-WORLD EXAMPLE

instanceevaluated

Scheduling horizon: 3 days

Time span: 2 hours

Nominal production: 200,000 m3/month

PRODUCTION SCHEDULE AND STORAGE INFORMATION

0

1

TK-4

4113

TK-4

3307

TK-4

3301

TK-4

3301

TK-4

3307

TK-4

3301

TK-4

3302

TK-4

4108

TK-4

3302

TK-4

4108

TK-4

3301

TK-4

4108

TK-4

3301

TK-4

4108

TK-4

3302

TK-4

3307

TK-4

3301

TK-4

4113

TK-4

3301

TK-4

3301

TK-4

3307

TK-4

3307

TK-4

3301

TK-4

4108

TK-4

4108

TK-4

3307

TK-4

3301

TK-4

3301

TK-4

3301

TK-4

3303

TK-4

3302

TK-4

3307

TK-4

3301

TK-4

3301

TK-4

3301

TK-4

3301

START END

UVO1 UVO2 CAP07 CAP20 FO1 FO2 FO3 FO4

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Each

inte

rval

= 20

m3 /h

diluent from TK-42221 (HG) diluent from TK-42208 (OCC+LCO)pure OCC from UFCC pure LCO from UFCC

FO1 (p=1)

02468

10

1 4 7 10 13 16 19 22 25 28 31 34 37

TK-43301 (i=1)

TK-43302 (i=2)

FO2 (p=2)

02468

1012

1 36

TK-43303 (i=3)TK-43304 (i=4)

FO3 (p=3)

02468

10

1 36

TK-43305 (i=5)TK-43306 (i=6)

FO4 (p=4)TK-43307(i=7)

02468

10

1 36

CAP-20 (v=4)

0

2

4

1 36

TK-44110 (q=6)TK-44115 (q=7)TK-44116 (q=8)

CAP-07 (v=3)TK-44108 (q=5)

0

2

4

1 36

UVO2 (v=2)

0

2

4

1 36

TK-44111 (q=3)TK-44112 (q=4)

UVO1 (v=1)

0

2

4

1 36

TK-44113 (q=1)TK-44114 (q=2)

Schedule of diluents in the mixer

Volume (x 10-3 m3) in product storage tanks

4514

6890

15121512

4465

2629

MINLP model MILP model

number of 0-1 variablesnumber of constraintsnumber of continuous variables

68907985

1512 19684465

6733

WITHOUT TRANS.CONSTRAINTS

WITH TRANS.CONSTRAINTS

number of 0-1 variablesnumber of constraintsnumber of continuous variables

case MIP model nodes iterations CPU time (s) objectiveMILP 937 15674 570.46 969.61A MINLP - 13815 335.36 966.99MILP 1296 16626 711.01 965.72B MINLP - 15508 391.45 961.14MILP 764 13086 490.86 954.99C MINLP - 23792 531.98 956.99MILP 1197 23080 851.78 950.65D MINLP - 12845 299.30 959.49

OIL-PIPELINE TO SÃO PAULO(WITH TRANSITION MODELING)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

LOCAL OIL-PIPELINE(WITH TRANSITION MODELING)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

MILP models

OUTLINE






CRUDE OIL SUPPLY PROBLEM

crude oil terminals oil refineries

MOTIVATION

• Increasing utilization of the system– Larger demand for crude oil in refineries– Outsourcing of transportation

• Potential economic impact– No systematic scheduling– Operations involve high costs and aggregated values

• Petrobras distribution complex– 4 integrated refineries

PETROBRAS DISTRIBUTION COMPLEX

Types of crude oil

PROBLEM SPECIFICATION

iDetermined by the petroleum origin

iApproximately 42 types of crude oil may be processed

Types ofcrude oil

Classes of crude oil

iSets of crude oil types with similar properties

iNecessary due to limited amount of tanks

i7 classes


Types of crude oil


Tankers

iTransport types of crude oil

iOverstay incurs in additional costs- US$ 10 k to US$ 20 k per day


Types of crude oil


Tankers

Piers

iDifferent capacities


TanksPiersiStore classes of crude

oil

iMinimum storage levels

iSettling time between loading and unloading operations

Types of crude oil


Tankers


Tanks

Pipe-lines


Tankers

Piers

iFlow rate at each pipeline limited by the density of the heaviest crude oil class

iPossible to connect to at most one tank at every timeTypes of

crude oil


Tanks

Pipe-lines

Sub-stations

Types of crude oil


Tankers

Piers

iBuffer operations between terminal and refineries

iStore difference in flow rate between inlet and outlet pipelines


Pipelines

Substations

Refineries

Full scale model unsolvable

PROPOSED STRATEGY

Terminal

Decomposition of the problem in three

formulations

MATHEMATICAL FORMULATION

• MILP model formulation• Time representation

– Continuous– Based on events

time

Vi Vi+1 Vi+2 Vi+3

Qi Qi+1 Qi+2 Qi+3

Xi Xi+1 Xi+2 Xi+3

Inventory level (cont. variable)

Amount generated (cont. variable)

Decision to produce (disc. variable)

Ti Ti+1 Ti+2 Ti+3Time events (cont. variable)

PROPOSED MODEL - VARIABLES

• Binary variables – Decisions– Assignment of ship n to pier p: – Unloading of ship n to tank t: – Unloading of tank t to oil pipeline o:

• Continuous variables– Timing– Inventory– Flowrates– Operating profit

pnA ,

etnLT ,,

eotUT ,,

PORT MODEL - CONSTRAINTS

• Decisions

– Assignment of tanker n:

– Operation of tank t:

– Operation of tanker n:

– Operation of oil pipeline o:

1, =∑∈ nPp

pnA

1,,,, ≤+ ∑∑∈∈ tt Oo

eotNn

etn UTLT

1,, ≤∑∈ oTt

eotUT

1,, ≤∑∈ nTt

etnLT

PROPOSED MODEL - TIMING

• Ships, tanks and pipelines– Timing variables in each time event

• Initial• Final

• Matching of the timing variables– Unloading from ship n to tank t

– Unloading from tank t to pipeline o

fet

fen TTTN ,, =s

ets

en TTTN ,, =

seo

set TDTT ,, = f

eofet TDTT ,, =

PROPOSED MODEL – CONSTRAINTS

• Matching of timing variables– Ships ↔ Tanks

– Tanks ↔ Pipelines

)1.()1.( ,,,,,,, etns

ensetetn

sen LTHTNTTLTHTN −+≤≤−−

)1.()1.( ,,,,,,, etnfen

fetetn

fen LTHTNTTLTHTN −+≤≤−−

)1.()1.( ,,,,,,, eotset

seoeot

set UTHTTTDUTHTT −+≤≤−−

)1.()1.( ,,,,,,, eotfet

feoeot

fet UTHTTTDUTHTT −+≤≤−−

PROPOSED MODEL – OBJECTIVE FUNCTION

( )

( )

( )

cost) (interface .

tankers)oil theofcost (overstay .

cost)n utilizatio(pier .

tanks)in thecost (oil .

port) in the revenue oil initial - (final .

)refineries the torevenue (oil .max

1

1,,,,

,,

,

0,

1

1'',,,

∑ ∑ ∑ ∑

∑

∑ ∑

∑ ∑

∑ ∑

∑ ∑ ∑ ∑ ∑

∈≠′

∈′

−

=′′

∈

∈

∈

∈ ∈ ∩∈

−

=

−

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

o CLOclcllc

CLOlc

E

eeolccl

facelccl

sen

n

sen

p Nn

startpn

endpn

pierp

c Nncn

crudec

cl Ttt

TEt

classcl

r CLRcl Oo TTt

E

eeot

classrcl

o o

p

c

cl

r r ocl

INTCOST

TCOST

COST

CCOST

VVREVP

QutREVR profit

ττ

REAL-WORLD PROBLEMREPLAN

RECAP

SEBATRPBC

GEBAST

SEGUA

REVAP

OSBAT III

OSBAT II

OSVAT I

OSVAT II

OSvAT III

OSVAT IV

OSBAT IV

P4

P2

P3

P1

São Sebastião

São José dosCampos

Paulínia

Guararema

Capuava

Cubatão

• Problem 1– Port Model

• Problem 2– Substation

Model

Problem 3– Substation

Model

• Problem 4– Substation

Model

COMPUTATIONAL RESULTS

• Smaller optimality gaps for the Port Model

• Large variation on computational times

Problem 1 Problem 2 Problem 3 Problem 4

Number of continuous variables 1996 4954 712 703Number of binary variables 1039 759 66 123Number of constraints 7203 10337 1158 1682Relaxed LP solution 21,768.32 23.00 11.00 11.39Best Integer Objective 20,073.96 42.00 21.00 15.00Optimality gap 7.78% 82.61% 90.91% 31.74%Nodes 1118 3784 3921 422Iterations 62313 74410 19321 5244CPU time (Pentium III 450MHz) 1,457.51 s 602.07 s 134.69 s 28.28 s

Port Model Substation Models

PROBLEM 1 – TANKERS AND TANKSPEDREIRAS

08

27

01020304050

30 35 40 45TBN01

B

0

20

40

60

60 62 64 66 68 70

FRONT BREA

05

0

30

60

90

120

10 15 20 25 30

REBOUÇAS

38

0

10

20

30

40

40 45 50

MURIAÉ

01a

01b

0

20

40

60

80

45 55 65 75 85

120

TBN02

C

0

5

10

15

20

85 86 87 88 89 90

RAVEN

D

0

20

40

60

90 95 100 105

TBN03

B

0

10

20

30

139 141 143 145

VERGINA II

38

0

30

60

90

85 90 95 100

NORTH STAR

26

0

50

100

150

95 100 105 110 115TBN04

E

0

20

40

60

154 161 168

PRESIDENTE

29a29b

0

20

40

60

80

90 100 110 120

CANTAGALO

A

0

5

10

15

20

0 1 2 3 4 5

TQ3210

Vmin

Vmax

07

14212835

0 24 48 72 96 120 144 168

TQ3208

Vmin

Vmax

07

14212835

0 24 48 72 96 120 144 168

TQ3214

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3219

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3237

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3241

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3215

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3233

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3238

Vmin

Vmax

07

14212835

0 24 48 72 96 120 144 168

TQ3242

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

TQ3217

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3234

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3239

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

TQ3243

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3218

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3235

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3240

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

TQ3244

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

17.4

58.2

58.2

17.4

35

16.9

38.0 (P4)

27.8

3.7 (P4)

11.9 (P4)

0.6 (P4)

25.4 4.7 (P4)

15 (P4)

5.3 (P3)

24.7 (P3)

37.8 (P2)

19.6

CANTAGALO

PRESIDENTE

FRONT_BREA NORTH_STAR

48.8

2.2

28.06.1 (P4)

28.0

25.4

53.3

24 Hrs

12.2 (P2)

42.4 (P2)

63.6 (P2)

26.0 (P2)

2.2

19.6

29.4 (P4)

1.4 (P2)

51.1 (P3)

30L (P-4)

2.8

19.6

55.5 (P4)

60.4

PEDREIRAS

MURIAE

6.2 (P2)

24.3 Hrs

26.0 Hrs 66.0 (P2)

50.3Hrs

27.8

34.4

24 Hrs

60.0 (P4)

11.5 (P4)

42.4

63.6

61.8

2.8

28.9 (P3)

24 Hrs

43.2 Hrs

REBOUCAS

VERGINA II

67.7

55.7 (P1)

62.4 (P2)

48.8

34.8

11.0

58.7

11.5

24 Hrs 60.0 (P4)

42.4

19.6

TBN01

16.9 (P1)

62.4

24 Hrs

63.6

11.5

28.0

2.8

4.5 (P4)

24 Hrs

62.4 (P1)

60.0

58.7

2.2

TBN02

16.9

46.4 Hrs

67.7

60.4

27.8

33.9

14.1

62.4

RAVEN

48.8

16.9

41

TBN03

60

19.6

61.8

65

TBN04

62.4

70.2

65.1 2.6

26.5

62.4 16.9 60 59.1

0 24 48 72 96 120 144 168

P-1

P-2

P-3

P-4

TQ3208

TQ3210

TQ3214

TQ3215

TQ3217

TQ3218

TQ3219

TQ3233

TQ3234

TQ3235

TQ3237

TQ3238

TQ3239

TQ3240

TQ3241

TQ3242

TQ3243

TQ3244

OSVAT

OSBAT

SEGUA/E

OSBATII/S

Tempo (horas)

PROBLEM 1 – GANTT CHART

OUTLINE






SCHEDULING OF A MULTIPRODUCT PIPELINE SYSTEM

• Pipelines transport large amounts of products in the fastest and safest mode.

• Development of a systematic approach for such operation.• amounts of products sent to all depots and operational

sequencing at the refinery, pipeline and at depots;

• inventory levels for each product at all locations.

• Oil company that operates with a refinery and depots in several locations.

DISTRIBUTION SYSTEM

1

p

P-1

P

REPLAN

.

.

.

.

.

.

1 p P-1 P

… ...Rib. Preto

Consumer Market

1 p P-1 P

… ...

Uberaba

Consumer Market

1 p P-1 P

… ...

Uberlândia

Consumer Market

1 p P-1 P

… ...Goiânia Consumer Market

1 p P-1 P

… ...Brasília Consumer Market

Petrobras OSBRA complex

PROBLEM DESCRIPTION

Distribution problem

• a refinery must distribute P products through a single pipeline;

• Set of D depots which are connected to consumer markets.

Subject to the following constraints

• upper and lower bounds for inventory levels for each product at all locations;

• flow rate bounds for the entire system;• arrival times for products sent by the refinery to their destination; • demands for all products established by each local consumer market

PIPELINE MODELING

Interface between two different products

Segment d

VOTp,d,k

Pack L-1 Pack L

VODp,d,k

VOTp,d+1,kPack 1 Pack 2

Feed (VOTp,d,k)

• Displacement of products;• Product contained in L;

• Sent to depot d (VODp,d,k);

No Feed VOTp,d,k=0

• Products remain in the same pack;

• Sent to segment d+1 (VOTp,d+1,k)

V p,d,l,k

Pack l

SYSTEM WITH D SEGMENTS

kdpkdpdpkdp VOMVODVDZEROVD ,,,,,,, −+= ∀p ,d, k=1

kdpkdpkdpkdp VOMVODVDVD ,,,,1,,,, −+= − ∀p, d, k=2,…,K

Constraints at Depots

kdpkdpkdp VDMAXVDVDMIN ,,,,,, ≤≤ ∀p, d, k

Refinaria

Consumer Market 1 Consumer Market d Consumer Market D

Depot 1 Depot d Depot D

Segmento 1 Segmento d... Segmento D...

Refinery

Segment 1 Segment d... Segment D...

∑∑∑∑∑∑∑

∑∑ ∑∑∑

= = = == = =

= = = = =

×+×+

×⎥⎥⎦

⎤

⎢⎢⎣

⎡×+×=

P

p

P

p

D

d

K

k

kdppppP

p

D

d

K

k

kdpkdp

P

p

K

k

P

p

D

d

K

k

kdpkdpkpkp

TYCONTACTVODCP

VDCEDVRCERC

1 1' 1 1

,,',',

1 1 1

,,,,

1 1 1 1 1

,,,,,, δ

Inventory Costs - RefineryInventory Costs - Depots

Pumping Costs Interface Costs

REAL-WORLD DISTRIBUTION SYSTEM

1

p

P-1

P

REPLAN

.

.

.

.

.

.

1 p P-1 P

… ...Rib. Preto

Consumer Market

1 p P-1 P

… ...

Uberaba

Consumer Market

1 p P-1 P

… ...

Uberlândia

Consumer Market

1 p P-1 P

… ...Goiânia Consumer Market

1 p P-1 P

… ...Brasília Consumer Market


OSBRA Example

Relaxed Solution [$ x 10-2 ] 27,277.89Solution [$ x 10-2 ] 30,245.97

CPU Time [s ] 1,775Nodes Visited 5,007

Continuous Variables 6,316Binary Variables 420

Equations 9,393

PIPELINE

k=0

k=1

k=2

k=3

k=4

k=5

k=6

k=7

k=8

k=9

k=10

k=11

k=12

k=13

k=14

k=15

0 400Segment REPLAN-Rib.Preto [x 10-2m3] 0 250Segment Rib.Preto-Uberaba [x 10-2 m3] 0 250Segment Uberaba-Uberlândia [x 10-2m3]

600k=0

k=1

k=2

k=3

k=4

k=5

k=6

k=7

k=8

k=9

k=10

k=11

k=12

k=13

k=14

k=15

0Segment Uberlândia-Goiânia [x 10-2 m3] 0 135Segment Goiânia-DF [x 10-2m3]

GASOLINE

JET FUEL.

LPG

DIESEL

STORAGE LEVELS

Diesel Oil

0

100

200

300

400

500

0 10 20 30 40 50 60 70

Time [h]

Inve

ntor

y Le

vel [

m3 ]

0

500

1000

1500

2000

LPG

0

50

100

150

200

0 10 20 30 40 50 60 70

Time [h]

Inve

ntor

y Le

vel [

m3 ] Aviation Fuel

50

100

150

200

250

0 10 20 30 40 50 60 70

Time [h]

Inve

ntor

y Le

vel [

m3 ]

0

200

400

600

800

Gasoline

0

50

100

150

0 10 20 30 40 50 60 70

Time [h]

Inve

ntor

y Le

vel [

m3 ]

500

1000

1500

Rib. PretoUberabaUberlândiaGoiâniaBrasíliaREF

OUTLINE






• To develop a general representation for refinery units

– streams with multiple inputs and destinations

– nonlinear mixing and process equations

– bounds on unit variables

• To apply to the production planning of a real world refinery

– diesel production

– to satisfy multiple specifications

– extension to supply chain systems

PLANNING MODEL FOR REFINERIES

TYPICAL PROCESS UNIT

UNIT EQUATIONS

- Feed flowrate:

- Feed Properties:

Pu,F,j = fj ( Qu’,s,u , Pu’,s,j ) u’ Uu, s Su’,u, j Js

- Total flowrate of each product stream:

Qu,s = f ( Qu,F , Pu,F,j , Vu ) j JF, s SU

- Unit product stream properties:

Pu,s,j = fj ( Pu,F,j , Vu ) j Js, s SU

- Product streams flowrates (splitter):

s SU

Qu F Qu s us Su uu Uu

, ' , ,,

=∈ ′′∈∑∑

Q Qu s u s u, , ,= ′u Us,u′∈∑

∈∈

∈

∈∈

∈∈∈

REAL-WORLD APPLICATION

Planning of diesel productionPetrobras RPBC refinery in Cubatão (SP, Brazil).

Three types of diesel oil:

Metropolitan Diesel. Low sulfur levelsMetropolitan areas

Regular Diesel. Higher sulfur levels

Maritime Diesel. High flashing point.

DIESEL SPECIFICATIONS

PropertyREGULAR

DIESELMETROPOLITAN MARITIME

DENSITYmin / max

0.82/0.88

0.82/0.88

0.82/0.88

FLASH POINTmin (°C)

- - 60.0

ASTM 50%min / max (°C)

245.0/310.0

245.0/310.0

245.0/310.0

ASTM 85%max (°C)

370.0 360.0 370.0

CETANE NUMBER min 40.0 42.0 40.0SULFUR CONTENT max

(% WEIGHT)0.5 0.2 1.0

MAIN RESULTS

Potential Improvement US$ 23,000 / day or US$ 8,000,000 / yrImplemented with on-line data acquisition

OUTLINE






GENERAL PETROLEUM SUPPLY CHAIN

Development of an optimization model

that is able to represent

a petroleum supply chain to support the

decision making planning process of

supply, production and distribution

OBJECTIVE

REFINERY - PROCESSING UNIT MODEL

SUPPLY, DISTRIBUTION – STORAGE MODEL

SUPPLY CHAIN MODEL

subject to:

• processing units

• tank

• pipeline

units that compose refinery topologyrefineries that compose the supply chain

•⎧⎨•⎩

petroleum and product tanks that compose refineries petroleum and product tanks that compose terminals refineries and terminals that compose the supply chain

•⎧⎪•⎨⎪•⎩

pipeline network for petroleum supply pipeline network for product distribution•⎧⎨•⎩

Max Profit = Revenues – Crude Oil Costs – Operating Costs –Inventory Costs – Transition Costs

Large Scale MINLP

INTEGRATED SUPPLY CHAIN

GENERAL CONSTRAINTS:Planning horizon: one / two time periods

Supply of 20 oil types

Generation of 32 products (6 transported with pipelines)

SCENARIOS:

1: Base Case model2: Pre-selection of some crude oil supplies3: Interruption of pipeline segment SG-RV

SUPPLY CHAIN EXAMPLE

SUPPLY CHAIN EXAMPLE – REVAP10905114047551

169451648911400

176419331001

600600660

SUPPLY CHAIN EXAMPLE – RPBC

138914081389

9824100759924544951775449

SUPPLY CHAIN EXAMPLE – OIL SUPPLY

542005420054200

360003600025992

902009020080192

850085008500 35500

3550035500

SUPPLY CHAIN EXAMPLE –PRODUCT TRANSFER

1764218311

362

33452889

10800

2454025208

0

4400440011660

177001770017700

640364036403

65456089

11000200182001920018

Case Case 1 Case 2 Case 3

Number of time periods 1 2 1 2 1 2

Constraints 2304 4607 2306 4611 2304 4607

Variables 2544 5087 2544 5087 2544 5087

Discrete variables 195 390 195 390 195 390

Solution time (CPU s) 116.8 656.2 152 915.6 157.8 2301

Objective Value ($ x106) 20.4 41.3 20.3 41.1 18.0 36.3


DECOMPOSITION STRATEGIESStrategy Primal subproblem Dual subproblems Multipliers update

1 Fixed assigment Lagrangean Subgradient

2 Fixed inventory Lagrangean Subgradient

3 Fixed inventory Surrogate Subgradient

4 Fixed inventory Lagrangean Modified Subgradient

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60Number of time periods.

CPU

seco

nds

Problem RMP Strategy 1

Strategy 2 Strategy3

Strategy4

OUTLINE






CONCLUSIONS

The LP based Branch and Bound Method• is satisfactory to generate “good” feasible solutions• no guarantee of global optimum solutions for all instances

Modeling Issues• time representation• blending/pooling • transitions

Problems can be modeled as large scale MILPs / non-convex MINLP• flexibility in representing general topologies• complex logical decisions and operating rules can be modeled• representation of realistic financial objectives

The OA/ER/AP Method • is efficient to circumvent the non-convexity problem• is satisfactory to generate feasible solutions• has computational performance similar to MILP model

CHALLENGES

The understanding of the problem itself can constitute the major difficulty

Main theoretical difficulties

The cooperation between the modeler and the practitioner is essential and remains as a major challenge

Continuous update necessary due to the dynamic nature of problems.

Complex problems with high combinatorial features;

NP-Complete Problems

Main practical difficulties

Exponential computational times

Multiple systems and interfaces

ModelingHorizontal Integration (e.g. Upstream-Downstream-Final customer) Vertical Integration (e.g. planning and scheduling operations)Multi country supply chains (royalties, tariffs)Modeling of uncertaintiesInventory design and management

Demand planning models (including forecasting)

Efficient solution methodsDecomposition (spatial, temporal, functional)Techniques (Lagrangean Relaxation, Cross Decomposition, Metaheuristics, Hybrid Methods)

RESEARCH NEEDS

RESEARCHERSM. Joly R. MásL. MoroR. RejowskiP. Smania Fo.

S. NeiroM. C. A. CarvalhoM. K. Hassimotto

FINANCIAL SUPPORT

ENGINEERSC.A. GrattiM. F. LehnerM.V. MagalhãesA.C. ZaninE. Almeida Neto

CENPES

ACKNOWLEDGMENTS

Scheduling, Logistics, Planning, and Supply Chain ... · TK-44114 (q=2) Schedule of diluents in the...

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