Oil Supply Chain Planning under Uncertainty and Risk Evaluation

Oil Supply Chain Planning under Uncertainty and Risk Evaluation

Marcelo Maia F. de Oliveira

October 15th, 2014

1. Introduction and Problem Definition

Wide variety of comercial, industrial and logistics operations occur over the midstream segment

Strong dependence among the operations and some gains can only

be estimated by considering the whole supply chain

Planning this segment is crucial to achieve the success of all

operations.

2. Oil Supply Chain in Brazil

3

4

56

1

2

Curde Oil:- Imports (1)- Exports (3)- Production (5)

Oil Products:- Imports (2)- Exports (4)- Market Selling (6)

~ 200 different crude oils

~ 50 different oil products

10 basins of oil production

43 terminals (marine and inside the country)

12 refineries

3. Refinery OperationsThere are two main operations executed in the refineries:

Process Units BlendingUnits types:

Physical Separation – Disttilation (first step of oil

processing)

Conversion – Cracking and Delayed Coker (residual oil and heavy fractions to gasoline and

diesel)

Treating – HDT Naf and HDT Diesel (remove impurities – sulfur

– and specify other qualities)

Blendin types:

1 – Oil blending aiming to generated intermediates with desired yields and qualities;

2– Intermediate blending to specify charge of process unities;

3 – Intermediate blending to produce final products with

specified qualities.

The two-stage stochastic problem (Higle, 2005) can be described as

presented by the equations:

e x ≥ 0

e y ≥ 0

𝑀𝑖𝑛 𝑐∗𝑥+ 𝐸[(ℎሺ𝑥,𝜔ෝ��ሻ]

s.a. 𝐴∗𝑥≥ 𝑏

Onde ℎሺ𝑥,𝜔ሻ= 𝑀𝑖𝑛 𝑔𝜔 ∗𝑦

s.a. 𝑊𝜔 ∗𝑦≥ 𝑟𝜔 − 𝑇𝜔 ∗𝑥

x is the first stage

variable.

Its value must be

determined before

the uncertainty ω

is unfold.

y is the second

stage variable.

Its value is

decided after the

uncertainty ω is

fully known.

4. Bibliographic Review: Stochastic Programming

Solution well posicioned in respect

with the possible realizations of uncertainty ω.

Second stage decisions in a

posicion to explore advantageable

values of uncertainty ω.

Where

&

4. Bibliographic Review: Scenario Generation Methods

Moment Matching – Statiscal Method proposed by

Hoyland e Wallace (2001) which applies a non-linear model

to generate a limited number of dicrete scenarios that

satisfy specific statistic properties.

Time Agregation – sampling method that uses Markov

Chain concepts (Ergodic Chains, Return Time and Mean

Path Lenght) and the Time Agregation method of Cao et al.,

2002.

The CVaR of a probability distribution with confidence level α:

Mean value of those scenarios which have the profits lower

than VaR and whose cumulative probability sums up to 1- α (Pineda e

Conejo, 2009)

4. Bibliographic Review: Cvar - Risk Measure

-15%

-10%

0% 5% 10%

15%

25%

35%

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-2% 0% 1% 2% 4% 6%

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-2% 0% 2% 4% 6% 8%

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10%

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30%

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90%

100%

Oil Production Brent Quotation Oil Products National Market

5. Uncertainties of Oil Supply Chain in Brazil

Uncertainty taken as the

prediction error

The value of each uncertain parameter is based on the

same 54 months period

3 parameters combined + de 150

thounsand possible

realizations

First Stage Second Stage

Month 1 Month 2

Oil import and export

Decisions: Oil allocation, Spot market oil import and export, unit utilization, oil products import and export.

6. Mathematical Model and Problem Approach


First Stage Constraints:

1. Global Oil Balance (import+ production = export + allocated);

2. Oil Import and Export Limits;

Second Stage Constraints – scenario dependent:

3. Global Oil Balance

6. Mathematical Model and Problem Approach – Recourse actions

Predicted Production – Actual Production

Production Surplus

Spot Market Export

Allocation in refineries

Production Deficit

Export Cancellation

Allocation Cancellation

Besides these options, it’s also possible to import oil in the Spot Market.

Second Stage Global Oil Balance:

𝐴𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛ሺ𝑟,𝑠ሻ𝑟 = 𝐴𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛− 𝐴𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝐶𝑎𝑛𝑐ሺ𝑠ሻ− 𝐸𝑥𝑝𝑜𝑟𝑡𝑆𝑝𝑜𝑡ሺ𝑠ሻ+ 𝐼𝑚𝑝𝑜𝑟𝑡𝑆𝑝𝑜𝑡ሺ𝑠ሻ+ 𝐸𝑥𝑝𝑜𝑟𝑡𝐶𝑎𝑛𝑐(𝑠)


First Stage Constraints:

1. Global Oil Balance (import+ production = export + allocated);

2. Oil Import and Export Limits;

Second Stage Constraints – scenario dependent:

3. Global Oil Balance

4. Oil Product Balance (import+ production = export + processed);

5. Oil and Product Balance on Terminals;

6. Products Market Selling;

7. Flow of oil and product limited to the deciosions of importation,

exportation, production and selling.


Second Stage Constraints – scenario dependent - Refinery

Operations:

1. Intermediates balance (produced by process unit= product blending +

charge blending);

2. Charge Balance (charge blending = consumed by process units);

3. Oil Products Quality Specification;

4. Charge Quality Specification;

5. Process Unit Capacity Limits;

6. Storage Limits;

7. Oil Product Balance (produced by blending + initial storage + received =

delivered + final storage).

Intermediate qualities

indexed to avoid non-linearity


Objective Function:

max𝑧= 𝑃𝑒𝑡𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒𝑃𝑟𝑜𝑓𝑖𝑡+ ሼሺ𝑂𝑖𝑙𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒𝐴𝑑𝑗𝑢𝑠𝑡ሺ𝑠ሻ+ 𝑂𝑖𝑙𝑆𝑝𝑜𝑡𝑃𝑟𝑜𝑓𝑖𝑡ሺ𝑠ሻ𝑠+ 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒𝑃𝑟𝑜𝑓𝑖𝑡ሺ𝑠ሻ− 𝑅𝑒𝑓𝑖𝑛𝑖𝑛𝑔𝐶𝑜𝑠𝑡ሺ𝑠ሻ− 𝐿𝑜𝑔𝑖𝑠𝑡𝑖𝑐𝐶𝑜𝑠𝑡(𝑠)ሻ∗𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜𝑃𝑟𝑜𝑏(𝑠)ሽ

7. Model Parameters: Products

Crude Oil Type Origin

A1 Condensate Imported

A2 Condensate National

B1 Extra-Light Imported

B2 Extra-Light National

C1 Light Imported

C2 Light National

D1 Crackable

Residue

Imported

D2 Crackable

Residue

National

E1 Medium Imported

E2 Medium National

F1 Heavy National

G1 Extra-Heavy Imported

G2 Extra-Heavy Imported

Derivados

GLP

Naphta

Gasoline

Kerosene

Diesel 10

Diesel 500

Fuel Oil

Coke

Crude Oil List Oil Product List

12

refineries

in the

country

Shared oil supply systems,

distribution of oil products

and market influence area

4 refineries (each

one with a

different

complexity)

7. Model Parameters: Refineries

Nodes: International Market (IM), National Production (PN), Terminal (Tn) and Refineries (4 Rn)

7 arcs: 1 for Import, 1 for Export, 1 for National Production e 4 for Oil Supply to Refineries

R1

R2

R4

R3

T1

IM

PN

MN

7. Model Parameters: Oil Logistics Operations

Nodes: International Market (IM), Terminal (Tn), Refineries (4 Rn) e National Market (MI)

14 arcs: 1 for Import, 1 for Export, 16 for flows between refineries and terminal e 4 for market delivery

R1

R2

R4

R3

T1

IM

PN

MN

7. Model Parameters: Oil Products Logistics Operations

Desti-lação

FCC

Coque

GLPNafta

Gasolina

Diesel 10

Querosene

Diesel 500

OC

Coque

GLP DD

GLP Coque

GLP FCC

NL DD

QUE DD

GO DD

RV DD

COQUE

Nafta Leve K

Nafta Pesada K

GOL K

GOP K

ODEC FCC

LCO FCC

Nafta Craq FCC

NL HDT

HDT NAF

NP DD

HDT Diesel

DL DD

DP DD

NP HDT

Petróleo

7. Model Parameters: Refineries

7. How does the uncertainty affect the scenario profit?

75%

85%

95%

105%

115%

125%

135%

19000000

19500000

20000000

20500000

21000000

21500000

22000000

22500000

Produção Cotação Demanda

Scen

ari

o P

rofi

t (t

ho

usan

d u

,m.)

Production Quotation Demand

Linear influence of Oil Production – the higher the

production, more oil is exported.

Smoother influence of Quotation, as both import costs and export revenue

varie.

The higher the demand, the bigger the supply cost, as internal prices are lower

than international ones.

8. Results – Scenario Generation Methods

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.060%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Cum

ulati

ve P

roba

bilit

y(%

)

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.080%

10%20%30%40%50%60%70%80%90%

100%

Cum

ulati

ve P

roba

bilit

y (%

)

Moment Matching Method

Cumulative Probability Curve for oil production uncertainty

Time Agregation Method

Moment Matching Method high concentration of Probability in

narrow range of the possible values.

Time Agregation Method uniformity and curves overlapped.

8. Results – Scenario Generation Parameter Selection

5 10 20 30 50 100 2 1 0.5 0.2Momento Markov

20400

20500

20600

20700

20800

20900

21000

21100

21200

21300

Obje

cti

ve F

uncti

on (

mil

u.m

)

1- Gain on objective function stability as the scenario tree grows, mainly for the Moment Matching Method.

8. Results – Objective Function and Scenario Profit (thousand u.m.)

00.10.20.30.40.50.60.70.80.9

1

Scenario Profit (mil u.m.)

Cum

uati

uve P

robabbil

ity

(%)

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0.91


Cum

ula

tive P

robabil

ity

(%)

Replication Moment Matching Time Agregation1 21.160 21.0452 21.168 20.9673 21.135 21.103 4 21.168 21.1085 21.162 21.112

Mean 21.159 21.067 Stand. Deviation 14 62

Moment Matching Time Agregation

Replication Revenue (K u.m.)

Products Sale Oil Export Product

Export1 35.751 70.3% 22.4% 7.3%2 35.621 69.9% 22.7% 7.4%3 35.467 70.5% 22.2% 7.3%4 35.650 70.2% 22.7% 7.1%5 35.615 69.9% 22.7% 7.4%


1- Similartity of each cost and revenue quotas

2- Time Agregation Method: higher product exchange – higher cost and revenue

8. Results – Revenue and cost

Replication Revenue (K u.m.)

Products Sale Oil Export Product

Export

1 36.573 69.6% 22.2% 8.2%2 36.267 69.3% 22.5% 8.2%3 36.573 69.4% 22.3% 8.3%4 36.473 70.1% 22.0% 8.0%5 36.221 69.5% 22.3% 8.3%

Replication Total Cost (K u.m.) Oil Import Product

ImportRefining

CostLogistic

Cost

1 14.614 60.4% 29.2% 6.1% 4.3%2 14.451 60.7% 28.7% 6.2% 4.4%3 14.369 60.0% 29.4% 6.2% 4.4%4 14.671 60.8% 28.7% 6.1% 4.3%5 14.442 60.9% 28.6% 6.2% 4.3%

Replication Total Cost (K u.m.) Oil Import Product

ImportRefining

CostLogistic

Cost

1 15.635 56.7% 33.4% 5.7% 4.1%2 15.417 58.0% 32.1% 5.8% 4.1%3 15.531 57.2% 32.9% 5.8% 4.1%4 15.458 56.9% 33.2% 5.8% 4.1%5 15.235 57.9% 32.1% 5.9% 4.1%

8. Results – First Stage Variables

Period Oil 1 2 3 4 5Month 1 A1 15.090 15.090 15.090 15.090 15.090 B1 892 892 714 1.700 893 E1 39.698 39.698 39.698 39.698 39.698 G1 3.038 2.940 1.768 2.749 3.076Month 2 B1 3.183 3.266 3.299 3.955 3.200 E1 15.989 12.875 13.352 13.360 13.084 G1 4.542 6.950 6.069 6.060 6.834

Period Oil 1 2 3 4 5Month 1 D2 17.890 17.793 17.303 17.972 17.844 E2 34.821 35.528 34.550 35.833 35.629Month 2 D2 17.439 17.793 17.303 17.946 17.946


1- High resemblance in first stage indications:

2- Oil A1 Import (low price and good yield) until the limit;

3- Oil D2 e E2 Export until the limit respecting the second stage uncertainties.

Import (thousand m³)

Export (thousand m³)

Period Oil 1 2 3 4 5Month 1 A1 15.090 15.090 15.090 15.090 15.090 B1 656 620 890 656 626 E1 39.698 39.698 39.698 39.698 39.698 G1 1.660 1.696 1.665 1.660 1.690Month 2 B1 3.109 3.109 3.109 3.109 3.109 E1 14.209 13.759 15.055 16.097 14.628 G1 5.130 5.580 4.284 3.242 4.710

Period Oil 1 2 3 4 5Month 1 D2 17.539 17.539 17.539 17.539 17.539 E2 34.291 34.291 34.530 34.291 34.291Month 2 D2 17.174 17.174 17.174 17.174 17.174

Import (thousand m³)

Export (thousand m³)

8. Results – Second Stage Recourse Actions

Moment Matching

1- Strong indication of allocation adjustment as oil production deficit happens.

2- The oil export decision is generally kept on the second stage.

Agregação temporal

Month A2 B2 C2 D2 E2 F1 G21 Deficit (K m³) 6 29 50 251 500 203 603

% Scenario 97% 97% 97% 97% 97% 97% 97%% Allocation Canc.

100%

100%

100%

94% 95%100%

100%

2 Deficit (K m³) 6 29 50 251 500 203 603% Scenarios 97% 97% 97% 97% 97% 97% 97%% Allocation Canc.

100%

100%

100%

95%100%

100%

100%

Month A2 B2 C2 D2 E2 F1 G2

1 Deficit (K m³) 18 81 139 699139

6566

1683

% Scenario 60% 60% 60% 60% 60% 60% 60%% Allocation Canc.

100%

100%

100%

83% 96%100%

100%

2 Deficit (K m³) 18 81 139 699139

6566

1683

% Scenarios 60% 60% 60% 60% 60% 60% 60%% Allocation Canc.

100%

100%

100%

97%100%

100%

100%

8. Results – Disttilation utilization

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5Month1 Month2 Month1 Month2 Month1 Month2 Month1 Month2

R1 R2 R3 R4

80%

82%

84%

86%

88%

90%

92%

94%

96%

98%

100%

102%

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5Month1 Month2 Month1 Month2 Month1 Month2 Month1 Month2

R1 R2 R3 R4

80%

82%

84%

86%

88%

90%

92%

94%

96%

98%

100%

102%Moment Matching Time Agregation

1 – Maximum utilization of disttilation on R3 and R4 - robust indication;

2 – Maximum utilization of distillation on R2 doesn’t seem to be interesting on the second month;

3 – Lower utilization on R1 for solutions using Time Agregation Method.

8. Results – Product QualitiesGasoline Diesel 10 Diesel 500 Fuel Oil

Method Month Refinery Octane Sulfur Sulfur Sulfur Sulfur Viscosity

Moment Month1 R1 100% 0% 100% 0% 100% 100%

Matching R2 100% 0% 100% 0% 100% 81%

R3 100% 0% 100% 0% 100% 100%

R4 100% 0% 100% 0% 100% 100%

Month2 R1 100% 0% 100% 0% 0% 100%

R2 100% 0% 100% 0% 100% 100%

R3 100% 0% 100% 0% 18% 100%

R4 100% 0% 100% 0% 0% 100%

Time Month1 R1 100% 0% 100% 0% 100% 100%

Agregation R2 100% 0% 100% 0% 100% 57%

R3 100% 0% 100% 0% 100% 100%

R4 100% 0% 100% 0% 100% 100%

Month2 R1 100% 0% 100% 0% 8% 100%

R2 100% 0% 100% 0% 99% 100%

R3 100% 0% 100% 0% 19% 100%

R4 100% 0% 100% 0% 6% 100%

8. Results – Risk Measure Impact(CVaR)


α=90% α=95% α=99% α=90% α=95% α=99% α=90% α=95% α=99%β=10% β=50% β=90%

18000000

18500000

19000000

19500000

20000000

20500000

21000000

21500000

Replication1 Replication2 Replication3 Replication4

Replication5

Obj

ectiv

e Fu

nctio

n (m

il u.

m.)

α=90% α=95% α=99% α=90% α=95% α=99% α=90% α=95% α=99%β=10% β=50% β=90%

18000000

18500000

19000000

19500000

20000000

20500000

21000000

21500000

Replication1 Replication2 Replication3 Replication4

Replication5

Obj

ectiv

e Fu

nctio

n (m

il u.

m.)

1- Clear difference of the risk measure on the Objective Function for each generation method;

2- Scenario trees built by the moment matching method are less susceptible to risk and the Objetive Function varies only when changing the risk aversion (β).

8. Results – Risk Measure Impact on Scenario Profit

Moment MatchingReplication 2

Time AgregationReplication 2

1- ↑ Risk Aversion (β) e ↑ Confidence Level (α) : to avoid low values of profits, the curve moves to the left, so higher profits are also avoided.

2- Confidence Level (α) effect on the solutions obtained by Time Agregation Method: desirable for decision taking in an uncertain environment .

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1Solução Original

Beta=10% alfa=90%

Beta=10% alfa=95%

Beta=10% alfa=99%

Beta=50% alfa=90%

Beta=50% alfa=95%

Beta=50% alfa=99%

Beta=90% alfa=90%

Beta=90% alfa=95%

Beta=90% alfa=99%


Cum

late

d P

robabil

ity(%

)

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0.9

1Solução Original

Beta=10% alfa=90%

Beta=10% alfa=95%

Beta=10% alfa=99%

Beta=50% alfa=90%

Beta=50% alfa=95%

Beta=50% alfa=99%

Beta=90% alfa=90%

Beta=90% alfa=95%

Beta=90% alfa=99%Scenario Profit (mil u.m.)

Cum

ula

ted P

robabil

ity (

%)

9. Conclusions

1. The instance built for this problem, even though simplified, reflect the

complexity of oil supply chain planning;

2. The results obtained are suitable for real operations and give some

important insights of how to deal with the uncertain factors considered;

3. Compairing the results obtained by both scenario generation methods

allows to identify qualities and disadvantages of each one;

4. It was clear that the Time Agregation Method has a more desirable

behaviour in function of risk measures parameters;

5. The problem here present could be closer do real operations, considering

the integer nature of oil and product import and export operations or

by taking into account other sources of uncertainty, such as asset

availability;

6. Other mathematical techniques could be applied, for example Lagragian

Decomposition, which would drive to a smaller computational effort.

Contact

[email protected]@petrobras.com.br

Oil Supply Chain Planning under Uncertainty and Risk Evaluation

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