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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%
0
2
4
6
8
10
12
14
16
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-8%
-6%
-4%
-2% 0% 1% 2% 4% 6%
0
2
4
6
8
10
12
14
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-8%
-6%
-4%
-2% 0% 2% 4% 6% 8%
0
2
4
6
8
10
12
14
16
0%
10%
20%
30%
40%
50%
60%
70%
80%
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
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)
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
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.
6. Mathematical Model and Problem Approach
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
6. Mathematical Model and Problem Approach
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
(%)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
Scenario Profit (mil u.m.)
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%
Moment Matching Time Agregation
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
Moment Matching Time Agregation
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)
Moment Matching Time Agregation
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 .
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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
late
d P
robabil
ity(%
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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