Integrated Model for Financial Risk Management in Refinery Planning

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Ind. Eng. Chem. Res. 2010, 49, 374–380

GENERAL RESEARCH Integrated Model for Financial Risk Management in Refinery Planning Jeongho Park,† Sunwon Park,*,† Choamun Yun,† and Young Kim‡ Department of Chemical and Biomolecular Engineering, Korea AdVanced Institute of Science and Technology (KAIST), 373-1, Guseong-dong, Yuseong-gu, Daejeon, Korea, and Energy Plant Research DiVision, Korea Institute of Machinery & Materials, 305-343, 104 Sinseongno, Yuseong-gu, Daejeon, Korea

An integrated model based on two-stage stochastic programming is developed for operational planning and financial risk management of a refinery. Downside risk, which rationally quantifies financial risk, is selected as the objective function to be minimized. Subsequently, the contract sizes and the operational plan are optimized on the basis of the developed model and the price scenarios. A case study shows that financial risk can be substantially reduced by diversifying suppliers with spot contracts and by cross-hedging with futures contracts. The former approach is particularly effective for low-target profits, whereas the latter is effective for relatively high-target profits. Furthermore, the target profit is closely related to risk propensity. A hightarget profit set in a refinery reflects risk-taking behavior, whereas a low-target profit indicates a risk-averse attitude. The developed model is beneficial for refineries because it aids in decision-making on operational and financial strategies. 1. Introduction Planning for business in an uncertain market is a challenging issue. Market conditions significantly affect the profits of chemical companies. Specifically, the profit of a refinery fluctuates greatly with the prices of crude oil and products. The fluctuations are rarely within expectations; this often sabotages the advantages of executing an optimal operational plan. Recent failures in profit management have stressed the importance of financial risk management in refineries.1 To date, only a few research groups have investigated this subject. In the pioneering work by Barbaro and Bagajewicz,2 a methodology for managing financial risk involving two-stage stochastic programming was proposed. They developed a model to obtain solutions consistent with the risk propensity of a decision-maker and used this model to examine the advantages of considering downside risk as a financial risk measure. Downside risk helps decrease the computational burden because it does not require any binary variables. In an extension of their study,3 option contracts were used to hedge the financial risk of capacity expansion by the same methodology. It was found that the usual assumption that option contracts reduce financial risk is not always true. Therefore, an appropriate model is required for effective financial risk management. Ponsakdi et al.4 used the same approach as Barbaro and Bagajewicz2 to manage financial risk while planning refinery operations. The amount of crude oil to be purchased and the production levels of different products were determined to maximize the profit on the basis of the demand forecasts. The developed stochastic model was found to yield a higher expected profit and lower risk than the deterministic model. The main purpose of this study is to develop a stochastic model for financial risk management in a refinery that takes into account the uncertainties in the prices of crude oil and its products. This study, which is an extension of previous * To whom correspondence should be addressed. Tel.: 82-42-3503920. Fax: 82-42-862-5961. E-mail: [email protected]. † Korea Advanced Institute of Science and Technology (KAIST). ‡ Korea Institute of Machinery & Materials.

studies,4-6 integrates financial risk management into refinery planning. Additionally, operational hedging using spot contracts and financial hedging using futures contracts are applied in the model. 2. Problem Description 2.1. Financial Risk of Purchasing Crude Oil. Refineries develop purchasing plans that are based on market predictions for crude oil in order to maximize profits. When executing a plan, they are exposed to financial risks due to the fluctuations in crude oil prices during the period between purchase and payment. If the price increases, a refinery must pay an amount greater than originally planned. For example, an increase of $1 per barrel of crude oil will cost a refinery an additional $2 million for a typical large crude oil container holding 2 million barrels. In fact, in the third quarter of 2008, when large fluctuations were observed in crude oil prices, significant discrepancies were reported in the profits of South Korean refineries. One way of lowering the financial risk related to crude oil purchases is to establish a portfolio of different types of contracts. There are three types of contracts mainly used for purchasing crude oil: long-term, spot, and futures contracts. 2.2. Long-Term and Spot Contracts. A refinery needs to consider two aspects of crude oil supply: stability and flexibility. For stability, refineries use long-term contracts to avoid possible failures in crude oil supply; a long-term contract with a specific supplier guarantees a regular supply of crude oil. In exchange for this advantage, refineries often pay a higher price than for spot contracts. If there are no stability concerns, refineries can also diversify suppliers by using spot contracts to search for the most favorable conditions. The importance of spot contracts has become greater with advanced blending technology, which now enables a refinery to use any type of crude oil. The best way to consider both stability and flexibility is by combining the two types of contracts. Refineries should purchase a certain amount of required crude oil with long-term contracts and the rest with favorable spot contracts.

10.1021/ie9000713 CCC: $40.75  2010 American Chemical Society Published on Web 11/06/2009

Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010

Figure 1. Hedging price risk using futures contracts. Table 1. Hedging Process of a Refinery stage

activities

cash transactions

1 2

plan production start production market products

buy crude oil sell products

futures transactions long crude oil futures long liquidation

2.3. Futures Contract. A futures contract is the right to buy commodities at a predetermined price known as the “strike price”. Crude oil futures contracts help a refinery to hedge the risk of price changes over a specific period by fixing the net purchase price. A refinery, which has a plan for purchasing crude oil, will buy futures contracts to hedge against the possibility of a price rise. If the crude oil price surges later, the price of its futures contracts will also increase. Hence, the net purchase price remains constant, as described in Figure 1. Table 1 lists the activities involved in the hedging process for a refinery. Futures contracts are standardized and briskly traded in futures markets. The most commonly used futures contract for risk hedging of crude oil prices is the West Texas Intermediate (WTI), which is traded at the Chicago Mercantile Exchange (CME). When a refinery buys a variety of crude oils, the corresponding futures contracts might not exist or might have different hedging periods. In this case, a refinery can hedge price risks by using alternative futures contracts with high price correlations and expiration dates similar to those of the crude oil of interest. This strategy is referred to as indirect or cross-hedging. 2.4. Assumptions. A simplified refinery process is presented in Figure 2. Assume that this refinery purchases crude oils from six different sources: from Dubai using a long-term contract and from Oman, Brent, Murban, Qatar, and Bonny using spot contracts. In addition, WTI crude oil futures contracts are traded for crosshedging. The futures with expiration dates closest to the day of payment are selected. The purchase prices are determined upon the arrival of the crude oil at the refinery. The time lag between purchase and payment is assumed to be 1 month, and the planning is established on a monthly basis. The amount of crude oil refined in a month is normally within the range of 20-30 million bbl; 12 million bbl is purchased with a long-term contract, and the rest is through spot contracts. In this study, the sizes of the spot and futures contracts were optimized separately by considering the separation theorem. According to this theorem, when a futures market exists and the production is nonstochastic, the production decisions in a corporation are based solely on the prices of raw materials and products, whereas hedging decisions are based on futures prices.7 Thus, if the gain from futures contracts correlates with the operating profit, production and hedging decisions can be made separately. 3. Developing a New Financial Risk Management Model for a Refinery 3.1. Refinery Planning Based on Two-Stage Stochastic Programming. Planning for uncertainty in general industrial processes has been a major issue over the past 50 years. Beginning with the study by Dantzig,8 stochastic optimization

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models have evolved into a rich set of tools and methodologies.9 Of these, two-stage stochastic programming (2-SSP) is the stochastic formulation method chosen for this study. In 2-SSP, uncertainties in model parameters are handled by following a procedure similar to a practical decision-making process: Decisions are divided into two stages that represent the cases before and after the realization of uncertainties.10,11 Table 2 lists the decisions to be made in each stage and the uncertainties involved. The fundamental idea behind 2-SSP is the concept of recourse, which is a corrective action taken after a random event occurs. Its objective is to minimize the expected value of the recourse cost calculated for each scenario. From its definition, it is natural to consider the recourse cost as identical to the financial risk resulting from the discrepancy between prediction and realization. Consequently, in this study, the objective function to be minimized is the financial risk quantified with a risk measure. 3.2. Selecting a Risk Measure. In general, the effectiveness of a risk management model is determined by the selection of a risk measure.12 A good risk measure appropriately reflects the utility function and risk propensity of a decision-maker. For example, the most widely used measure is variance. However, it might not be appropriate for financial risk management as it assigns equal weights to pessimistic and optimistic possibilities. The general meaning of financial risk is the probability of acquiring less profit than the target. In other words, the utility function of a decision-maker is asymmetric; everyone wants to avoid the pessimistic results and seek optimistic ones. For this reason, the probabilistic financial risk [Risk(x,Ω)] is defined as the probability of having profits lower than the target profit Ω, expressed as Risk(x, Ω) ) P[profity(x) < Ω] or Risk(x, Ω) ) E[λy(x, Ω)] )

∑ F λ (x, Ω)

(1)

y y

y∈Y

where Fy is the probability of scenario y and λy(x,Ω) is a binary variable defined for each scenario as λy(x, Ω) )

{

1 if profit < Ω 0 otherwise

(2)

The cumulative risk curve in Figure 3 shows the level of financial risk incurred at each profit level for a given plan x.2 The value of Risk(x,Ω) for a specific Ω can be easily obtained from this curve. Although Risk(x,Ω) is suitable to visualize the risk propensity of a decision-maker, it is not a suitable objective function. Figure 4 shows the risk curves of two plans: Plan I yields the optimal results for Risk(x,Ω) minimization, and plan II yields suboptimal results. Note that the financial risk in accomplishing the target profit Ω with plan I [Risk(1,Ω)] is lower than that in the case of plan II [Risk(2,Ω)]. However, plan I is riskier than plan II because the maximum loss in plan I [Loss(1)] is larger than that in plan II [Loss(2)]; moreover, the variance of profit in plan I is larger than that in plan II. To minimize Risk(x,Ω), plan I can be chosen over plan II, although the latter involves less overall risk than the former. This example shows that the optimization of a single objective, namely, Risk(x,Ω) may not provide reliable solutions. To avoid this issue, other research groups have proposed a multiobjective approach using multiple target profits or the inclusion of additional constraints such as the minimum allowable loss.2,13 However, those approaches generally involve high computational loads and complicated formulations.

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Figure 2. Refinery process.

Figure 3. Cumulative risk curve. Figure 5. Downside risk. Table 2. Decisions and Uncertainties in a Refinery first-stage decisions second-stage decisions uncertainties (N scenarios) long-term contracts

Figure 4. Disadvantage of Risk(x,Ω) minimization.

All of the aforementioned problems can be solved by using another financial risk measure, downside risk, which was first introduced by Eppen et al.14 This measure was suggested as a useful means to measure the financial risk in capacity expansion planning for the automobile industry. It is defined as the absolute expected value of the negative deviation from the specific target profit Ω, that is DRisk(x, Ω) ) E[δy(x, Ω)] )

∑ F δ (x, Ω) y y

(3)

y∈Y

Here, δy(x,Ω) is the negative deviation from the target profit Ω for plan x and scenario y and is defined as

{

Ω - profity(x) if profity(x) < Ω δy(x, Ω) ) 0 otherwise

(4)

It has been shown that downside risk is identical to the area under the cumulative risk curve below the target profit Ω, as shown in Figure 5 (see Appendix B, Supporting Information).2,13 Because it is not a point measure, there are no such problems as caused by using Risk(x,Ω) as an objective function. It also has the following relationship with the expected profit E[profit(x)] ) ξ¯ - DRisk(x, ξ¯ )

(5)

spot contracts futures contracts production

crude oil price product price

where ξj is the maximum profit that can be obtained among all scenarios. This equation indicates that minimizing downside risk at the maximum profit ξj results in the maximization of the overall expected profit (see Appendix C, Supporting Information). Thus, downside risk is the most suitable objective function for risk management. Decision-makers can determine target profits according to their risk propensities. If the decision-makers of a refinery are risk-averse, they focus on reducing the possibility of loss. Thus, the target profit for financial risk management should be relatively low, as shown for Ω1 in Figure 6. In contrast, risktaking decision-makers might want to seek a high profit involving high financial risks. In such a case, they should select a relatively high-target profit Ω2. When decision-makers face difficulties in setting a target profit, they can determine the target profit by analyzing the expected consequences of various risk curves. 4. Formulation Downside risk is selected as a risk measure for establishing a two-stage stochastic model. The effects of employing spot and futures contracts in financial risk management are examined with two models: In the first model, the downside risk is minimized using spot contracts, whereas in the second model, both spot and futures contracts are used. In a refinery, multiple products are manufactured from the intermediate streams in a crude distillation unit (CDU). Therefore, the product yields depend on the crude oil selected and the operating conditions of the CDU. The solutions are further constrained by the quality requirements of products, as well as unit capacities and mass balances of the process.


4.1. Optimizing the Sizes of Spot Contracts. The optimal sizes of spot contracts, Spotc, and the required amount of MTBE are determined to minimize the downside risk of target profit, as follows

∑ Spot )WTR

FRs ) (Long +

c

377

(13)

s

c

The production amounts for the products are determined using the expressions

minimize DRisk(x,Ω) FCC gasoline: where DRisk(x,Ω) ) E[δy(x,Ω)] δy(x, Ω) )

VolumeFCCg ) VolumeRDfcc

Gasoline:

{

productiongasoline ) (Long +

Ω - profity(x) if profity(x) < Ω 0 otherwise

(6)

∑ Spot )(VTR c

(14)

ln

+ VTRHN +

c

VTRFCCg) + MTBE

(15)

The profit corresponding to the realization of each scenario is profity(x) )

∑

Diesel: productionp,ypricep,y - Long × priceLong,y -

p

∑ Spot price c

∑ Spot )VTR

DO

(16)

∑ Spot )VTR

kero

(17)

c

c

- MTBE × priceMTBE,y (7)

c,y

c

Equations 8-22 are the constraints for the refinery process shown in Figure 2. The total load of a CDU should be greater than its minimum capacity and less than its maximum capacity CapacityL e Long +

productiondiesel ) (Long +

∑ Spot

c

Kerosene: productionkero ) (Long + Bunker-C: productionbunker ) (Long +

+ MTBE e CapacityU

c

c

∑ Spot )VTR c

RDYieldb

c

c

(18)

(8) The weight and volume transfer ratios of each CDU fraction are determined by the expressions WCutLong,sLong +

c,sSpotc

c

c

VCutLong,sLong +

∑ VCut

c,sSpotc

c

VTRs )

Long +

∑ Spot

∑ WTR

ss

+ 0.5WTRs)

(19)

ss

(9)

∑ Spot

Long +

MidWTRs ) 100(

∑ WCut c

WTRs )

The midpoint weight transfer ratios of the CDU fractions are calculated using the expression

(10)

The octane numbers of Gross Overhead (GO) and Heavy Naphtha (HN) and the pour points of Light Distillate (LD) and Heavy Distillate (HD) follow the empirical relationship propertys ) a0 + a1(MidWTRs - b) + a2(MidWTRs - b)2 (20)

c

c

The sums of the weight and volume transfer ratios of CDU fractions should be 1

The properties of each product should satisfy quality constraints. For gasoline blending:

∑ WTR

s

)1

(11)

ONL e propertylnFRln + propertyHNFRHN + ONMTBEMTBE e ONU productiongasoline (21)

∑ VTR

s

)1

(12)

Here, ONL and ONU are 92 and 94, respectively.

s∈S

s∈S

For diesel blending: propertyDO e PPU

The mass balances between the intermediate streams can be obtained as

(22)

Here, the upper limit of the pour point, PPU, is 473.69 K. Table 3. Downside Risk Reduction by Spot Contract Optimization downside risk ($1,000)

Figure 6. Setting a target profit according to the risk propensity.

target profit ($1,000)

only long-term

with spot

reduction

400,000 300,000 200,000 100,000 0 -100,000 -200,000 -300,000

346,961 252,531 166,567 95,531 45,940 18,638 6,227 1,913

343,954 252,557 164,194 89,483 38,664 12,348 3,403 745

-3,007 (-0.87%) 26 (0.01%) -2,373 (-1.42%) -6,048 (-6.33%) -7,276 (-15.84%) -6,290 (-33.75%) -2,824 (-45.35%) -1,168 (-61.05%)

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profit′y(x) ) profity(x) + (Fy,1 - Fy,0)Futures

4.2. Optimizing the Sizes of Futures Contracts. The optimal sizes of futures contracts, Futures, are determined to minimize the downside risk of a target profit; this is done by considering both futures and spot contracts as follows

(24)

The constraints of the refinery process are identical to eqs 8-22. 5. Results and Discussion

minimize DRisk′(x, Ω)

5.1. Optimizing the Sizes of Spot Contracts. The downside risk, DRisk(x,Ω), is minimized by using spot contracts for eight different target profits ranging from -$300 million to $400 million. In Table 3, downside risks with the optimal sizes of spot contracts added to a constant amount of long-term contracts are compared to the downside risks that involve only long-term contracts. The downside risk is reduced by additionally employing spot contracts, except when the target profit is $300 million. The percentage of downside risk reduction for low-target profits (-$300 million to $0 million) is significantly high. As stated previously, a low-target profit reflects risk-averse behavior. Thus, this result suggests that a refinery with a risk-averse strategy

where DRisk′(x, Ω) ) E[δ′y(x, Ω)]

δ′y(x, Ω) )

{

Ω - profit′y(x) if profit′y(x) < Ω 0 otherwise

(23)

The gain from trading futures contracts is added to the operating profit Table 4. Purchase Amounts and Profit Distribution purchase amounts (1,000 bbl)

profit distribution ($1,000)

target profit ($1,000)

Oman

Brent

Murban

Qatar

Bonny

MTBE

total

mean

dev

min

max

400,000 300,000 200,000 100,000 0 -100,000 -200,000 -300,000

3,115 2,511 1,103 1,456 1,598 2,052 2,407 2,864

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

13,237 11,009 5,818 5,217 4,923 3,985 3,252 2,307

0 0 0 358 513 1,005 1,390 1,885

1,648 1,477 1,080 968 966 958 952 944

18,000 14,997 8,000 8,000 8,000 8,000 8,000 8,000

63,015 58,695 48,631 47,350 46,852 45,266 44,027 42,431

220,608 199,123 152,633 151,017 150,516 149,300 148,764 148,612

-697,513 -644,844 -522,134 -526,671 -528,333 -533,635 -537,775 -543,109

793,394 722,432 559,724 547,279 543,980 533,452 527,124 523,970

Table 5. Downside Risk Reduction by Futures Contract Optimization downside risk ($1,000) target profit ($1,000)

total crude (1,000 bbl)

futures (1,000 bbl)

hedge ratioa (%)

before hedge

after hedge

reduction

400,000 300,000 200,000 100,000 0 -100,000 -200,000 -300,000

30,000 26,997 20,000 20,000 20,000 20,000 20,000 20,000

29,672 21,400 14,074 7,906 4,354 3,187 2,059 0

98.91 79.27 70.37 39.53 21.77 15.93 10.30 0.00

343,954 252,557 164,194 89,483 38,664 12,348 3,403 745

307,723 228,708 150,139 83,693 36,558 11,879 3,292 745

-36,231 (-10.53%) -23,849 (-9.44%) -14,055 (-8.56%) -5,790 (-6.47%) -2,106 (-5.45%) -469 (-3.79%) -111 (-3.26%) 0 (0.00%)

a

Hedge ratio is defined as the ratio of traded futures contracts to the total purchase amounts.

Figure 7. Risk curve comparison of spot contract optimization.


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Figure 8. Risk curve comparison of spot and futures contracts optimization. Table 6. Comparison of Two Results with Downside Risk Reduction downside risk ($1000) target profit ($1000)

only long-term (A)

with spot

reduction from A

with spot and futures

reduction from A

400,000 300,000 200,000 100,000 0 -100,000 -200,000 -300,000

346,961 252,531 166,567 95,531 45,940 18,638 6,227 1,913

343,954 252,557 164,194 89,483 38,664 12,348 3,403 745

-3,007 (-0.87%) 26 (0.01%) -2,373 (-1.42%) -6,048 (-6.33%) -7,276 (-15.84%) -6,290 (-33.75%) -2,824 (-45.35%) -1,168 (-61.05%)

307,723 228,708 150,139 83,693 36,558 11,879 3,292 745

-39,238 (-11.31%) -23,823 (-9.43%) -16,428 (-9.86%) -11,838 (-12.39%) -9,382 (-20.42%) -6,759 (-36.26%) -2,935 (-47.14%) -1,168 (-61.05%)

should use spot contracts to effectively manage the financial risk involved. In contrast, downside risk reductions for hightarget profits (from $100 million to $400 million) are small, indicating that there is a limit to managing financial risk with spot contracts when a refinery plans a risk-taking strategy. The changes in the purchase amounts of crude oil and the corresponding profit distributions for eight target profits are listed in Table 4. As the target profit decreases, the refinery is recommended to reduce the amount purchased from Qatar and increase that from Bonny. From Table 4, it can be seen that the mean and deviation for the profit distribution increase as the target profit increases. This result is consistent with the assumption that a risk propensity can be reflected by the level of target profit: a risk-taking refinery sets a high-target profit. When the expected value (mean) of a profit increases, the risk (deviation) also increases because of the trade-off between risk and return. As a result, the profit distribution in the case of a risk-taking strategy has a larger mean and deviation than does that for a risk-averse strategy. The difference in risk propensities according to target profits can easily be compared by comparing their cumulative risk curves, as shown in Figure 7. In region 1, the financial risk of high profit decreases as the target profit Ω increases, and vice versa in region 2. Here, the differences between the cumulative risk curves are small, implying that the effect of spot contracts is limited. Moreover, the curves do not improve further for target profits lower than -$300 million or higher than $400 million. This is because the prices of different types of crude oil are inevitably related to one another. The generally strong correlation between the prices of different types of crude oil restricts financial risk reduction by diversified purchasing using spot contracts. Therefore, a cross-hedging strategy involving WTI crude oil futures contracts is proposed;

in this method, the negative correlation between the prices of crude oil and its futures contract are taken into account. 5.2. Optimizing the Sizes of Futures Contracts. The downside risk, DRisk′(x,Ω), is minimized by using futures contracts for eight different target profits ranging from -$300 million to $400 million. From Table 5, it is seen that the optimal hedge ratio increases from 0 to approximately 1 as the target profit increases. The downside risk is reduced by up to 10% through cross-hedging. When compared to the results listed in Table 3, the risk reduction is more significant for high target profits with high hedge ratios. Therefore, a refinery considering a risk-taking strategy should increase the size of futures contracts to reduce the financial risk involved. Cumulative risk curves with spot and futures contracts are shown in Figure 8. As the target profit Ω increases, Risk(x,Ω) for achieving a high profit is reduced in region 1 and vice versa in region 2; this is similar to the results shown in Figure 7. However, the deviations of the curves in Figure 8 are larger than those in Figure 7. This implies that cross-hedging using futures contracts enables effective management of the financial risks involved with various risk propensities. 5.3. Discussion. All of the results are collected in Table 6 for comparison. In the target profit range from $200 million to $400 million where the downside risk remains approximately same with spot contracts, the risk can be further reduced by using futures contracts. Overall, the downside risk can be reduced by at least 9% for any target profit. Therefore, a refinery should employ both spot and futures contracts in addition to long-term contracts to achieve the best results in its financial risk management. The results also show that “here-and-now” (first-stage) decisions for 2-SSP can be managed in relation to the target of a decision-maker: spot and futures contracts should be factored in at the decision-making time, not afterward as control actions. It is essential for any

380


company to simulate all possible scenarios and to evaluate and manage the expected financial risk. The developed model is expected to facilitate more efficient risk management than does current heuristic planning that depends on experience. 6. Conclusions An integrated model was developed for financial risk management in refinery planning. Two-stage stochastic programming approach and downside risk were selected because of their inherent capabilities of describing real decision-making processes. Financial risk was significantly reduced by optimizing the sizes of spot and futures contracts. It was found that these two types of contracts have different performances depending on the risk propensities. Diversified purchases using spot contracts effectively reduce the financial risk of risk-averse strategies, whereas cross-hedging using futures contracts is effective for risk-taking strategies. It was observed that the target profit is closely related to the risk propensity of the decisionmaker. The risk curve of a high-target profit shows a risk-taking behavior, and a low-target profit shows a risk-averse behavior. The proposed model is expected to benefit refineries by enabling them to determine the optimal sizes of contracts according to their risk propensities or target profits. Supporting Information Available: Scenario generation (Appendix A), relationship between downside risk and cumulative risk curve (Appendix B), and relationship between downside risk and expected profit (Appendix C). This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature Indices c ) set of spot crude oils {Dubai, Oman, Brent, Murban, Qatar, Bonny} p ) set of products {gasoline, kero, diesel, bunker} s ) set of streams {LN, HN, FCCg, RD, DO} ss ) set of streams with boiling points higher than that of s x ) set of plans {1, 2, ..., N} y ) set of scenarios {1, 2, ..., M} Parameters ξj ) maximum profit in a plan ($) Fy ) probability of scenario y pricec,y ) price of crude oil c in scenario y ($) priceLong,y ) price of the long-term contract in scenario y ($) priceMTBE,y ) price of MTBE in scenario y ($) pricep,y ) price of product p in scenario y ($) CapacityL ) lower bound of the total load of CDU (bbl) CapacityU ) upper bound of the total load of CDU (bbl) fcc ) FCC conversion ratio (%) FRs ) flow rate of stream s (bbl) Long ) purchasing amount of a long-term contract (bbl) MidWTRs ) midpoint weight transfer ratio of stream s (%) ONL ) lower bound of the octane number (MON)

ONU ) upper bound of the octane number (MON) PPU ) upper bound of the pour point (°F) propertys ) property of stream s VCutc,s ) volume cut ratio of spot crude oil c in stream s (%) VCutLong,s ) volume cut ratio of the long-term crude oil in stream s (%) Volumep ) volume of product p (bbl) VTRs ) volume transfer ratio of each CDU stream s (%) WCutc,s ) weight cut ratio of spot crude oil c in stream s (%) WCutLong,s ) weight cut ratio of the long-term crude oil in stream s (%) WTRs ) weight transfer ratio of each CDU stream s (%) Yieldb ) yield of bunker C (%) Variables Ω ) target profit of financial risk management ($) Futures ) trading amount of futures contracts (bbl) MTBE ) purchasing amount of MTBE (bbl) productionp,y ) production amount of product p in scenario y (bbl) Spotc ) purchasing amount of spot crude oil c (bbl)

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ReceiVed for reView January 16, 2009 ReVised manuscript receiVed September 17, 2009 Accepted October 21, 2009 IE9000713

Integrated Model for Financial Risk Management in Refinery Planning

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