Integrated Operational and Financial Hedging for Risk Management in

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Integrated Operational and Financial Hedging for Risk Management in Crude Oil Procurement Xiaocong Ji, Simin Huang, and Ignacio E. Grossmann Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b00903 • Publication Date (Web): 01 Sep 2015 Downloaded from http://pubs.acs.org on September 5, 2015

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Industrial & Engineering Chemistry Research

Integrated Operational and Financial Hedging for Risk Management in Crude Oil Procurement Xiaocong Ji,† Simin Huang,† and Ignacio E. Grossmann∗,‡ Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China, and Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States E-mail: [email protected]

Abstract This paper presents a general framework for the integration of operational hedging and financial hedging strategy in the crude oil procurement process. The main purpose of the proposed approach is to manage the risk in oil procurement process due to oil price fluctuation. The problem is formulated as one-stage stochastic programming model that incorporates Conditional Value-at-Risk (CVaR) as the risk measure. By introducing production flexibility such as inventory and the nonlinear CDU Fractionation Index (FI) model, as well as financial derivatives like futures, put option and call option, the integrated hedging strategy enables industrial managers to obtain the desired balance between profitability and risk tolerance. In addition, a Sample Average Approximation (SAA) method is applied to solve the stochastic problem. Numerical studies illustrate the benefits of the proposed approach and also provide useful managerial insights. ∗

To whom correspondence should be addressed Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China ‡ Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States †

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Keywords: Risk Management, Crude Oil Procurement, Integrated Operational and Financial Hedging; Conditional Value-at-Risk

Introduction In the petroleum industry, raw material procurement is an important activity 1–3 that has received significant attention in the literature. However, the procurement problem under price uncertainty has not received much attention in process system engineering despite the fact that its cost takes up a large proportion of the operational costs. Table 1 summarizes the crude oil procurement costs for SINOPEC which accounts for more than 75% of their total operational costs. Even 1% improvement in procurement will translate into millions of cost savings. Due to the great volatility of crude oil price, petroleum companies face large procurement risks. Figure 1 shows the price of WTI and Brent benchmark oils for the period 2004-2014. Managers are continuously seeking for better strategies to manage the procurement risk while aiming for profitability. Table 1: Operational costs composition of SINOPEC from 2007 to 2013 4 (Billion CNY).

Total Operational Costs Procurement Costs % of Procurement costs to total operational costs

2007

2008

2009

1123.7 970.9

1473.8 1285.2

1260.2 990.5

86.4%

87.2%

78.6 %

2010

2011

1807.9 2401.3 1482.5 2031.5 82%

84.6%

2012

2013

2687.4 2301.2

2783.5 2371.9

85.6%

85.2%

As Carneiro et al. 5 point out, petrochemical production has many types of flexibility, such as yield ratio, blending of crude oil and end products, etc., which provides the possibility of hedging procurement risks. Readers can refer to Pinto et al. 6 for background description of refinery operation. Besides the aforementioned operational hedging strategy, the global oil financial market also provides various types of derivatives for companies. Readers can also refer to Barbaro and Bagajewicz, 7 Kouvelis et al. 8 and Calfa and Grossmann 9 for background description of financial contracts that are used as hedging tool. Some widely 2


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used financial tools are futures contract, 8 and call/put option 8 that gives the owner the right, but not obligation, to buy/sell commodity at the strike price 8 on the expiration date. 8 '%!" '$!" '#!" '!!" &!" %!" $!" #!" !"

!"#$%&'()*% %+,-./''*01

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2/$*

Figure 1: Illustration of crude oil price, from www.eia.gov. This research focuses on the integration strategy through operational hedging using inventory and nonlinear Fractionation Index 10 (FI) CDU model, together with financial hedging using crude oil futures and call/put option to manage the crude oil procurement risk. The main contributions are listed as follows: • A general framework is proposed which integrates operational hedging strategy and financial hedging strategy. By introducing CVaR as a risk measure, the model is capable of assessing the effectiveness of hedging strategies. • In addition to inventory, which is widely regarded as a hedging tool 7,8 , the unique nonlinear FI CDU model is also introduced, which significantly improves procurement decisions. • Useful insights are drawn from the numerical experiments, which not only illustrate the benefits of the suggested approach, but also help managers to improve the procurement decision making process. The remainder of the paper is organized as follows. Section 2 presents a review of the relevant literature. Then, the problem is described in Section 3. Section 4 formulates the

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problem as one-stage stochastic programming model for which the Sample Average Approximation (SAA) method 11 is applied to tackle the resulting MINLP model. Numerical experiments are conducted in Section 5 that illustrate the benefits of the proposed integrated hedging strategy and provide useful insights. Finally, we summarize the research and discuss future research directions.

Literature Review Risk management in process system engineering belongs to the area of planning under uncertainty, which has drawn significant attention. Many papers discuss exogenous uncertainty (e.g. price, demand, etc.) and endogenous uncertainty (e.g. yields, etc.) in this area. For systematic review, please refer to Sahinidis 12 , Grossmann 13 , Verderame et al. 14 , etc. Some widely adopted methods for risk management in process system engineering are stochastic programming, dynamic programming, stochastic robust programming, and fuzzy programming. 15 This research uses a stochastic programming model that incorporates a risk measure, so we mainly focus on the relevant research in this area. According to risk measures (e.g., financial risk, downside risk, CVaR, etc.), problem field (e.g., planning, investment, pricing, process design, etc.), source of uncertainty (e.g., price, demand, due time, etc.), and model type, we segregate the relevant literature in Table 2. Some widely used risk measures are downside risk, financial risk, VaR and CVaR, etc. Next, we review the literature according to the risk measure they apply. Barbaro and Bagajewicz 7,16,17 have conducted a series of studies in the risk management of production planning in the process industry. They propose a two-stage stochastic programming model with downside risk 16 proposed by Eppen et al. 18 as a risk measure, where they modify the deterministic process industry planning problem to address the uncertainty in product price and build a two-stage model. Later, they extend their work by considering inventory and option contracts 7 to hedge financial risk in the process design problem

4


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addressed by Liu and Sahinidis 19 which considers product demand and price uncertainty, and they use a two-stage stochastic programming model to formulate the problem. They also suggest financial risk as a new risk measure, which has been widely used in investment planning 20,21 , pricing decisions 22–24 , and product and process design 25,26 . Bonfill et al. 27 address risk management problem for multiproduct batch plants with uncertain demand that incorporates options to hedge the risk, and consider three different risk measures, namely financial risk, downside risk and worst-case scenario. Pongsakdi et al. 28 also use financial risk as a risk measure to study the refinery planning problem considering oil price and product demand uncertainty. Later, Park et al. 29 extend the work of Pongsakdi et al. 28 , and analyze how spot contract, futures contract and option contract influence procurement decisions. You et al. 15 develop a two-stage stochastic programming model for the supply chain planning problem with uncertainty in demand and freight rate. In addition to financial risk and downside risk, they also use variance and variability index as risk measures. Similar to the aforementioned downside risk and financial risk, CVaR is another widely used risk measure. Carneiro et al. 5 discuss the Brazil oil supply chain optimization problem with a two-stage stochastic model incorporating CVaR, where they address product demand and price, oil supply and price as uncertainty. To solve the problem, they apply a scenariobased approach. In addition, Verderame and Floudas 30 also use CVaR to address batch plant planning under product demand, due time uncertainty. Another two-stage stochastic programming model is built to formulate the problem. To our knowledge, the most relevant article is Barbaro and Bagajewicz 7 . Our work extends their research by introducing the nonlinear FI model proposed by Alattas et al. 10,31 as another operational hedging strategy. Unlike the financial risk or downside risk used by Barbaro and Bagajewicz, CVaR is used as the risk measure. Moreover, the SAA 11 method is applied to solve the problem to reduce the size of the problem. In addition, our research considers raw material price uncertainty, which determines that there is no recourse

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in the problem and one stage stochastic programming is proper framework to formulate the problem. So we use one stage model in this research.

6


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Downside Risk Financial Risk Financial Risk Financial Risk, downside risk, worst-case scenario Financial Risk Financial Risk Financial Risk Financial Risk

Bagajewicz and Barbaro 16 Guill´en et al. 22 Koppol and Bagajewicz 26


7 Financial Risk Financial Risk Financial Risk Financial Risk Financial Risk, downside risk, variability index CVaR CVaR

Lavaja et al. 21 Pongsakdi et al. 28 Lakkhanawat and Bagajewicz 23 Park et al. 29

Carneiro et al. 5

Verderame and Floudas 30

Demand, price crude oil supply Demand, due time

Supply chain Planning Planning

Investment Planning Pricing Planning Supply chain Management

Pricing

Price Price Demand Demand, price Demand, lead time price Demand Demand, price Demand, price Demand, price Demand, freight rate

Demand

Price Demand Demand, price

Planning Planning Investment Process design

Planning

Planning Pricing Process design

Problem

The Proposed model CVaR Procurement Oil Price 1-stage sp: 1-stage stochastic programming; 2-stage sp: 2-stage stochastic programming.

You et al. 15

Financial Risk

Guill´en et al. 24

Barbaro and Bagajewicz 7 Barbaro and Bagajewicz 17 Aseeri et al. 20 Bagajewicz 25

Bonfill et al. 27

Risk Measure

Literature

Uncertainty

sp sp sp sp

sp sp sp sp sp

1-stage sp

2-stage sp

2-stage sp

2-stage sp

2-stage 2-stage 2-stage 2-stage

2-stage 2-stage 2-stage 2-stage 2-stage

2-stage sp

2-stage sp 2-stage sp 2-stage sp

Model

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 2: Summary of literature review.

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Fc,i,j+1,t = P Dc,i,j,t ,

∀c ∈ C, i ∈ I, j ∈ J, t ∈ T,

(1)

The mass conservation for component i in cut j is given by

Fc,i,j,t = P Dc,i,j,t + P Bc,i,j,t ,

∀c ∈ C, i ∈ I, j ∈ J, t ∈ T,

(2)

where P Bc,i,j,t is the component i in the bottom stream of the corresponding cut j. If the component i is lighter than the light key components LKj which is associated with cut j, it only occurs in the top product stream. If the component i is heavier than the heavy key components HKj , it only occurs in the bottom stream. This product distribution relationship is represented as follows.

Fc,i,j,t = P Dc,i,j,t , P Bc,i,j,t = 0,

∀c ∈ C, j ∈ J, t ∈ T, and i < LKj ,

(3)

Fc,i,j,t = P Bc,i,j,t , P Dc,i,j,t = 0,

∀c ∈ C, j ∈ J, t ∈ T, and i > HKj .

(4)

• Splitting of components at each unit. For component i with boiling temperature T bi less than the cut point temperature Tc,j,t , the rectifying index F Irj is used. Otherwise the stripping index F Isj is used. The separated components at each cut are calculated using the FI value with the disjunctive constraints, which are given by, 

 qY cutc,i,j,t   γ  c,i,j,t = F Irj  T bi ≤ Tc,j,t





  Y cutc,i,j,t   ∨ γ   c,i,j,t = F Isj   T bi ≥ Tc,j,t



  ,  

∀c ∈ C, i ∈ I, j ∈ J, t ∈ T.

(5)

Equation (5) can be exactly represented with mixed integer constraints using the convex hull formulation suggested in Raman and Grossmann, 33 which can be expressed as follows, 11



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γc,i,j,t = F Irj (1 − Y cutc,i,j,t ) + F Isj Y cutc,i,j,t ,

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∀c ∈ C, j ∈ J, t ∈ T, LKj < i < HKj , (6)

T bi + ML Y cutc,i,j,t ≤ Tc,j,t ,

∀c ∈ C, j ∈ J, t ∈ T, LKj < i < HKj ,

Tc,j,t ≤ T bi + Mu (1 − Y cutc,i,j,t ),

∀c ∈ C, j ∈ J, t ∈ T, LKj < i < HKj ,

(7)

(8)

where ML and Mu are sufficient large numbers. • Bottom product stream quantity. Based on the FI value, Alattas et al. 31 express the flow rate of component i in the bottom product for cut j as

P Bc,i,j,t =

Fc,i,j,t P γc,i,j,t P D c,i,j,t Pi Kc,i,j,t i P Bc,i,j,t

+1

,

∀c ∈ C, j ∈ J, t ∈ T, LKj < i < HKj ,

(9)

where the equilibrium constant Kc,i,j,t is given by,

Kc,i,j,t =

P vc,i,j,t , ∀c ∈ C, i ∈ I, j ∈ J, t ∈ T. P ci

(10)

The vapor pressure P vc,i,j,t for simple components (e.g., C2, C3, IC4, C4, IC5, C5) is calculated by

P vc,i,j,t

P V Bi )2.303 , ∀c ∈ C, i ∈ I, j ∈ J, t ∈ T. (11) = exp (P V Ai − Tj + P V Ci − 273.15

12


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For pseudo-components, 10,31 the vapor pressure is calculated by, P vc,i,j,t =P ci exp{[−5.96346(1 − T rc,i,j,t ) + 1.17639(1 − T rc,i,j,t )1.5 − 0.559607(1 − T rc,i,j,t )3 − 1.319(1 − T rc,i,j,t )6 ]/T rc,i,j,t + ωi [−4.78522(1 − T rc,i,j,t ) + 0.41399(1 − T rc,i,j,t )1.5 − 8.91239(1 − T rc,i,j,t )3 − 4.98662(1 − T rc,i,j,t )6 ]/T rc,i,j,t },

∀c ∈ C, i ∈ I, j ∈ J, t ∈ T. (12)

The critical temperature is calculated by

T rc,i,j,t =

Tc,j,t , T ci

∀c ∈ C, i ∈ I, j ∈ J, t ∈ T,

(13)

∀c ∈ C, j ∈ J, t ∈ T.

(14)

and Tc,j,t ≥ Tc,j+1,t ,

Constraints Other constraints are required to describe the material flow conservation, inventory, unit capacity, product property, product demand, and availability of crude oil and financial derivatives. • Crude oil inventory conservation and capacity. In the multiperiod framework, the inventory level of crude oil c at the beginning of each period t + 1, which is represented as Invc,t+1 , is given by,

Invc,t+1 = Invc,t + BCc,t − F Cc,t + Qderc,f utures,t−1 ,

∀c ∈ C, t ∈ T,

(15)

where BCc,t , F Cc,t and Qderc,f utures,t−1 denote procurement quantity, refining quantity and futures contract payment quantity of crude oil c, respectively. Note that we assume

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one period time lag between contract purchase and payment, which means the contract purchased at t−1 is exercised at t, and only futures contract is paid by crude oil delivery. Moreover, short selling is not allowed so that all the inventory level of crude oil must be greater than 0, which is expressed by

Invc,t ≤ Cap,

Invc,t ≥ 0,

∀c ∈ C, t ∈ T

(16)

• Production unit capacity. The total quantity of outlet streams from unit k, which represents the production quantity, is bounded by the unit capacity as,

XX

STc,l,k,t ≤ Capacityk ,

∀k ∈ K, t ∈ T,

(17)

c∈C l∈L

and the outlet stream is determined by the yield relationship, which is given by,

STc,ˆl,k,t =

X

βk,l,ˆl,c STc,l,k,t ,

∀c ∈ C, ˆl ∈ L, k ∈ K, t ∈ T,

(18)

l∈L

where STc,l,k,t =

P

i∈I

P Bc,i,l,t and βk,l,ˆl,c is the yield ratio of outlet stream ˆl from the

input stream l in unit k. • Product property. The quality of the end product is also considered, which is expressed by forcing that the net property of each outlet stream lies between the lower bound and P P the upper bound. Note that l∈L k∈K P rr,l,k,c,t STc,l,k,t equals to the net properties of

type r from all the outlet stream. We then describe the product property constraints as follows.

STc,p,t =

X

STc,l,k,t βk,p,l,c ,

∀c ∈ C, p ∈ P, t ∈ T,

l∈L,k∈K

14


(19)

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X

STc,p,t P RUp,r,t ≥

X

STc,p,t P RLp,r,t ≤

c∈C

c∈C

X

P rr,l,k,c,t STc,l,k,t ,

∀p ∈ P, r ∈ R, t ∈ T,

(20)

X

P rr,l,k,c,t STc,l,k,t ,

∀p ∈ P, r ∈ R, t ∈ T.

(21)

l∈L,c∈C,k∈K

l∈L,c∈C,k∈K

• End product demand. The total production quantity of end product p is calculated by the summation of all the outlet streams of product p,

P Ep,t =

X

STc,p,t ,

∀p ∈ P, t ∈ T,

(22)

c∈C

The demand for the end product p must be satisfied, that is,

P Ep,t ≥ Demandp,t ,

∀p ∈ P, t ∈ T.

(23)

• Availability on crude oil and derivatives. The procurement quantity of crude oil c in period t is limited by the availability, which is given by,

BCc,t ≤ AvailCc,t ,

∀c ∈ C, t ∈ T

(24)

Meanwhile the purchase quantity of financial contracts also has the upper bound limit,

0 ≤ Qderc,d,t ≤ AvailDc,d,t Zderc,d,t ,

∀c ∈ C, d ∈ D, t ∈ T

(25)

Risk Measure and Objective Function In this research, CVaR, which is also known as Mean Excess Loss or Mean Shortfall, is selected as the risk measure. According to Rockafellar and Uryasev, 34 given a return distribution, the α−CVaR is the conditional expectation of losses above the lowest amount for 15




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The entire model is then given by the MINLP formulation with objective function (27) subject to the constraints (1)-(26). As for total cost, which consists of the spot procurement cost, payoffs of financial derivatives, production cost, and holding cost of crude oil, we define, Cost as the total costs; Costst as spot procurement cost in period t; Costdt as cost associated with financial derivatives in period t; Costpt (Z, Q) as production cost in period t; Costht as holding cost in period t. The total cost is then given by,

Cost =

X

Costst + Costdt + Costpt + Costht ,

t∈T

and hence, the total expected cost is expressed as ES∈Ω [Cost]. P The crude oil procurement cost in each period is Costst = c∈C BCc,t sc,t .

Since the futures contract must be paid with crude oil delivery, the cost associated with

the futures contract equals to the contract setup cost Zderc,d,t scc,d plus the strike price multiplied by the contract amount. Note that the strike price for a futures contract is the spot price when signing the contract, that is sc,t−1 . As for the call option, if the spot price sc,t is greater than the strike price spc,d,t−1 then the contract will introduce a benefit as (sc,t − spc,d,t−1 )Qderc,d,t−1 . Otherwise, because the owners of this call option have the right to give up this contract, the payoff of this contract is zero. Therefore, the cost associated with such call option is the contract setup cost minus the payoffs. The calculation of the put option is similar to the call option. Thus, the cost

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associated with three types of contracts is given by,   P   d = futures  c∈C {Zderc,d,t scc,d + sc,t−1 Qderc,d,t−1 },    P + Costdt = c∈C {Zderc,d,t scc,d − (sc,t − spc,d,t−1 ) Qderc,d,t−1 }, d = call option      P   c∈C {Zderc,d,t scc,d − (spc,d,t−1 − sc,t )+ Qderc,d,t−1 }, d = put option, where the operator (x)+ = x if x ≥ 0, and = 0 otherwise. The production cost is expressed by the summation of production cost of each unit, which is given by, Costpt =

X

{P rodCostk

XX

STc,l,k,t },

c∈C l∈L

k∈K

while the inventory holding cost is given by, Costht =

X

Invc,t hc .

c∈C

SAA Solution Method The well known SAA method is widely used in stochastic programming. 11 By generating a random sample {s1 , s2 , . . . , sN } of the stochastic price S, we can solve the deterministic approximation of objective function (27) as, N 1 X 1 min{qα + (Costsi − qα )+ } qα∈R N i=1 1 − α

(28)

where N is the pre-defined sample size, and Costsi is the total cost associated with oil price sample si . Equation (28) is also used as the estimator suggested by Trindade et al., 38 which has been proved to have some good mathematical property. In this research, the oil prices are assumed to follow the Geometric Brownian Motion (GBM), which is an assumption often made in previous research. 39,40 Let St denote the 18


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while the property data for simple hydrocarbons are obtained from Poling et al.. 41 The production process consists of five production units including catalytic reforming, catalytic cracking, hydrotreatment and blending, producing 6 end product. All the relevant data are available upon request. Note that in order to simplify the presentation of the results, we use scaled data here to illustrate the results. All of the tested models are implemented with GAMS 22.4 in Core i7 2.93 GHz CPU and RAM 4.0 GB. To solve the MINLP problem, the convex solvers DICOPT is applied, while MIP problem is solved with CPLEX.

General Results To quantify the benefit obtained by introducing the integrated risk hedging framework, we conduct two comparison studies. Case 1. The Fixed Yield (FY) model where the yield of crude oil in CDU is fixed are used for sensitivity study. This case study first solve the FY model, then, we use the same data as input, and fix the financial hedging decision variable obtained by the FY model to solve the proposed FI model. Under this setting, the results reveal the benefits of introducing the FI model. Note that the difference between FY model and the proposed FI model is that the distillation yield of the CDU in the FY model is constant. The results of minimizing CVaR for Case 1 are shown in Table 3, in which we also report the corresponding VaR, total expected cost, procurement cost and derivatives cost obtained form the optimization. As can be seen, the proposed method yields nearly a 10% reduction in CVaR (24,021 vs. 21,552) and a 17% reduction in total cost (23,792 vs. 19,913). This result verifies the benefits of introducing the proposed FI model as an operational hedging tool. Case 2. We compare the deterministic model where price is substituted by the mean value, with the proposed model. Both of the two models (denoted as FI-d and FI, respectively) consider financial contract and FI CDU model, and this comparison helps to 20


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demonstrate the benefits of considering the stochastic model. We also report the results of minimizing CVaR for Case 2 in Table 3. Similarly to the conclusion in Case 1, the proposed FI model yields nearly 13% (23,074 vs. 20,137) and 14% (21,593 vs. 18,596) reduction in CVaR and total cost, respectively. Table 3: Comparison of CVaR and cost composition. Case

1

2

Model

CVaR

VaR

Total Expected Cost

Procurement Cost

Derivatives Cost

FY model FY-FI model % of reduction FI-d model FI model % of reduction

24,021 21,552 10.28 23,074 20,137 12.73

23,792 20,087 15.57 22,513 19,976 11.27

21,908 19,913 16.92 21,593 18,596 13.88

17,561 16,039 14.41 14,553 8,405 42.24

2,318 2,318 0 4,597 5,904 -28.43

Another issue of concern is how the proposed integrated risk hedging framework performs in terms of computational requirements. In this study, the aforementioned FY model is also used to compare with the proposed FI model. Note that different sample size is considered, e.g. FY-300 represents FY model with sample size equals to 300. We also compare the cases of the deterministic FY and FI model where the oil price is substituted by the mean value, denoted as FY-d and FI-d, respectively. The computational results are given in Table 4. Note that each group consists of 10 independent instances and the average values are recorded for comparison. Also note that according to Pflug, 35 the SAA method guarantee that the approximation of the objective function will converge to the optimal solution ultimately. For moderate sample size (e.g., 3000), the optimal value for FY model can be obtained on average in 5.89s, whereas the optimal value for the FI model can be obtained in 31.51s, which demonstrates that the proposed integrated risk hedging framework together with the SAA method can provide optimal solutions within acceptable computational times.

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bound are shown in the secondary axis (right axis). We can see from Figure 7 that the impact of the inventory is significant, which yields about 10% CVaR reduction. This result can help managers to realize that expanding the inventory upper bound will lead to the improvement of risk management. Note that when the inventory capacity is very small (e.g.,100), spot buying is preferred over contract buying.

Impact of FI CDU Model In this section, the FY model considering financial contracts is used for comparison study. Note the only difference between FY model and the proposed FI model is that FY model uses simplified fixed yield, which enables us to analyze the benefit of introducing the nonlinear FI CDU model. By minimizing CVaR of both models, Figure 8 shows the results of CVaR and the corresponding VaR and total cost in each case. !"#$%&'(#$)%' )"###$

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Integrated Operational and Financial Hedging for Risk Management in

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