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Integrated Decision Support Model for Hedge Trading and Production Planning in the Petrochemical Industry Hweeung Kwon,† Kyungjae Tak,† Jae Hyun Cho,‡ Jiyong Kim,*,§ and Il Moon*,† †

Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei ro, Seodaemun-ku, Seoul 03722, Korea Engineering Development Research Center (EDRC), Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea § Department of Energy and Chemical Engineering, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Korea ‡

ABSTRACT: Using an optimization technique, this study proposes a new decision support system to improve the economics of petrochemical industries. In achieving the goal, we first develop two optimization models to support the decisions on (1) the hedge trade by minimizing purchase costs of raw materials, and (2) the production planning by maximizing profits from product sales. We then integrated these two models into a single decision support system using a recursive two-stage programming framework. On the basis of the integrated framework, we systematically identify the optimal solution, that is, the maximum profit, by simultaneously determining timing, amount, and price of raw materials to purchase, and the strategies for facility operation and product sales. To illustrate the capability of the proposed system, it was then applied to the business model of the petrochemical company in Korea. As a result, compared to the base case, it is revealed that the profitability of the petrochemical company could be improved by up to 4.82% by optimized hedging trades and 4.30% by optimizing the production plan. ology for financial risk management using the SP approach, in conjunction with real applications. Their model included downside risk as a major financial risk, and considered the risk tendency of the decision-maker. This group also used a business model and theory (e.g., short- or long-term option contracts) to hedge against financial risks in inventory and logistics management.9 Ponsakdi et al.10 proposed a new method, namely optional contracts, for the stable management of financial risks in the scheduling and planning of refinery operations. In other study, Leiras et al.11 applied a stochastic price estimation model to the planning problem of refinery operation under various uncertainties. As the global petroleum and petrochemical industry continues to become more competitive, new theories and applications for planning and scheduling in the petrochemical and refinery industries have recently been presented in attempts to ensure profitability. Lee et al.12 developed an optimization model in the form of a mixed integer linear

1. INTRODUCTION Strategic decision-making and business planning in the petrochemical industry is a challenging issue, particularly given that the process takes place under changeable and uncertain market conditions. With recent increases in the competitiveness in this environment, the ability to secure a stable source of cheap raw materials has become important in ensuring the sustainable profitability of the petrochemical industry. Exacerbating this issue is that the international trade prices of raw materials (e.g., naphtha, ethane, and condensate) can significantly fluctuate, which means enterprises must plan and make decisions using advanced business models and rigorous optimization tools.1 In attempts to address financial risk and to support business management in the petrochemical industry, a number of studies have developed new approaches and models.2−7 Of particular note, two-stage stochastic programming (SP) has been widely used owing to its theoretical pliability in dealing with practical issues.6 For instance, the first stage of this approach enables high-level decisions to be made on, for example, raw material supply, demand forecasts and sales, and production rates, while the second stage facilitates optimization of detailed operation schedules. Barbaro and Bagajewicz8 proposed a new method© XXXX American Chemical Society

Received: Revised: Accepted: Published: A

September 12, 2016 January 2, 2017 January 17, 2017 January 17, 2017 DOI: 10.1021/acs.iecr.6b03527 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 1. Life stages of naphtha as a raw material in the petrochemical industries.

optimizing business decision-making and production planning in petrochemical plants.

programming (MILP) to address operational issues such as product unloading, blending, and inventory management. Other studies have focused on developing a new MILP model for the scheduling of a production system, one that includes both continuous and batch tasks.13,14 Zhang et al.15 presented an optimization-based approach for refinery planning that integrates external material networks such as hydrogen and steam. Kim et al.16 proposed an optimization model for procurement and production planning based on the effect of corrosion in refinery processes. Mouret et al.17 then introduced a new mixed integer nonlinear programming (MINLP) model to solve the large-scale problem of integrating refinery planning and crude oil operation scheduling. Reddy et al.18 proposed an MINLP model and innovative solutions for the scheduling of loading and unloading of storage tanks. To ensure maximum business profitability, a number of studies have developed and implemented business models and further optimization techniques. These include an in-house optimization model for the Norwegian petrochemical industry,19 and MILP models that address geopolitical issues of the Korean petrochemical industry.20 Product management, supply chain management, and logistics are included in these models as essential topics.21−24 To efficiently resolve complex problems in petrochemical plants, businesses, and markets, diverse objectives have been considered as the objective function in these optimization frameworks, which include minimizing costs, minimizing raw material requirements and stock levels, minimizing harmful environmental impacts, and maximizing annual profit.25−27 While many studies have addressed the profitability of the petrochemical industry, few studies have yet to provide effective solutions for strategic decision-making and business planning against fluctuating supply and demand markets. Importantly, the petrochemical industry requires a dynamic model, one providing well-informed solutions for the trading value and direction (e.g., quantity, timing, and pricing) of a broad range of petrochemical commodities. In particular, strategic insights into hedging against business risks in a rapidly changing market is critical for ensuring the regional and value-chain competitiveness of the petrochemical industry. In this study, we propose a new system dynamics capable of supporting decision-making with regards to the timing and pricing of naphtha, a key raw material in the petrochemical industry. In particular, this model facilitates better hedging against business risks by adopting a robust price forecasting methodology that consolidates the many influences on prices in the petrochemical markets. In achieving the goal, we then develop a new optimization model using a nonlinear programming (NLP) technique, which maximizes profit by

2. PROBLEM DESCRIPTION We address here decision-making problems in the hedge trade of naphtha, along with production planning. Note that the hedge trade is one of the business strategy used to protect an investment or portfolio against the probability of a negative event (i.e., loss) by buying securities in the opposite position to the asset being protected. Most petrochemical companies have adopted the hedge trade system to protect their investment from fluctuations in the prices of chemicals. The objectives of this study are to (1) determine naphtha purchase costs and timing for profitable hedge trades and (2) develop an operational strategy for efficient production planning. We assume here that there is one naphtha supplier, while the prices and costs of industrial materials are predictable.28 We then solve the problem by developing a new optimization model that allows us to identify optimal hedge trade and plant operation solutions. Note that the model is subject to economic and technical conditions such as (1) satisfying demand with regard to the timing and quantities of products, (2) product sales based on market prices, (3) purchasing naphtha using price forecasting, and (4) limited naphtha production yields due to chemical reactions in the manufacturing plant. A typical life cycle of naphtha as feedstock in the petrochemical industry is depicted in Figure 1. Naphtha from a production site is transported to a storage facility and then fed to a petrochemical facility for the manufacturing of value-added products. The system boundary of this study is from transportation to the usage of naphtha, as shown in Figure 1. Decisions related to the lifecycle of naphtha are made using the proposed decision support model, ranging from the timing, quantity, and price of naphtha purchases to the production schedule in the facility during the planned period.29 The planning model maximizes a profitable hedge or total profit involving the transportation system and operation. Some system rules depend on the planning horizon. The major assumptions of this study are as follows: (1) naphtha purchases and the sale of products occur once a month; (2) transport vessels deliver once a month; (3) product yields are fixed during this study period; (4) product inventories are assumed considering the amount of output from the cracking unit; (5) economic factors such as sea waiting costs, pumping costs, and changeover costs are ignored; and (6) naphtha trade consists of one future and two spot trades (i.e., three months). The petrochemical industry typically establishes naphtha purchase plans based on forecasts of raw material markets. For B

DOI: 10.1021/acs.iecr.6b03527 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research example, the naphtha purchase process for petrochemical companies in Korea normally takes two months from confirmation of the purchase plan to arrival at the plant. Most petrochemical companies in Korea import naphtha from the Middle East and India, and engage in arbitrage in Europe; they typically import more than 90% of naphtha from suppliers in the Middle East. Typically, when petrochemical companies execute a purchase plan, they are exposed to financial risks owing to fluctuations in the naphtha price that occur during the period from when the raw material is purchased to when payment is made. For example, when large fluctuations occurred in naphtha prices as a result of the global economic crisis in the third quarter of 2008, a significant gap in naphtha prices was reported in the profits of the petrochemical plants in South Korea. One important way to reduce the financial risk considering naphtha purchases is thus to develop a portfolio using a hedging model. A futures trade refers to the right to buy commodities at a specific future date. Specifically, naphtha future trades help to avoid the financial risks of price fluctuation by fixing the naphtha purchase price. A petrochemical company that has a naphtha purchase plan will purchase a futures trade to avoid the possibility of a naphtha price rise, that is, if the naphtha price suddenly increases, the price of futures trade will increase at the same time.

(3)

AP(i , i + 3) ≥ 0

(4)

AILi

AIUi

where and denote the lower and upper levels of inventory in month i, respectively. 3.2. Optimization Model for Production Planning. Planning for the petrochemical industry market under uncertain conditions is a challenging issue. Kwon et al.30 optimized petrochemical process planning using price prediction and process modeling. Petrochemical companies are generally affected by rapidly changing market conditions, which directly affect their net profit. In particular, the net profit fluctuates significantly with raw material prices, such as naphtha, ethane, and condensate and final products. Therefore, it is difficult for most petrochemical companies to establish an optimal management plan. Petrochemical plants can produce various products from a wide range of processes and raw materials, such as naphtha, natural gas, and condensate. In general, they prefer to produce the most profitable products. However, these opportunities might be limited by factors such as product demand in the global market. This study presents a plan for hedging trades for purchasing raw materials and processing in order to satisfy the demand, and at the highest profit. The decision variables are naphtha procurement decisions, product sales, and inventory management. Here, the period for the optimization model is 1 month, owing to the data set. This model includes predicted prices for naphtha, actual product prices, and the amount of naphtha procured, as well as the inventory capacity in the given period. 3.2.1. Objective Function. The objective of the optimization model is to maximize the total profit realized over a specified planning horizon. The function considers various product sales, hedging trades of raw materials, operation costs, and inventory costs in a planning period t. Equation 5 gives the objective function as

3. DEVELOPMENT OF DECISION SUPPORT MODEL 3.1. Optimization Model for Hedge Trades. 3.1.1. Objective Function. The objective function minimizes the average naphtha purchase price. Naphtha purchase price optimization considers hedging trades and the amount of naphtha purchased. The average naphtha purchase price is calculated as the final procurement plus the profitable hedge trade. In addition, the price includes inventory costs and naphtha forecasting prices during the following two or three months. Equation 1 presents the objective function of the NLP model that minimizes the purchase price. Minimized Naphtha Purchase Price. ⎛(AP(i , i + 1) + AP(i , i + 2)) + AP(i , i + 3) × PPi ⎞ ⎜ ⎟ ⎟ min⎜+AP(i + 1, i + 2) + AP(i , i + 3) × PPi + 1 ⎜ ⎟ ⎜+AP ⎟ (i + 2, i + 3) ⎝ ⎠

AIi L ≤ AIi ≤ AIi U

maximum profit =

∑ Tpt ,

∀t∈T (5)

t∈T

and Tpt = pst + ht t − oc t − ic t − rt

(1)

(6)

where Tpt, pst, htt, oct, ict, and rt denote the total maximum profit, the total revenue from product sales, the profitable hedging cost considering naphtha purchases and sales, the operation cost, inventory cost, and financial risk in planning period t, respectively. Total Revenue from Product Sales.

where PPi denotes the price of the purchase in month i and AP(i,i+1) is the amount of the hedge in month i + 1 that was purchased in month i. Inventory Managements. Inventory levels are managed based on existing inventory, the amount of naphtha, and the running capacity of the petrochemical plant. In this study, the total inventory capacity is 300 000 tons and the minimum level of inventory is 80 000 tons. The amount of naphtha in the cracking unit is assumed to be 300 000 tons.

pst =

∑ ∑ Pm,t PM m,t m ∈ Ms t ∈ T

(7)

where Pm,t denotes the price of product m during period t, and PMm,t denotes the amount of product m sold in the market during period t. The total profit is subsequently expressed as the product price multiplied by the amount of each product. Profitable Hedge. For the hedge cost, refer to section 3.1. Operation Cost. In this study, the operation cost is considered to be the cost of unloading from the vessel to an inventory tank.

AIi + 1 = AIi + AP(i − 2, i + 1) + AP(i − 1, i + 1) + AP(i , i + 1) − AC (2)

where AIi denotes the amount of inventory in month i, and AC is the amount of raw material in the cracking unit. 3.1.2. Constraints. The constraints for the inventory level management are as follows:

NUr , p , i = NUR ru, p , iUTr , p , i C

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∑∑ ∑

material purchased and product production. The initial and final amounts of inventory of raw material r or product m in period t are expressed as follows:

NUr , p , i = TSp (9)

r ∈ R p ∈ P i ∈ IMr

where NUr,p,i denotes the amount of raw material r unloaded and transferred from p to i; NURur,p,i denotes the transferred rate of raw material r from p to i; UTr,p,i indicates the time taken for p to unload raw material r into i; and TSp is the total size of parcel p. In general, the unloading cost depends on the amount of naphtha purchased. Inventory Cost. The inventory cost includes the cost of storage tank management for both raw materials and final products. ic t =

IM r , i , t = IM r , i ,(t − 1) +

p∈P

IVr , i , t =

m ∈ Mi t ∈ T

IVm , i , t =

s

(10)

VLr,i

(12)

where AOFm,t denotes the amount of product m from the cracking unit during period t; AFt denotes the amount fed into the cracking unit during period t; and ym is the percent yield of the cracking unit for a specific raw material. 3.2.2. Constraints. Demand Constraints. (13)

DmL , t ≤ PM m , t ≤ DmU, t

(14)

where LMm,t denotes the amount of lost demand for product m during period t; Dm,t indicates the amount of demand for product m during period t; and DLm,t and DUm,t are the lower and upper bounds on the demand of product m during period t, respectively. Availability Constraints for Raw Material. APrL, t ≤ APr , t ≤ APrU, t

(18)

IVrL, i ≤ IVr , i , t ≤ IVrU, i

(19)

IVmL , i ≤ IVm , i , t ≤ IVmU, i

(20)

IVUr,i

and denote the lower and upper levels of raw material r in storage tank i, respectively, and IVLm,i and IVUm,i are the lower and upper inventory levels of product m in storage tank i, respectively. 3.3. Integration of Decision Models. For a comprehensive model capable of supporting the decision-making process in a petrochemical business, from hedge purchases to plant operation, we developed a new model by integrating the above two optimization models in the framework of recursive twostage programming. Recursive two-stage programming is an attractive option for operation strategies because it allows the decision-maker to explicitly analyze uncertainties in the chemical markets. It deals with situations in which some (or all) of the parameters of a decision-making problem are described by uncertain (or random) variables, rather than by deterministic quantities. This technique consists of two optimization models: a raw material purchase model (section 3.1), and a facility planning model (section 3.2), as shown in Figure 2. In the first stage, the purchase cost in the hedge trade market of naphtha is determined, and the production plan is then optimized in the second stage. The rule of the first stage, which determines the price and quantity to be purchased, is dependent on the hedge trade, and is constrained by the operation features of the inventory. The optimal production plan is then established in the second-stage model, based on the results of the first-stage model. Accordingly, the key constraints of the second stage are the purchase price, quantity, and timing of naphtha as a raw material. To apply the heuristics to a scheduling model, we need to implement a solving procedure, which can be described as follows: • We assume initial approximated values for PP and AP (i.e., PPi=1 and AP(1,2)). The initial values are determined using the first optimization model, which is only subject to the inventory level constraints at period i. • The initial approximations for PP1 and AP1,2 are then used to execute the second optimization model, starting with the assumed hedge period. We identify major

(11)

PM m , t + LM m , t ≥ Dm , t

(17)

where IMr,i,t denotes the amount of raw material r at the end of period t; Rc denotes the amount of raw material r in the cracking unit; IVr,i,t is the total inventory level of raw material r in storage tank i during period t; and IVm,i,t indicates the total inventory level of product m in storage tank i during period t. In addition, inventories of the raw material and product should satisfy the following constraints:

where PNt denotes the financial penalty in period t; Riskt(p,Ωt) is the probability of having profits lower than the target profit (Ωt); ρs is the probability of scenario s ∈ S in period t; and λs(Ωt) is a binary variable in which the value is 1 if the profit of the scenario s is less than the target profit in period t, otherwise, the value is 0. Note that although the risk management is very important when purchasing naphtha, we ignore financial risk owing to its relatively small effect compared to the large and profitable contribution by the hedge trading. Yield Equation.

AOFm , t = AFt ym

(16)

∑ ∑ IM m,t m ∈ Ms t ∈ T

where IPr,t denotes the inventory cost for raw material r during period t; IMr,t denotes the amount of inventory of raw material r during period t; IPm,t denotes the inventory cost for raw material r during period t; and IMm,t presents the amount of inventory of product m during period t. This study uses naphtha as a raw material r. Financial Risk. The risk cost accounting for the penalty by occurred financial risks can be expressed as31 rt = PNt Risk t(s , Ω t ) = PNt ∑ ρλ (Ω t ) s s

∑ ∑ IM r ,t r∈R t∈T

∑ ∑ IM r ,tIPr ,t + ∑ ∑ IM m,tIPm,t r∈R t∈T

∑ NUr ,p,i − Ac

(15)

where APr,t denotes the amount of raw material purchased during period t, while APLr,t and APUr,t are the lower and upper bounds of the availability of the raw material during period t, respectively. Inventory Constraints. In general, a certain level of inventory must be maintained in both periods to ensure raw material or product availability, given the amount of raw D

DOI: 10.1021/acs.iecr.6b03527 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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In general, analysis methods based on this scenario have been proven to give reliable and practical results of optimization under uncertainty, despite the resulting sharp increase in the problem size and the number of uncertain parameters.32,33 These cases confirm the accuracy of the proposed model in this study; we also present realistic possibilities for the model in petrochemical plants. The following describes the results and analysis of this research. 4.1.1. Case study 1: Normal Trading, Considering Naphtha Price Predictions (Two Months). Purchased naphtha takes an average of two months to be transported from the supplier to the petrochemical plant. Thus, most petrochemical companies determine the amount of naphtha they need to purchase two months in advance. Figure 3 shows the process from naphtha purchase to arrival.

Figure 3. Naphtha purchase process (two months).

In Case Study 1, futures trading takes place in the first month before the shipment, followed by spot trading in the second month between shipment and arrival. For example, if a petrochemical company has traded 20 000 tons with another buyer as futures in the first month after they purchase 100 000 tons, and spot trading does not take place in the second month, 80 000 tons of naphtha will be unloaded at the petrochemical plant. In this way, naphtha purchase prices are optimized based on the NLP model, by considering hedge trades over two months. Table 1 shows a comparison of actual and proposed approaches for naphtha price predictions over two months. Figure 2. A recursive optimization framework for integrated decisionmaking.

Table 1. Comparison of Trading Methods (Two Months) actual trade

decision variables related to facility planning, such as the amount of product and raw materials required, inventory levels, and facility operability. • The iterative step described in Figure 2 is subsequently repeated until the solutions of the two different strategies are determined as values that lie within the initially assumed upper and lower boundaries in successive iterations, or until the maximum number of iterations has been reached.

total purchase quantity (million ton) average purchase price (USD/ ton) total cost (million USD) profit savings (million USD)

conventional trade

optimized trade

1.86

1.88

1.90

938.24

925.06

913.93

1,745.12

1,736.71 8.41

1,731.91 13.21

In Table 1, actual trade means that the same quantity of naphtha is purchased continuously per month. Conventional trade indicates buying naphtha based on the heuristics of the buyer. The results of heuristics are determined based on variances of the price obtained using the forecasting model. Finally, optimized trade shows the purchase of naphtha based on the optimization results of a numerical model. Figure 4 presents a comparison of naphtha purchase prices from three trades. In general, naphtha purchase prices per month for the three trades display similar trends. In the figure, conventional trade based on heuristics saves USD 8.41 million over the actual trade. However, the optimized trade using hedging could save USD 13.21 million more than the actual trade, and USD 4.80 million more than conventional trade.

4. RESULTS AND DISCUSSION The integrated decision support model is implemented in the General Algebraic Modeling System and solved using the NLP solver of gPROMS. 4.1. Naphtha Purchase Strategy. Here, we illustrate a practical application of the NLP model. In this study, we focus on two aspects, considering practical details of the petrochemical industry: • normal trading, considering naphtha price predictions • two-month prediction • three-month prediction • hedge trading in the case of increasing inventory levels and naphtha purchases. E

DOI: 10.1021/acs.iecr.6b03527 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Table 2. Comparison of Trading Methods (Three Months) actual trade total purchase quantity (million ton) average purchase price (USD/ ton) total cost (million USD) profit savings (million USD)

conventional trade

optimized trade

2.76

2.82

2.80

938.24

909.93

883.09

2,589.53

2,563.81 25.72

2,542.65 46.88

million tons per year. Figure 6 illustrates the optimal purchase price per month in 2011.

Figure 4. Comparison for optimal naphtha purchase price of three trades (two months).

4.1.2. Case Study 2: Normal Trading Considering Naphtha Price Predictions (Three Months). Petrochemical companies consider predicted naphtha purchases for two months and for three months in attempts to increase their net profits. If the predicted naphtha price increases after three months at the present point, they could decide to sell naphtha on the way back to the supply point. Figure 5 highlights the naphtha purchase process based on a three-month prediction.

Figure 6. Comparison of optimal naphtha purchase prices of three trades (three months).

This study also compares the total purchase costs, which are based on optimizations that resulted in a profit savings of USD 20.50 million per year for petrochemical companies. For example, the sales for H petrochemical company in Korea were USD 7.9 billion, generating a profit of USD 549.6 million in 2013. This savings cost reduced the price of naphtha by 8.53% in comparison with the business profit in 2013. Overall, the model result using optimization is preferable to the heuristic method. The purchase price of the heuristic method was similar to the actual price, but the average price of the optimized trade was approximately 55.15 USD/ton cheaper than the actual price. 4.1.3. Case study 3: Naphtha Trade with Increased Naphtha Purchase Amounts and Inventory Levels. This study indicates that the total purchase quantity and unit average purchase price are greatly influenced by the amount of naphtha purchased and the inventory tank capacity. As mentioned above, the inventory tank capacities ranged from a minimum of 80 000 tons to a maximum of 300 000 tons. First, let us focus on increasing the inventory tank capacity, which helps to create profit for a petrochemical company. However, if the company fails to adjust their inventory, they could incur enormous losses. Therefore, the company should manage their inventory capacity effectively in order to improve their gross profit. Increasing the inventory capacity has the following expected effects: • reduction of average naphtha unit purchase price • reduction of total naphtha purchase cost • improvement of profit savings Cases 1 and 2 of Tables 3 and 4 present the optimization results for increasing the naphtha inventory capacity, and include naphtha price predictions for two or three months, respectively. Notably, Table 3 shows that increasing the inventory capacity is not really influenced by the total purchase

Figure 5. Naphtha purchase process (three months).

In this study, the system dynamics (SD) forecasting model is posited as providing the best results. The innovative SD model is valuable for determining the point of purchase because it considers both quantitative and qualitative data. Lyu et al.34 predicted values for naphtha demand and supply based on a causal SD model; an SD model based on a causal loop considering human and psychological heuristics was also applied to naphtha price forecasting. Using heuristics is an important approach to decision-making at the point of purchase, and the efficacy of the approach can affect naphtha purchases. This type of heuristic approach allows companies to reach reasonable solutions. Case Study 2 shows the optimization results for minimizing the naphtha purchase price. The total purchase quantity of naphtha and the optimal naphtha purchase price per month are analyzed with regards to futures and spot trading from one to three months. The buyer determines the naphtha purchase after considering the predicted naphtha price.30 Therefore, naphtha price prediction is seen to be an important factor for minimizing the average purchase price, which is generated using optimization for the naphtha purchase based on the NLP model. Table 2 compares the results of the actual and proposed trading methods. The results of this optimization problem consider hedge trading per month, the amount of naphtha purchased, inventory levels, and the naphtha prediction price. In Table 2, the average purchase prices of the actual, conventional, and optimized trades were 938.24 USD/ton, 909.93 USD/ton, and 883.09 USD/ton, respectively. The total quantities of the purchased naphtha for each approach were 2.76, 2.82, and 2.80 F

DOI: 10.1021/acs.iecr.6b03527 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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naphtha, they could save 52.09 USD/ton compared to the actual trade. The total costs for the optimized trade in each case were USD 1686 and USD 1664 million, respectively, for profit savings of USD 58.40 and USD 80.21 million. As such, companies could improve business profits by adjusting naphtha procurement amounts. Case 4 of Table 4 presents the optimization results for increasing the naphtha procurement by ±100 000 tons. This case includes the additional purchases of approximately 0.18 million tons of naphtha. The average unit price for naphtha procurement and the total purchase cost were dramatically reduced using this optimization model, resulting in profit savings of 66.75 USD/ton and USD 101.81 million, respectively. 4.2. Facility Operation Strategy. On the basis of the results of the first stage, the production planning model in the second stage was executed to maximize the total profit. The case studies for production planning are as follows: • case 1: baseline • case 2: increasing the amount of naphtha in the cracking unit (+50 000 ton in comparison with the base case) • case 3: increasing the inventory capacity (+20% in comparison with the base case) • case 4: Extending the range of amount of naphtha hedge trades (±50 000 ton in comparison with base case) The optimization results of these cases show that a maximum profit is achieved in the proposed model. In addition, this study suggests a production plan that considers various practical environments. The results are as follows. Note that for the parameters for the base case (i.e., Case 1), we adopted industrial data from Korean petrochemical industries as the initial conditions.30 Table 5 shows the initial conditions of the optimization problem.

Table 3. Case Studies of Optimized Trades Considering Increasing Inventory Capacity and Naphtha Purchased (Two Months)a case 1 total purchase quantity (million ton) average purchase price (USD/ton) total cost (million USD) profit savings (million USD)

case 2

case 3

case 4

1.87

1.82

1.87

1.88

915.88

906.02

904.41

886.15

1,708.10 37.02

1,648.96 96.16

1,686.72 58.40

1,664.91 80.21

a

Note: case 1, inventory capacity (+50 000 ton); case 2, inventory capacity (+100 000 ton); case 3, amount of naphtha purchased (±50 000 ton); case 4, amount of naphtha purchased (±100 000 ton).

Table 4. Case Studies of Optimized Trades Considering Increased Inventory Capacity and Naphtha Purchased (Three Months)a case 1 total purchase quantity (million ton) average purchase price (USD/ton) total cost (million USD) profit savings (million USD)

case 2

case 3

case 4

2.91

2.93

2.94

2.95

881.00

877.59

859.08

844.16

2,561.31 28.22

2,574.96 14.57

2,522.78 66.75

2,487.72 101.81

a

Note: case 1, inventory capacity (+50 000 ton); case 2, inventory capacity (+100 000 ton); case 3, amount of naphtha purchased (±50 000 ton); case 4, amount of naphtha purchased (±100 000 ton).

quantity. In Case 2 of Table 3, with the increased inventory tank capacity of 100 000 tons, the total purchase quantity is reduced by 40 000 tons, and the average naphtha unit purchase price was reduced by approximately USD 32.22 per ton compared with the actual trade. Furthermore, the profit savings for each optimized trade obtained by increasing the inventory tank capacity (+50 000 tons, +100 000 tons) were USD 37.02 million and USD 96.16 million, respectively. Cases 1 and 2 of Table 4 show the optimized trade, including hedging for three months, considering an increased inventory tank capacity of 100 000 tons. As the inventory tank capacity was increased by 50 000 and 100 000 tons, the total purchase quantities were 2.91 and 2.93 million tons, respectively. In other words, the amounts of naphtha purchased because of the optimized trades were 0.15 and 0.17 million tons more than in the actual trade. Furthermore, the total profit savings for each case were USD 28.22 and USD 14.57 million. Note that the total profit savings in Case 2 was less than that in Case 1, because more naphtha could be purchased. Importantly, a petrochemical company using inventory tank management could more cheaply purchase naphtha than in the previous trade, at a maximum of 60.65 USD/ton, though the average purchase price was greatly affected by the amount of naphtha purchased. This study was applied to basic procurement increases in the range of ±50 000 tons and ±100 000 tons. Cases 3 and 4 of Tables 3 and 4 present the optimization results for increasing purchases based on hedge trades, respectively. Cases 3 and 4 of Table 3 consider hedge trades for two months, in which the total purchase quantities were not significantly affected by the additional procurement. However, the average unit price for naphtha procurement was significantly reduced after considering hedge trades. For example, if petrochemical companies buy 100 000 tons more

Table 5. Lists of Initial Condition list of initial condition purchase amount (ton) inventory capacity (ton) naphtha ethylene propylene butadiene BTX others thermal cracking yield ethylene propylene butadiene BTX others

information 300 000 190 000 190 000 20 000 15 000 5 000 7 500 15 000 0.33 0.16 0.10 0.21 0.20

The monthly naphtha purchased in the four cases examined is summarized in Table 6, with the resulting profits depicted in Figure 7. First, the figure shows that the monthly profits for the four cases are similar due to the identical sale price of the product. For instance, the monthly profit in March and April shows the highest value across all cases, because the products are sold at the highest price. Next, the amount of naphtha purchased in hedge trading is determined using actual product prices. If the actual product prices of the next month decrease, the producer tries to sell more products during this month. G

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approximately 500 000 tons more naphtha was purchased in Case 2 than in the other cases. In addition, 600 000 tons more product was produced than in the other cases, with the maximum quantity nearly sold per month. For these reasons, the total profit is very high. In particular, the quantity of naphtha purchased in June was higher than in either May and July. However, the total profit in June was lower because of the decreased prices of naphtha and most other products. The total profit in case 2 was calculated to be 19 billion USD, which had contributions from the sales of ethylene, propylene, butadiene, BTX, and others (14.3 × 106 tons, 7.0 × 106 tons, 4.3 × 106 tons, 9.1 × 106 tons, and 8.7 × 106 tons, respectively). Similar to case 1, if the product price in the next month increases, the minimum quantity of the product of the current month can be sold after the maximum levels are stored in each inventory tank. The results of case 3, in which the inventory capacity is increased by 20% in comparison to the base case, are shown in Figure 7c. The maximum inventory capacities of naphtha or other products (ethylene, propylene, butadiene, BTX, and others) in case 3 are 360 000 tons, 120 000 tons, 60 000 tons, 48 000 tons, 72 000 tons, and 60 000 tons, respectively. In Case 3, the amount of naphtha purchased was approximately 100 000 tons larger than in case 1 due to the increased room of the inventory tank. This increase in inventory capacity resulted in additional profit, which can be used to offset additional expenses incurred by the larger-inventory management and operation. The total profits from case 3 is USD 18.3 billion, based mainly on the selling of ethylene, propylene, butadiene, and BTX; the amount is 12.4 × 106 tons, 6.0 × 106 tons, 3.8 × 106 tons, 7.9 × 106 tons, and 7.7 × 106 tons, respectively Figure 7d shows the results of case 4, which considers facility operation based on increased naphtha hedge trading. Relative to the naphtha hedge trading range in case 1 (±200 000 tons),

Table 6. Monthly Profit and Amount of Naphtha Purchase Per Month for Each Case [1000 ton] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

case 1

case 2

case 3

case 4

190 320 310 305 155 300 375 273 252 300 300 300

320 310 305 155 300 375 273 252 300 300 300 300

190 372 361 240 344 413 300 315 348 377 341 349

345 323 311 111 300 400 263 237 300 300 300, 300,

Therefore, in the case of ethylene, the maximum quantity should be almost completely sold out because the product price decreases the next month. As the base case, we solved case 1 in which the production planning is designed to maximize the total profit based on constraints on the amount of naphtha purchased and on the inventory capacity of either naphtha or another product. Here, the total profit and profit per month were examined using the actual product price and hedging cost. Figure 7a presents the results of this optimization problem, with monthly profits used as the basic strategy for production planning. Figure 7b shows the resultant profits for case 2, in which the amount of naphtha in the cracking unit is increased by 50 000 tons in comparison with the base case (case 1); that is, the maximum amount of naphtha that can be processed in the cracking unit is 350 000 tons per month. This increase in the capacity of the cracking unit can lead to increased room for purchasing naphtha and selling products. As a result,

Figure 7. Monthly profit by selling the products of (a) case 1, baseline; (b) case 2, increased capacity of naphtha cracking unit; (c) case 3, increased inventory capacity; and (d) case 4, increased availability of naphtha due to hedge trade. H

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Industrial & Engineering Chemistry Research an additional amount (i.e., ±50 000 tons) is allowed in case 4. Similar to the other cases, most of the profit is determined by the product prices, that is, the profit per month increases with higher selling prices. Overall, the amount of naphtha purchased is seen to be considerably influenced by the predicted naphtha price. As shown in Figure 7d and Table 6, in April, companies could purchase a smaller amount of naphtha than in other months because the naphtha prediction and the actual product prices dramatically decreased. The larger amount of naphtha in the petrochemical plant in June indicates that the decisionmaker of the petrochemical company bought a minimum amount of naphtha, based on the operational quantity of the plant, owing to the decrease in predicted prices in April and May. Naphtha was constantly purchased after September owing to various constraints. The total amounts of ethylene, propylene, butadiene, BTX, and other products purchased were approximately 12.4 × 106 tons, 6.0 × 106 tons, 3.8 × 106 tons, 7.9 × 106 tons, and 7.5 × 106 tons, respectively. This study performed optimizations based on the changing values for the amount of naphtha to be purchased using hedge trading, the inventory capacity of naphtha and products, and the amount of naphtha in the cracking unit. Figure 8 shows the

the actual trade. Notably, an optimal production planning model that included price forecasting and hedging models was developed, which gave rise to an increase in savings of 4.30% against the base case. In conclusion, this study combined an optimal production and logistics network plan for a petrochemical plant with a hedging model for predicting naphtha prices. In this way, the study makes a significant contribution to support better decision-making processes for business activities in the petrochemical industry, such as naphtha purchasing and production planning under highly changeable chemical market conditions. The optimization-based decision model in this study can be extended further to address different issues in business activities in the petrochemical industry, such as uncertainty in chemical prices, new investment strategies, optimal inventory management, and business risk management. It is expected that the systematic approach and high-level analysis based on this study can be used to determine international chemical trades and investment by extending the boundaries of the business activities considered here. In addition, the model could be used to analyze different industries, such as refineries, the gas industry, or new energy businesses.

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AUTHOR INFORMATION

Corresponding Authors

*Jiyong Kim: Tel.: +82.32.835.8875. Fax: +82.32.835.0797. Email: [email protected]. *Il Moon: Tel.: +82.2.2123.2761. Fax: +82.2.312.6401. E-mail: [email protected]. ORCID

Il Moon: 0000-0003-1895-696X Notes

The authors declare no competing financial interest.

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Figure 8. Comparison of four case studies.

ACKNOWLEDGMENTS This work was supported in part by the Yonsei University Research Fund (Post Doc. Researcher Supporting Program) of 2016 (Project No. 2016-12-0243) and the Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry, and Energy (MOTIE), Korea.

total profit and amount of naphtha purchased, in which the total profit savings from cases 2−4 are USD 786 million, USD 150 million, USD 234 million, respectively. The reasons for purchasing more naphtha in cases 3 and 4 were that the capacity and range of hedge trades increased by 50 000 tons and ±50 000 tons, respectively. Notably, case 2 is seen to have a very high total profit compared to the other cases; relative to case 1, the savings for cases 2−4 are 4.3%, 0.8%, and 1.3%, respectively.

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NOMENCLATURE

A. Indices

r = raw material m = product i = storage tank t = time interval y = scenario p = plan

5. CONCLUSION We developed a new decision support system for maximizing profit in the petrochemical industry using an optimization technique. In developing the system, we proposed two optimization models: (1) hedge trades for minimizing purchase costs, and (2) production planning for maximizing the profit of a petrochemical business; we then integrated the models using a recursive two-stage programming framework. As such, the decision support system was simultaneously capable of determining an optimal naphtha unit purchase price and optimal production plan for a petrochemical plant. Furthermore, we confirmed that the developed system was sufficiently robust to suggest optimal purchase prices and production strategy against unexpected, irregular fluctuations. The application of this hedging model over two months (±100 000 tons) yielded an increase in savings of 4.82% over

B. Naphtha Purchase Model

AC = amount of raw material into the cracking unit AIi = amount of inventory in month i AILi , AIUi = lower and upper levels of inventory in month i AP(i,j+1) = amount of hedge in in month i + 1 which was purchase in month i PPi = price of naphtha purchase in month i C. Naphtha Production Model

AFt = amount of feed into cracking unit during time period t AOFm,t = amount of product m from cracking unit during time period t I

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APr,t = amount of raw material purchased during time period t APLr,t, APUr,t = lower and upper bounds of the availability of raw material during time period t Dm,t = amount of demand for product m during time period t DLm,t, DUm,t = lower and upper bounds on the demand of product m during time period t htt = hedging cost considering naphtha purchased and sold in planning period t ict = inventory cost in planning period t IMm,t = amount of inventory of product m during time period t IMr,t = amount of inventory of raw material r during time period t IMr,i,t = amount of raw material r at the end of time period t IPm,t = inventory cost for raw material r during time period t IPr,t = inventory cost for raw material r time period t IVm,i,t = total inventory level of product m in storage tank i during time period t IVLm,i, IVUm,i = lower and upper inventory levels of product m in storage tank i IPr,i,t = total inventory level of raw material r in storage tank i during time period t IVLr,i, IVUr,t = lower and upper levels of raw material r in storage tank i LMm,t = amount of lost demand for product m during time period t NUr,p,i = amount of the raw material r unloading transferred from p to i NURur,p,i = upper on the rate of the raw material r transferred from p to i oct = operation cost in planning period t Pm,t = price of product m during time period t PMm,t = amount of product m sold to market during time period t pst = total revenue from various product sales in planning period t rt = possible financial risk considering probability Tpt = total maximum profit in planning period t TSp = total size of parcel p UTr,p,i = time for which p unloads the raw material r into i ym = percent yield of cracking unit for the specific raw material Ω = target profit for financial risk

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