Risk Management of Chlor-Alkali Industry based on CVaR

Transcription

1 Proceedings of the Intertiol MultiConference of Engineers and Comuter Scientists 2017 Vol II,, March 15-17, 2017, Hong Kong Risk Magement of Chlor-Alkali Industry based on CVaR Dong Chen, Tomohiro Murata Abstract In recent years, risk magement has increased widely from fincial institutions, regulators and ortfolio magers, such as Value-at-Risk (VaR) and Conditiol Value-at-Risk (CVaR). Using this model can measure the risks in uncertainty factors and decisions the roduction lanning for a lant. Now, Chi's Chlor-Alkali industries had to face the grim situation. Comaring with other industries, roduction lanning of Chlor-Alkali industries is more comlicated. Esecially for an imbalance between demand and resonse in Chlor-Alkali roducts market, how to reduce the loss is a major roblem for the olicymaker. In the current market environment, the lant must make a viable decision while considering the risks from market. That required a market risk alysis. In this aer, we roosed a risk measurement model with a restrictive condition which can otimize the roduction while taking uncertainties into consideration, such as material rice, electricity rice, roduct rice, order changes, and esecially the restriction of liquid chlorine inventory. Eventually, a case study is submitted to demonstrate the feasibility of the develoed model, and verify the effectiveness of the algorithm emloyed. Index Terms uncertainty inventory restriction Conditiol Value-at-Risk I. INTRODUCTION Comaring with other countries, although Chi s Chlor-Alkali industries started relatively backward, there also some great rogress has been achieved after 30 years of develoment. At the end of 2010, the full caacity of Chi s caustic soda roduction Chi s had already reached the first lace in the world. But raid rogress also brought serious roblems. Esecially in recent years, under the influence of irratiol industrial structure and vicious cometition, Chi's Chlor-Alkali lant is in the face of the grim situation. Now that, Chi's Chlor-Alkali industries have entered a eriod of adjustment. Now most of the Chlor-Alkali industry research were concentrated on the roducing technology [1] and ollution control [2]. In aer [3], it roosed a circular economy that can Manuscrit received December 20, Dong Chen is a master student in Graduate school of Information, Production and System, Waseda University, Jaan. ( cireck@akane.waseda.j). Tomohiro Murata is a rofessor in Graduate school of Information, Production and System, Waseda University, Jaan. ( t-murata@waseda.j). be utilized to reduce the environmental ollution. And aer [4] suggested a risk magement aroach in chemical industry suly Chain, but this research didn t mention the loss in risk factors. Nevertheless, all researchers ignore a roblem that there are fluctuations in actual markets. Here we take the market between as an examle, caustic soda roducts rices rose as 45%, while the rice of liquid chlorine roducts decreased about 70%. In the current market environment, Chlor-Alkali lant must make a viable decision while considering the risks from the market. That requires a risk alysis of comlex markets. Another issue we should take into consideration is that due to the accident risk of the liquid chlorine, there is the restriction on the liquid chlorine inventory if the limit has been exceeded meanwhile the lant must discontinue the whole roduction line. In recent years, risk magement is increasing widely from fincial institutions, regulators and ortfolio magers, such as Value-at-Risk (VaR) and Conditiol Value-at-Risk (CVaR). The greatest advantage of VaR is that it can describe the estimated loss of a ortfolio with a given confidence level in a value [5]. However, aer [6] indicated that it is not a coherent risk measure since it fails to the subadditivity and does not consider the losses over the value. Because of the limitations, a new risk measurement has been ut forward that is CVaR. It is suerior to VaR as a risk measure because it measured the exected loss than the VaR at a secified confidence level [7]. In aer [8], based on recent data in the actual stock market, the otimal ortfolio is calculated by comuting the ratio of the minimum risk CVaR. Paer [9], alied this method in the electricity market and established a risk evaluation model. In this aer, we will consider the restriction of liquid chlorine inventory and the uncertainties caused by risk factors, such as raw material rices, market rices, electricity rices, the delivery ratio of orders and so on. Here we roosed a risk measurement model with a restrictive condition which can otimize the roduction lanning for Chlor-Alkali lant and ensure normal roduction. II. SOME CHARACTERISTICS IN CHLOR-ALKALI INDUSTRY PRODUCTION Here we take ion-exchange membrane electrolysis as an examle [10]. The Chlor-Alkali rocess roduces caustic soda,

2 Proceedings of the Intertiol MultiConference of Engineers and Comuter Scientists 2017 Vol II,, March 15-17, 2017, Hong Kong chlorine and hydrogen through the electrolysis of sodium chloride solution. 2NaCl + 2H2 O = 2NaOH + H2 + Cl2 (1) Through t chemical equation, we could know the articularity of the roducts of Chlor-Alkali industry. Usually, 1kg caustic soda roduction is accomanied by the 0.89kg of chlorine and 0.025kg of hydrogen. In some literature, it is called the balance industry [11]. According to the Equation (1), if the roduction lanning of the caustic soda is determined in ith month, the consumtion of the crude salt and the roduction of the chlorine could be determined at the same time. We assume the following as this formula. Q P ( i )= r 1 Q P ( i )= r 2 Q P ( i ) (2) Where the Q P,, Q P reresent ith month roduction of caustic soda and chlorine, and Q P reresent ith consumtion of the crude salt, and r 1, r 2 are the rate of the roduction. Actually, caustic soda roducts can be divided into 32% solution, 50% solution, and solid caustic soda. In this aer, we take 32% solution caustic soda solution roduction to discuss (50% and solids can be obtained from it). Similarly, liquid chlorine as the chlorine roduction was made because it was used in marketing. There is no consideration of hydrogen roduction because its outut is low and the market rice is stable. Comared with the individual roduction lanning, it has become a more comlex lan for Chlor-Alkali lant to consider the market demand and rices of the two roducts searately. Caustic soda roducts are in short suly because of its wide range of uses in marketing. However, liquid chlorine market is just the oosite. Taking one roduct of caustic soda solution Sodium Hydroxide 32% as an examle, in Chinese market the cost is about 180 US$ er t, and market rice is as high as 350 US$ er t (on 100% basis rice). Unfortutely, liquid chlorine roducts are about 160 US$ er t in cost and 15US$ er t in market sales, and the rice may be lower at disosal. In the current rofitable market state of caustic soda roducts, decision makers may then choose a relatively high-risk roduction lan in order to obtain more benefits, but they often have to consider a serious roblem of dealing with the excessive loss of liquid chlorine. And another roblem of the roduction lanning is influences under the uncertainty factors. III. UNCERTAIN FACTORS FROM MARKET A. cost imact factors Generally, the costs of Chlor-Alkali lant inude fixed costs and variable costs []. Fixed costs inude equiment dereciation, transortation, labor fee, water fee and ollution treatment fee. And the variable costs are mainly considered the raw material costs and the electricity costs. The cost of the ith month can be exressed as: C( i) = C ( i) + C ( i) + C ( i) (3) el fix Where the C (i) reresents salt costs of the ith month, C el (i) reresents ith month electricity costs, C fix (i) reresents ith month fixed costs. This aer focuses on the variable costs which inude crude salt and electricity costs. Presently, the framework contract is rimarily alied in the rocurement of raw materials crude salt. But the rices will still have a fluctuation in the market. In order to simulate these uncertain effects, here we use P r to reresent changes of the salt rices, and assume P r follows the normal distribution to reresent changes of the crude salt rice which means value μ r and standard deviation σ r. If the crude salt rice P r (i) in ith month can be simulated, then the cost of crude salt would be: C ( i) = Q ( i) P ( i) (4) r The other variable cost is electricity rice. Esecially for high consumtion industries, the rice changes will have a huge imact [13]. Existing literature shows that the Geometric Brownian motion could better simulate seasolly changing trends [14]. So here we use the geometric Brownian motion to describe the electricity rices changes. The formula is as follow: 2 σ P P ex(( μ - + σw ) (5) t = 0 ) t 2 The electricity rice is denoted by P t at time t with the exected return by μ, and the standard deviation by σ if the initial electricity rice P 0 was given, we can use Equation (5) to calculate the rice at each time. About w t is a Brownian motion. μ and σ are constants and can be estimated through statistical alysis of historical data. According to roduction electricity consumtion rate r 3 the cost of electricity could be calculated as: Cel ( i) = r3 Q ( i) Pel ( i) (6) C el and P el are the electricity cost and electricity rice of the ith month. B. order and rice factors. Here we will discuss the uncertain factors of the market and their effects on roduct rice and order. In this aer, caustic soda roducts and liquid chlorine roducts will be discussed searately due to their different market situations. Usually, marketing of caustic soda roducts inudes two ways, order contract and trade market. Most art of the roduction is selected to deliver orders, while the other art of the roduction is sold in the trade market. The amount of caustic soda order Q d and rice P of order contract are relatively stable, but the trade market is subject to considerable changes. The rices in trade market P may be higher than the order rice, but sometimes lower. Here we also use a normal distribution P (μ, σ ) to describe the rice changes in the market. In contrast to short suly of caustic soda roduct market, liquid chlorine roducts market is not so otimistic. In the overall current tight market, its orders and rices are lower than the caustic soda roducts. Because of the total inventory constraints, the rice may be reduced to sell the redundant art. Comared with the order rice P, the disosal rice P has a highly unstable, and sometimes there exists a negative rice. That means the lant will ay extra money to the disosal of remanding roducts that usually haen in the market. Here we

3 Proceedings of the Intertiol MultiConference of Engineers and Comuter Scientists 2017 Vol II,, March 15-17, 2017, Hong Kong also use a normal distribution P (μ, σ) to describe the rice changes. However, there still exist some uncertainties in the imlementation of the contract, transort caacity and quality of roduction. In order to reresent the order change, here we assume that both the amount of orders Qd and Qd follows a normal distribution with mean values μd, μd, and standard deviations σd, σd. Through the above discussion, we can get the sales of ith month caustic soda and liquid chlorine. (7) S (i) Qd (i) * P (i) (Q (i) - Qd (i))* P' (i) aer [7] introduced an aroximate method by adding a new function Fβ (x, a) to solve this roblem. The exected value of that Fβ (x, a) could be aroximated by samle mean. And the samling calculation of Fβ (x, a) can be assumed by F β (x, a). We introduce the variables Zk= ( R (x, y) α) + (k=1,2,,n) for simlification. The CVaR model for Chlor-Alkali lant has been established as described in formula ()-(21). Objective: min Fˆβ ( x, α ) = min( α + S (i) = Q d (i) * P (i) + Q' (i) * P' N 1 Z ) N (1 - β ) k =1 k () (8) Where S (i) and S(i) are the two roduct sales in the ith month. IV. FORMULATION OF THE MODEL First, we will describe the constraints of liquid chlorine inventory in the roduction lanning. Fig 1 show the new liquid chlorine inventory rocess. The formula is (9) Q inv(i) = Q (i) - Q d (i) - Q (i ) Where the Q ( i ) reresents the monthly amount of disosal and Qinv ( i ) shows the monthly roduction of new liquid chlorine inventory. Subject to: (i ) = {Q d (i ) * P (i ) + (Q (i ) - Q d (i ))* P' (i )} (i ) = {Q d (i ) * P (i ) + Q' (i ) * P' } C el E( (16) C (i ) + Cel (i ) + C fix (i ) ) -1 e inv(i ) = Q (i ) - Q d (i ) - Q (i) inv (i ) Qca Zk= ( R (x, y) α) + 0 Fig 1 liquid chlorine inventory In order to guarantee the normal roduction of the factory, the liquid chlorine inventory of months must less than the inventory caacity Qca. (10) Q inv (i ) Q (20) (21) Where i =1,2,,; k=1, 2, N; Equation (13) -(14) described the sales of two roductions in months. Equation (15) -(17) described the cost of one year. Equation (18) is the exected return of the Chlor-Alkali lant and e stand for the lower bound of the exected return rate. (where 0 e 1) Equation (19) -(20) are the constraints of liquid chlorine inventory. ( R (x, y) α) +mean max ( R (x, y) α, 0). Using the Monte Carlo Samling method to generate a samle of the random vector y, and calculated the CVaR with a linear rogramming roblem. V. CASE STUDIES AND DISCUSSION ca Through the above alysis, let R (x, y) be the revenue function of the Chlor-Alkali lant. Where xt = [Q (1), Q (2), Q ()] mean the roduction lan and it is a decision vector. yt= [Pr,Pel, Qd, Qdc, P, P ] is the random vector. The function as follows: (11) R ( x, y ) (19) Q (17) (18) (i ) + (i ) C (i) (i ) P(i )} (i ) = r3 {Q (i ) Pel (i )} C (i) = C Q {Q (14) (15) (i ) = (13) (i ) (i ) C (i) - So, we define the loss function of the Chlor-Alkali lant would be R (x, y). In general, CVaR calculation is comlicated, in A. Data of the Case First, we use the geometric Brownian motion to simulate the electricity rice trends for months form historical data at Fig.2. The initial electricity rice as US$ er kwh. Generally, it is difficult to forecast the electricity rice accurately. But to redict its future trend according to the historical rice data and economic trend is feasible. Therefore, this aer tries to simulate the changing trends of rice, rather than to find methods to accurately redict the rice.

4 Proceedings of the Intertiol MultiConference of Engineers and Comuter Scientists 2017 Vol II,, March 15-17, 2017, Hong Kong Here we take the caacity of caustic soda roduction Q 200,000 ton one year the Chlor-Alkali lant as an examle. The monthly average of caustic soda order is 15,000 tons, and the average of liquid chlorine order 11,00 tons. Liquid chlorine inventory caacity 200t and the initial value is 0, and crude salt quantity is enough. With the current market rice [15], here we set the caustic soda order rice as 350 US$ er t, liquid chlorine roducts order rice as 15US$ er t, crude salt rice as 35 US$ er t, liquid chlorine disosal rice as 5 US$ and the fixed cost is 20 US$ er t. r 1, r 2 and r 3 is1.46,0.89 and 2600Kwh/t. The other random arameters in the model are generated through Monte Carlo method with100 samles and Parameters Values are shown in Table I Calculation the CVaR in different exected return rates by MATLAB. Table I Parameters Values Para Value Para Value US$ σ d 0.15 x10 4 ton σ 35 US$ σ d 0.11 x10 4 ton σ 2 US$ Q ca. 200 ton σ r 3 US$ B. Results and discussion Fig.2. electricity rice changes in month. Based on the values of the arameters given in Table 1 with the Monte Carlo Samling Method. We calculated results of otimization of roduction lanning in Fig.3 and sensitivity alysis of CVaR and exected return rate was shown in Fig.4. Fig.3 Otimization result of roduction lanning

5 Proceedings of the Intertiol MultiConference of Engineers and Comuter Scientists 2017 Vol II,, March 15-17, 2017, Hong Kong The results show that here is a lower roduction when the cost increases. A high roduction needs to consider the liquid chlorine disosal of the cost reduction. The lant should determine a minimum safe yield to reude running out of suly due to fluctuation in orders. Fig.4. CVaR in different confidence levels with different exected return rates. Fig.4 shows the calculation results of CVaR with different confidence levels with different exected return rates. Through the alysis, we can realize that the two curves are increasing. The increasing exected return rate will inevitably lead to an increase in CVaR. At the same exected return rate, and the CVaR value increases as the confidence level increases. This is also consistent with the current market and the validity of the model is verified. [3] Jacob Parka, Joseh Sarkis, Zhaohui Wu Creating integrated business and environmental value within the context of Chi s circular economy and ecological modernization Jourl of Cleaner Production Volume 18, Issue 15, November 2010, Pages [4] Liing Liu,Jianhua Ji,Tijun Fan" Risk Magement in Chemical Industry Suly Chain" IEEE Intertiol Conference /SOLI [5] S Basak, A Shairo "Value-at-risk-based risk magement: otimal olicies and asset rices" Rev Fianc Stud, 14 (2) (2001), [6] P. Artzner, F. Delbaen, J.-M. Eber, D. Heath"Coherent measures of risk"math. Fince, 9 (3) (1999), [7] R.T. Rockafellar, S Uryasev "Otimization of conditiol value-at-risk" J Risk, 2 (2000), [8] Yuling Wang; Junhai Ma Alication of mean-cvar otimization model in investment ortfolio 2010 Intertiol Conference on Comuter, Mechatronics, Control and E Pages: [9] R. Dahlgren, Chen-Ching Liu,J. Lawarree "Risk assessment in energy trading" IEEE Transactions on Power Systems ( Volume: 18, Issue: 2, May 2003 ) [10] Robert M. Hruda; Jack R. Harbaugh Fault Contribution of Chlor - Alkali Cell Line IEEE Jourls & Magazines Volume: IA-17 Pages: 95-97, [11] HONDA massahiro "Present and future of electrolytic Soda Industry"The Chemical Society of Jaan Chemical education 61(9), , [] Yongkui Shi; Xin Zhou; Songmei Zhang The Design of Safety Early Warning System for Chlor-Alkali Chemical Industry Engineering Design and Manufacturing Informatization Year: 2010, Volume: 2 Pages: 3-6, [13] A. K. David and F. S. Wen Market ower in electricity suly IEEE Trans. on Energy Conversion, vol. 16, , Dec., 2001 [14] C. W. Wang, M. B. Wang, Z. F. Tan and P. J. Xie Calculation model of retail rice based on ool urchase rice simulated by Brownian motion Power System Technology, vol. 32, no. 9, , May, 2008 [15] "Chi chemical roducts net" htt:// VI. CONCLUSION We should take a risk measurement to consider the uncertain factors bring risks of lants. In the cometitive market, making roduction lanning under different demand and suly of the two roducts is extremely imortant to Chlor-Alkali lants. In this aer, we roosed a restrictive condition rogramming CVaR model to otimize the roduction lanning while taking uncertainties into consideration, such as material rice, electricity rice, roduct rice, order delivery, and esecially the restriction of liquid chlorine inventory. A case study is resented to demonstrate the feasibility of the develoed model, and verify the effectiveness of the algorithm emloyed. Also, how to accurately reflect the changes in market rices will be the future work in research. REFERENCES [1] Imad Moussallema, Stefan Pinnowa, Norbert Wagnerb, Thomas Tureka, Develoment of high-erformance silver-based gas-diffusion electrodes for chlor-alkali electrolysis with oxygen deolarized cathodes Chemical Engineering and Processing Volume 52, February 20, Pages [2] Xiaoing Jiaa, Gang Xi, Yi Qia, Yu Qianb Sectoral co-control of air ollutants: case of a chlor-alkali/olyvinyl chloride sector in Chi Jourl of Cleaner Production Volume 1, Part 2, 20 January 2016, Pages