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Optimization of naphtha purchase price using a price prediction model
Accepted Manuscript Title: Optimization of naphtha purchase price using a price prediction model Author: Hweeung Kwon Byeonggil Lyu Kyungjae Tak Jinsuk Lee Jae Hyun Cho Il Moon PII: DOI: Reference:
S0098-1354(15)00273-2 http://dx.doi.org/doi:10.1016/j.compchemeng.2015.08.012 CACE 5263
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
9-12-2014 19-8-2015 22-8-2015
Please cite this article as: Kwon, H., Lyu, B., Tak, K., Lee, J., Cho, J. H., and Moon, I.,Optimization of naphtha purchase price using a price prediction model, Computers and Chemical Engineering (2015), http://dx.doi.org/10.1016/j.compchemeng.2015.08.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights
The average optimization value is approximately 45.07 USD/ton cheaper than
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the actual purchase price.
Nonlinear Programming (NLP) model was developed to optimize the naphtha
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purchase price.
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Proposed SD model give best prediction accuracy for Europe naphtha price (FAP 92.28).
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Proposed SD and optimization model would be of great significance for industry
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decision-makers.
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Optimization of naphtha purchase price using a price prediction
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model
Hweeung Kwona, Byeonggil Lyua, Kyungjae Taka, Jinsuk Leeb, Jae Hyun Choc,
Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei ro,
an
a
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Il Moona,*
Seodaemun-ku, Seoul 120-749, Korea
Hanwha total Corporation, 411, Dokgot-ri, Daesan-eup Seosan-si, Chungcheongnam-do
356-711, Korea c
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b
Engineering Development Research Center (EDRC), Seoul National University, 1, Gwanak-
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ro, Gwanak-gu, Seoul 151-744, Korea
*Corresponding author: Il Moon, [email protected]; Tel.: +82 2 2123 2761; Fax: +82 2312-
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6401
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Abstract In order to meet company needs, various models of naphtha price forecasting and optimization models of average naphtha purchase price have been developed. However, these
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general models are limited in their ability to predict future trends as they only include quantitative data. Furthermore, naphtha price predictions based on fluctuation trends have not been published in the literature. Thus, we developed a system dynamics (SD) model
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considering time-series data, mathematical formulations, and qualitative factors. The results obtained from our model were compared with the published literature. The best result of the
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SD is the European naphtha forecasting price model, and the forecasting accuracy percentage shows 92.82%. Furthermore, an nonlinear programming (NLP) model was developed to
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optimize the purchase price by considering the naphtha price of the forecasting models. In addition, the average optimization value was approximately 45.07 USD/ton cheaper than that
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of the heuristic approach.
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dynamics, Heuristics
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Keywords: Purchase price optimization, Artificial neural network, Forecasting model, System
1. Introduction
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Naphtha plays an important role in the world economy as it is used to produce widely used products including ethylene, propylene, and butadiene as well as aromatic products such as benzene, toluene, and xylene through thermal cracking. Naphtha price trends tend to follow that of crude oil (Asche et al., 2003). Fig. 1 shows the trends of West Texas Intermediate
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(WTI) crude oil and naphtha prices from March 1996 to November 2011. This close relationship means that naphtha price forecasting has a great influence on all loss factors in
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petrochemical industries. For example, the point of purchase of oil has a significant effect on the total profit of oil refiners. If the oil price falls by $1, oil refiners suffer an operating profit
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loss of $10 billion.
Naphtha price is also affected by the supply and demand for the product as well as ocean freight costs, both of which have political consequences (Chen & Hsu, 2012; Gao et al.,
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2014; Holland, 2013; Kang et al., 2014; Lee et al., 2012; Montroll, 1978; Wen et al., 2014; Wong et al., 2013). Therefore, decision makers want to reduce the uncertainty of future prices.
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However, decisions on the point of purchase of naphtha require the domain knowledge of chemical engineers. General mathematical models including the statistical model (SM), exponential smoothing model (ESM), and artificial neural network (ANN) are well known in
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the chemical engineering field, but these general models are now being applied to naphtha
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price forecasting for the first time. In addition, the innovative system dynamics (SD) model is very valuable for determining the point of purchase because it considers integrated data and
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heuristics. These considerations prompted us to predict naphtha price using the SM, ESM, and ANN forecasting models. An SD model based on a causal loop considering human and psychological heuristics was also applied to naphtha price forecasting. Heuristics is a very important approach for producing decisions at the point of purchase, and their efficacy can affect naphtha purchase. The heuristic approach allows us to reach reasonable solutions for planning decisions.
This paper considers short-term planning for the naphtha purchase problem, which includes the number of naphtha purchases, inventory levels, and running capacity for cracking units. We assume that a naphtha purchase plan is determined by petrochemical industry planning, and this research analyzes the optimization problem to minimize the costs included in spot trading to achieve optimal naphtha purchase planning. Furthermore, we developed a general nonlinear programming (NLP) model to optimize the purchasing unit price and compared its results with the heuristic results. The purpose of this research is to develop a reliable forecasting model. Moreover, the average purchase price was minimized by naphtha
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procurement planning using the predicted price. The numerical results of this paper verify the effectiveness of the optimization model. In summary, the NLP model can help decision makers to plan purchase opportunities, so naphtha can be bought at an optimal price.
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2. Literature review
Predictions of crude oil prices have been carried out by many investigators all over the
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world (Fan et al., 2008; Gori et al., 2007; Kang & Yoon, 2013; Lara et al., 2007; Rao & Parikh, 1996; Regnier, 2007; Wei et al., 2010; Ye et al., 2005, 2006) but studies on naphtha
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price forecast are scarce (Lyu et al., 2014; Rao & Parikh, 1996; Sung et al., 2012; Visetsripong et al., 2008). Various approaches to forecasting oil price have used both linear
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and nonlinear models. Lara et al. applied a simple linear regression model to predict crude oil prices and stochastic models to calculate patterns of volatility in oil prices (Lara et al., 2007). Instead of using a single autoregressive model for all horizons, Kang reported a multi-period-
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ahead forecasting autoregressive model selected separately for each horizon and found that forecast performance depends on optimal order selection criteria, forecast origins, forecast
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horizons, and the time series to be forecasted (Kang, 2003). Kang and Yoon (2013) studied the forecasting potential of the ARIMA–GARCH,
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ARFIMA–GARCH, ARFIMA–IGARCH, and ARFIMA–FIGARCH models by using the daily spot prices of WTI crude oil. Their results for unleaded gasoline suggested that the
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ARFIMA–FIGARCH model better captures the long-memory properties of the returns and volatility, even though there was no unique model for all three types of petroleum products. Kang et al. attempted to find the best model to forecast volatility in three crude oil prices (WTI, Brent, and Dubai). They evaluated the volatility of the three crude oil prices using daily spot prices during the period January 6, 1992 to December 29, 2006 by considering the out-of-sample forecasts of the 1, 5, and 20-day forecasting horizons, corresponding to 1-day, 1-week, and 1-month trading periods, respectively. It was found that for Brent and Dubai crude oil, the FIGARCH model was superior to other models (GARCH, IGARCH, and CGARCH) for all three forecast horizons, from 1-day to 1-month. However, in the case of WTI crude oil, the CGARCH model outperformed the other models (Kang et al., 2009). Visetsripong et al. studied naphtha forecasting using the adaptive neuro-fuzzy inference system (ANFIS) and the statistical method for nonlinear time-series data (Visetsripong et al., 2008). It was found that 86% of the comparison tests showed that the ANFIS model
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forecasting power achieved more accurate results than the exponential smoothing method. It was concluded that the neuro-fuzzy system method is more accurate and more reliable than the statistical method when used to forecast nonlinear time-series data. Wei et al. (2010) compared nine linear and nonlinear GARCH-class models: RiskMetrics, GARCH, IGARCH,
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GJR, EGARCH, APARCH, FIGARCH, FIAPARCH and HYGATCH. They concluded that the nonlinear GARCH-class models are capable of capturing long-memory and/or
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asymmetric volatility and exhibit greater forecasting accuracy than linear ones, especially in volatility forecasting over longer time horizons, such as five or twenty days, for WTI and
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Brent crude oil. Masih et al. investigated the impact of ethylene prices in the naphtha intensive ethylene markets of the Far East, North West Europe, and the Mediterranean on WTI crude oil price (Masih et al., 2010). They observed that the ethylene prices in North
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West Europe and the Mediterranean were weakly endogenous, but the Far East ethylene price was weakly exogenous, both in the short and long term. It was even found that the results
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were consistent during the period under review, which had a surge in demand for ethylene throughout the Far East, especially in China and South Korea. However, during the postsample forecast period, as evidenced in their variance decomposition analysis, the emergence
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of WTI as a leading player was found to be consistent with the recent surge in WTI price.
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This change reflects the growing importance of input costs in determining the dynamic interactions of the input and product prices.
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The results of these studies showed that (a) the time-series model was adequate for forecasting oil prices in the short run but had limited forecasting ability in the medium and long-term, (b) time-series models proved to be accurate forecasts of oil price volatility, but a single model could not be used in every case, and (c) oil prices and their volatility displayed significant nonlinearity, which indicates that small shocks to the economy could have large and unpredictable implications for oil prices and their volatility. Recently, the application of artificial neural networks (ANN) has been reported in many fields. An ANN model is a computational model inspired by the brain’s central nervous system (Raida, 2002). Zhang and Qi (2005) proposed a hybrid model in time series prediction using both the autoregressive integrated moving average (ARIMA) and the ANN models. The hybrid model was able to improve the forecasting accuracy in the time series data. Khashei et al. (2009) integrated the ARIMA and ANN models with fuzzy logic in order to overcome the linear and data limitations of ARIMA models to get more accurate results. The proposed models were more reliable in forecasting future prices. Another approach that is
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used by many researchers in different fields is the system dynamics model (SD) using a causal loop (Aslani et al., 2014; Jeon & Shin, 2014; Mao et al., 2013; Movilla et al., 2013; Peng et al., 2014; Qudrat-Ullah, 2013). Ullah explained the dynamic variables acting in the electricity supply and demand of Canada using a causal loop diagram of SD (Qudrat-Ullah,
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2013). Aslani et al. (2004) developed a system dynamic model with the role of renewable energy resources for energy security investigations in Finland. Jeon and Shin (2014)
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proposed a long-term technology valuation method for renewable energy technologies with a system dynamics model combined with the Monte Carlo method. This study considered a
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causal loop diagram under the 3E framework. Peng et al. (2014) proposed a system dynamics model considering the uncertainties related to forecasting post-seismic road networks and delayed information. Movilla et al. (2013) developed a model based on SD to understand the
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behavior of the photovoltaic sector in Spain and its expectations under possible scenarios. Decision making on naphtha purchases is very important for petrochemical industries.
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Numerous important scheduling and planning problems have been analyzed in recent decades. Lakkhanawat and Bagajewicz (2008) addressed how much crude oil has to be purchased. Procurement methods can be very valuable in refineries. However, they do not provide
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sufficient information to decision makers because it is not important what crude oil is
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purchased. Their proposed model only considers six crude oil types and three time horizons. In addition, it indicates that the proposed model is not appropriate as a supporting method for
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decision makers. Julka, Srinivasan, and Karimi (2002a, 2002b) developed an agent-based decision support systems (DSSs) framework for a supply chain and a petroleum refinery integrated supply chain modeler and simulator (PRISMS) for a decision-supporting tool for crude oil procurement. These systems facilitate integrated decisions in terms of the refinery business. However, their studies only provide insight into responding to changes in domestic policies and unexpected events in an international environment. Göthe-Lundgren, Lundgren, and Persson (2002) solved the scheduling problem based on the mixed-integer programming (MIP) model, including utilization of the production process. They formulated an optimization model for production scheduling that can support the decisions of procurement planners at the strategic, tactical, and operational planning levels. However, the developed model is only designed to integrate planning with production scheduling and does not focus on support for procurement or purchase plan decisions. Zhang, Wen, and Xu (2012) introduced mixed integer nonlinear programming (MINLP) for optimization of crude oil blending and purchase planning with uncertainty. This is a significant contribution to
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decision support that considers short-term crude oil blending and long-term purchase planning simultaneously. However, it has limitations based on the given information, such as the estimated crude oil price and crude oil type. Most previous work has aimed to develop a rigorous optimization model for short-term
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crude oil unloading, the inventory management of crude charging and mixing tanks, and crude distillation unit (CDU) operation scheduling. The objective of these papers is to
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minimize operation costs, which involve inventory costs, crude vessel sea waiting and harboring costs, and changeover costs for each CDU. Lee et al. (1996) developed an
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optimization model based on the mixed integer linear programming (MILP) model for shortterm refinery scheduling by considering crude oil unloading and inventory management. Oil procurement planning in refineries is addressed with an innovative two-stage solution
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approach using the MINLP model. The developed model easily handles crude oil types and
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quality parameters compared with existing papers.
3. Data preparation and normalization
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The current study considers the actual price of naphtha and 37 major factors, such as the naphtha demand, naphtha supply, European naphtha price, and Asian naphtha price. First,
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naphtha demand takes into consideration downstream products (e.g. ethylene, propylene, butadiene, benzene, toluene, and xylene), the operation rate, and margin in the petrochemical
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industry. Second, naphtha supply includes the production quantities of BTX (benzene, toluene, and xylene), naphtha production of the refinery, T/A of the refinery, operation rate of the refinery, and type of oil. Third, the European naphtha price is assumed to be influenced by the naphtha inventory, oil price, Europe gasoline and propane price, and seasonality. Finally, the Asia naphtha price is assumed to be influenced by the Asian naphtha demand and supply interrelated with the European naphtha price. The naphtha price and the 37 major factors have different values. Therefore, this actual data and the value of the 37 major factors are normalized from 0 to 1.
3.1. Data preparation The naphtha price data (in USD/ton) was obtained from the Mean of Platts Japan (MOPJ) as the representative naphtha price for this analysis. The MOPJ indicates the monthly data on the naphtha price, which is treated as the benchmark naphtha price for the international
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market. The naphtha prices and 37 major factors for the previous trading month were used in the SD model. The datasets consisted of 37 points for the naphtha monthly price from May 2010 to September 2012. The naphtha price is presented for every month, which includes five
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days per week except for weekends (here Fridays and Saturdays) and official holidays.
3.2. Data normalization
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Data normalization is the process of removing redundant data from various variable datasets. Data normalization is needed to compare price and other major factors. The following
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equation is used for data normalization:
X max Maxdata 1.02 ~ 1.07 ,
X i X min . X max X min
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X i,normalization
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X min Mindata 1.02 ~ 1.07 ,
(1)
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where X i is the value of the ith data point, X min is the minimum value among all the data
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points, and X max is the maximum value among all the data points. The advantages of data normalization include the ability to maintain data integrity, a maximum price correlation with
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the 37 major factors, and a minimum standard deviation. All the major factors in the data were normalized in a range from 0 to 1. 3.3. Proposed forecasting methodology This section describes the three different approaches used for forecasting: (a) The SM, (b) ESM, and (c) ANN models. Another model based on SD was also developed in this study. The methodology was applied to naphtha price forecasting as shown in the flowchart in Fig. 2. This study included 45 data values of actual naphtha price and 37 major factors. Among the four datasets in the SM and ESM models, the first 50% of all the data was used as the training set to find the optimal model parameters, and the remaining 50% was used for verification purposes or prediction ability. The model parameters were obtained through training. The concepts of each approach are detailed in Fig. 2. If the predicted variance of the naphtha price has the same trend as the actual naphtha variance, the predicted value is treated as correct. Otherwise, the predicted value is treated as incorrect. The forecasting accuracy percentage
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(FAP) is computed by dividing the number of correct predictions by total predictions as follows: FAP
Number of correct predictions 100 . Number of total predictions
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(2)
4. Results and discussion
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4.1. Statistical method model
The statistical method (SM) model was developed using the Statistical Package for the
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Social Sciences (SPSS) tool. The SM method was used to model the linear relationships between one dependent variable and several independent variables. It is based on multiple linear regressions. The SM equation, with the error term, is defined as follows:
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f x1 , x2 , , xn Ft 0 1 x1,n 2 x2,n n xn ,t n . (3)
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where n is the parameter, and xn ,t is each major factor value for a specific time. Each
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parameter of the SM is estimated such that the sum of the squares of error is minimized.
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Therefore, the forecasting equation is given by
Ft ' 0' 1' x1,n 2' x2,n n' xn,t . (4)
where the symbol (’) denotes the estimated parameter values. The error term includes multiple regression residuals and is defined as follows:
n' Ft Ft ' . (5)
Here, Ft and Ft ' represent the actual value and the predicted value of the nth month, respectively. The regression residuals measure the nearness of the actual and predicted values in the calibration periods.
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The results reported in this section were collected after training the data of the SM model. We used a time-series method for forecasting. In order to carry out the simulation, we divided the data into four datasets (50:50, 60:40, 70:30, and 80:20). The results of the model used for the training and verification steps were compared with the real data of the normalized
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naphtha prices. The naphtha prices for a continuous 29-month (May 2010 to September 2012) period and 37 factor values were selected. The best prediction of these four datasets (i.e.,
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50:50) of the normalized naphtha price variance for the 29 months was compared with the normalized actual values of the corresponding months in Fig. 3. The FAP of the normalized
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SM was 67.86% for this duration of 29 months. The SM model generally has one problem: n data values are contained in the average, and then the n-1 values of the previous data must be included for future forecasts.
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4.2. Exponential smoothing method model
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carried forward in order to be combined with the real observation values. The past data was
The exponential smoothing method (ESM) was introduced by Robert G. Brown in 1944. ESM can be applied to time-series data, and it is one of the most efficient forecasting
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methods when the time-series data has neither seasonality nor trend. ESM assigns weights to
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past data and adjusts for past inaccuracies in prediction. To achieve this, the ESM model uses a weighting factor in which the weight reflects the most recent values. The time-series data is
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a sequence of observations. The following simple form of ESM is given by F1 x0 ,
F1
Y1 Y2 Yt Y Y Yt 1 t t 1 , t t
F1 xt 1 1 Ft 1 . (6)
where Ft is the forecast value at period t. In this equation, the forecasting value Ft applies the weighting factor of the previous observation data xt 1 . The weighting factor of ESM is , which ranges from 0 to 1. The value of the weighting factor determines the smoothing degree applied to the fluctuations of the data. A small shows a visible ESM trend, and a large provides a quicker response to recent changes in a time series. If the value is close
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to 1, the prediction value will contain an effective adjustment for the error in the preceding forecast whereas when the value is close to 0, the prediction value is similar to the preceding real data. The ESM can quickly produce accurate forecasting values and change the weighting factor value to fit the model adequately in some external environments.
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However, the ESM model often produces forecasts that lag behind the trend of the real values. In addition, the forecasting values considered in the ESM model are very sensitive to the
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standard of the smoothing constant.
The ESM model applies the exponential smoothing technique to the existing model. The
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results reported in this section were collected after training the data of the ESM model. The ESM model simulates the same method as the SM model. Fig. 3 shows the best dataset (50:50) of the normalized naphtha price variance for 29 months compared with the
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normalized actual price. The forecasting values of the ESM appear as if they were delayed by one month for the normalized actual price. The FAP of the ESM is 75.00 for the total period.
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This model is usually used for short-term predictions because it does not operate well if the time-series data have seasonal or cyclical variations.
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4.3. Artificial neural network model
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A neural network (NN) finds a pattern or correlation with a large amount of data in a very complex structure; therefore, it is useful for future predictions. NNs have many features, such
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as an adaptive system, many simple process elements, and high interconnectivity. The ANN is used for computing nonlinear problems, and it has an enormous number of nonlinear group neurons that fix the input and output signals. The ANN model is a typical method of feedforward network modeling for time-series forecasting, which was proposed by Zhang and Qi (2005). The nonlinear group numbers determine a complex relationship with high prediction between the neurons. Fig. 4 shows a typical ANN model with a three-layer architecture consisting of the following three layers of node: input, hidden, and output. The mathematical relationship between the input and output in the ANN model is as follows: k
n
j 1
i 1
F1 b0 W j tan sig (b0,k Wi , j Ft 1 ) et ,
(7)
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where Wi , j and W j are the connecting weight factors of the model parameters, n is the input node number, and k is the output node number. The hyperbolic tangent transfer function is used as a hidden layer, and the equation is as follows:
e x e x e x e x
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f ( x)
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(8)
.
This function has a range from -1 to 1. The ANN model using Eq. (11) is formulated as a
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nonlinear equation form, taking past-observed data in order to predict a future value. The ANN model is valuable when predicting an output value from many input variables
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(Bulsari, 1995). It has nonlinear characteristics, and it can be applied to various chemical engineering fields (Himmelblau, 2000). In this study, the values of 37 major factors were used in the input layer of the ANN model and applied to a feedforward back-propagation
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network system (Fig. 4). The forecast for one output value was calculated through the three hidden layers used for the hyperbolic tangent transfer function. A comparison of the normalized naphtha price forecast by the ANN model for 29 months and the normalized
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actual values for the corresponding months is shown in Fig. 3. The FAP of the normalized
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ANN model is 85.71 for the total period.
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4.4. System dynamics model
The system dynamics (SD) model is an appropriate methodology for describing complex behavior, such as forecasting problems, and overcoming the disadvantages of linear models. SD describes the complex mutual interactions between factors and considers many functions, such as the time-delayed relationships of factors, and offers causal loop diagrams. Here, we propose an SD model using Vensim software to forecast naphtha supply, naphtha demand, and naphtha price by employing not only simulation but also optimization. This SD model was divided into three sub-models: Asian naphtha supply, Asian naphtha demand, and Asian naphtha price including European naphtha price.
4.4.1. Naphtha supply sub-model The demand for naphtha is almost the similar as the demand for petrochemical products. Therefore, the capacity of petrochemical plants and their rate of operation are the main factors of demand. The rate of operation is affected by the economic situation and T/A.
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Additionally, the use of liquefied petroleum gas (LPG), an alternative to naphtha, affects the demand for naphtha. If petrochemical plants have a large capacity, the demand for naphtha is high. However, the operation rate of plants is not always 100%. Thus, the main factor in demand for naphtha is the operation rate of a plant. A naphtha demand model considers the
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petrochemical margin, utility operating rate, T/A, and heuristics. The factors governing naphtha supply are shown in a causal loop in Fig. 5. A comparison of the normalized actual
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naphtha supply and its supply forecast is shown in Fig. 6, and the FAP of the normalized
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naphtha supply is 64.29.
4.4.2. Naphtha demand sub-model
While demand for naphtha can be calculated using a petrochemical company’s operation
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rate, the supply of naphtha can be calculated using the production of an oil company. The amount of naphtha used to make para-xylene (PX) is also an important factor in determining
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the supply of naphtha. While petrochemical plants need more naphtha when their capacity increases, more naphtha can be obtained at these times. The T/A and margin also affect an oil plant’s rate of operation as economic and non-economic factors. The margin is defined as the
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difference in the oil price and the product price. The analysis of the relationship between the
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margin, rate of operation, and T/A enables calculation of the supply of naphtha. Oil plants produce PX, a high-value petrochemical product, from naphtha. Because oil plants do not
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supply naphtha to petrochemical plants, but consume it, the amount of naphtha used to make PX should be excluded from the supply of naphtha. Therefore, production of PX reduces the supply of naphtha. By considering the operation rate of oil plants and the production of PX, the actual supply of naphtha to petrochemical plants can be determined. A naphtha demand causal loop considering all these factors and heuristics is shown in Fig. 7. The normalized naphtha demand forecast from May 2010 to September 2012 is close to the normalized actual demand (Fig. 8). The FAP of the normalized naphtha demand presented in Fig. 8 is 89.29.
4.4.3. Asian naphtha price model including European naphtha price The causal loop diagram (Fig. 9) for this model is divided into two parts: The forecast of the Asian naphtha price model and the European naphtha price model. The Asian naphtha price can be forecast by considering the European naphtha price, Asian supply and demand, export, Brent oil price, and seasonality. The European naphtha price and the Asian naphtha price
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affect each other, and there is a time delay between the two factors. The Asian naphtha price is influenced by the Asian naphtha supply and demand, and the Asian naphtha and European naphtha prices are time delayed. Fig. 9 shows a causal loop diagram of the Asian naphtha price, including the European naphtha price. Comparisons of the normalized European
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naphtha price forecast with actual European prices and the Asian naphtha price forecast with actual Asian prices from May 2010 to September 2012 (29 months) are shown in Figs. 10 and
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11, respectively. The FAPs of the normalized European and Asian naphtha prices were found
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to be 92.28 (Fig. 10) and 82.29 (Fig. 11), respectively.
4.5. Comparison of the proposed models with the published literature
As there are no studies in the literature on naphtha price forecasting, and the trends of the
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actual prices of crude oil and naphtha are similar, the present forecasting results are compared with the crude oil forecasting results in the literature. Morana (2001) predicted crude oil
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prices using a semiparametric approach, and the FAP was 46.67. Ghaffari and Zare (2009) forecast WTI crude oil prices through the ANFIS model using the without smoothing procedure (WSP) model and the smoothing procedure (SP) model. The FAPs of the WSP and
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SP models were 48.33 and 70.09, respectively. Fan et al. (2008) proposed an approach based
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on a genetic algorithm. The historical time-series data of the Brent and WTI crude oil prices were calculated using GPMGA. The FAP for the WTI crude oil price of their predicted model
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was 62.07. Moreover, Gori et al. (2007) used an ANFIS model to propose a method to predict WTI crude oil prices with a FAP of 46.56. Table 1 summarizes the FAPs of the results of the naphtha price forecasts in the present study along with the crude oil forecasts in the literature.
5. Optimization of the naphtha purchase price using price prediction The entire naphtha trading configuration of planning problems corresponds to the multi-step system, including inventory, amount of naphtha, and running capacity. The existing optimization models in the literature section do not provide decision-making support for product purchases, such as oil and naphtha. Therefore, this study develops practical approaches for formulating and solving the naphtha purchase problem using NLP models and
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connects to the appropriate techniques. For planning periods, this model indicates how much of the available naphtha to purchase and keeps track of the inventory levels per month. The decision variable of the naphtha purchases is future trading for the next three months. The purchase order indicates how much naphtha is needed for the petrochemical industry to
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be able to operate cracking units. Once a purchase order is determined for a planned date, it provides the amount of naphtha trading, the amount of the naphtha purchase, the storage tank
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capacity, and the purchasing unit price of the optimal naphtha. This research omitted the naphtha loading and unloading cost because it is relatively small and not sensitive to a given
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period.
The particular purchase problem used in this study is closely related to the point of purchase of naphtha. The optimization model included the following information. First, the estimated
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monthly prices for the SD forecasting model were used. Second, the amount of initial inventory in the storage tank and the lower and upper bounds for the naphtha storage tank
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capacity were given. Finally, the monthly flow rate was specified. In addition, future purchase orders, storage tank inventory, and purchase price were determined by optimization. The initial inventory levels and running capacity were based on real standards from
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collaborating petrochemical industries. There were three types of storage tanks: Two 60,000-
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ton, six 33,000-ton, and four 20,000-ton tanks. The overall capacity of each tank was approximately 300,000 tons, and the minimum level of the total tank was 80,000 tons. The
Ac ce p
feed flow rate was set to 300,000 tons per month for the entire period. All storage tanks were available to take the naphtha and feed the cracking unit. The current optimization model was allowed to purchase the naphtha every month under the circumstances of future trading. The optimization approach used is explained by the event tree in Fig. 12 (Hellevik, Langen, and Sorensen, 1999). In addition, the newest monthly updated data was used (e.g., the actual and predicted price information, amount of purchase, and inventory capacity) when the optimization was carried out in the time interval. Generally, future purchases of naphtha are determined by the predicted price. The inventory and storage tank level fluctuates with the predicted price and future purchases of naphtha. The objective function of the optimization is to minimize the average purchase price in this study. The purchase price considers hedge trading and the amount of naphtha purchased. The price is calculated as the finalized procurement plus the hedge cost of the future. Constraints include the capacity limitations of inventory tanks and the amount of naphtha purchased. Eq.
Page 16 of 39
(9) presents the objective function of the NLP model aimed at minimization of the purchase price.
( HE 2t 1 HE 2t 1 ) Pt 1 HE 3t 2 Pt 1} / ( FN t 1 FN t 2 FN t 3 ) (9)
ip t
MinP {FN d 1 Pd 1 FN d 2 Pd 2 ( HE1t HE 2t HE 3t ) Pt
cr
Eqs. (10), (11), and (12) illustrate the amount of naphtha purchased including hedge trading.
us
FN t 1 FN d 1 HE1t (10)
an
FN t 2 FN d 2 HE 2t HE 2t 1 (11)
M
FN t 3 HE 3t HE 3t 1 HE 3t 2 (12)
d
FN d 1 and FN d 2 are the amounts of naphtha of the finalized procurement. HE1t , HE 2t ,
te
HE 2t 1 , HE 3t , HE 3t 1 and HE 3t 2 are the amounts of naphtha by hedge trading.
Ac ce p
Eq. (13) gives the amount of naphtha procurement constraint at time t. FN tL FN t FN tU , t T
(13)
FN t is the amount of naphtha purchased at time t, and Ft L and FtU are the lower and upper limitations at that time.
Eqs. (14), (15), and (16) indicate the storage tank capacity at each time horizon. FTt 1 FTt FN t 1 RC (14) FTt 2 FTt 1 FN t 2 RC (15)
Page 17 of 39
FTt 3 FTt 2 FN t 3 RC (16)
Eq. (17) describes the storage capacity constraint of the tank.
cr
FTt L FTt FTtU , t T
ip t
RC is the fixed running capacity of the process.
us
(17)
FTt is the naphtha storage tank at time t. FTt L and FTtU are the lower and upper limitations
an
at that time. Short sales are impossible during hedge trading, as shown in Eqs. (18) to (23). FN t 1 0
M
(18) FN d 2 HE 2t 0
Ac ce p
(20)
te
FN t 1 0
d
(19)
HE 3t 0 (21)
HE 3t HE 3t 1 0 (22)
FN t 2 0 (23)
Table 2 shows the comparative results of the actual and proposed approaches when the best model is selected for forecasting the price based on SD. The procurement planner determines the naphtha purchases after analyzing the future naphtha price. Generally, if the price is predicted to rise in the next month, most buyers will purchase a greater amount of naphtha than they would have already agreed to purchase. Then, in the next month, buyers can sell the
Page 18 of 39
purchased naphtha by considering the future naphtha forecasting price in case the actual naphtha price increases. However, if the actual price decreases, buyers can purchase more naphtha. Therefore, naphtha price prediction is a very important factor for minimizing the average purchase price. This price is minimized by the naphtha purchase process based on the
ip t
NLP model. The optimized purchase price is affected by the predicted price, amount of naphtha, and future trading. In order to minimize the purchase price, all naphtha purchases
cr
consider the future trading of the next three months.
This study was performed to compare the average purchase units and amount of naphtha
us
purchases for actual trade, the heuristics approach, and the optimization results. The actual trade purchasing method indicates that buyers constantly purchase the same naphtha quantities for one year. Heuristic values depend on the variance of the predicted price using
an
the forecasting model. The heuristics approach applies to multiplying the weighting when purchasing naphtha according to the predicted price variance of the last and current months.
M
The average purchase prices of actual trade, heuristics, and optimization were 938.24, 900.46, and 892.54 USD/ton, respectively. Furthermore, the total quantities of the purchased naphtha for each methodology were 2.40, 2.49, and 2.50 million tons per year. This paper
d
compared their total purchasing costs. The total purchasing cost based on optimization
te
resulted in profit savings of USD 20.50 million per year in petrochemical companies. This saving cost reduced the price by 4.8% in comparison with business profits in 2013. Based on
Ac ce p
these results, it appears that the optimization model is preferable to the heuristic approach. The average purchase price with the heuristic approach was similar to the actual price, but the average optimization value was approximately USD 45.07 cheaper than the actual price.
Page 19 of 39
ip t
5. Conclusions The point of purchase of naphtha is very important as it is related to business profit in petrochemical industries. In order to prevent companies from having an operating loss, this
cr
research has proposed various models for naphtha price forecasting to predict naphtha price variation, which is of great interest to decision makers, as it would enable them to purchase
us
naphtha at the appropriate time. In addition, an optimization model was developed using naphtha price prediction. The point of purchase of naphtha was determined by the fluctuation
an
trends of the naphtha prediction price and optimization model. The SM, ESM, and ANN models only considered the time-series data, and their FAPs were 67.86%, 75.00%, and 85.71%, respectively. The FAPs of these general models exhibited decreased accuracy for
M
long-term forecasting as they only considered related data. Therefore, the SD model was developed by considering qualitative factors and the existing data, and it was found to show
d
the highest FAP (92.28) for the European naphtha price. The present naphtha forecasting results were also compared with the published crude oil forecasting results. The optimization
te
model of the naphtha average purchase price was found to be superior to the heuristic approach. The average purchase prices of the optimization and heuristic approaches were
Ac ce p
892.54 and 938.24 USD/ton, respectively, and the average optimization value was approximately 45.07 USD/ton cheaper than the heuristic approach. Thus, the SD model developed in this study provided the best forecasts of European naphtha prices, and an optimization model that considers naphtha price prediction can determine the optimal point of purchase of naphtha. This is of great significance for decision makers looking to improve the economic benefits for petrochemical companies.
Acknowledgement Financial support from Samsung Total Petrochemicals Co. Ltd and the BK 21 Program funded by the Ministry of Education (MOE) of Korea are gratefully acknowledged. Also, this
Page 20 of 39
research was supported by the Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry, and Energy (MOTIE).
ip t
Nomenclature
cr
FN d 1 , FN d 2 past finalized purchases of naphtha
FTt 1 , FTt 2 , FTt 3
us
FN t 1 , FN t 2 , FN t 3 amount of naphtha purchased at time t+1, t+2, and t+3 level of storage tank at time t+1, t+2, and t+3
an
HE1t hedging trading in the first month HE 2t , HE 2t 1 hedging trading in the second month
M
HE 3t , HE 3t 1 , HE 3t 2 hedging trading in the third month
te
Ac ce p
RC running capacity
d
Pt , Pt 1 , Pt 2 naphtha price at time t, t+1, and t+2
Page 21 of 39
References
Ac ce p
te
d
M
an
us
cr
ip t
Asche, F., Gjølberg, O., & Völker, T. Price relationships in the petroleum market: an analysis of crude oil and refined product prices. Energy Economics 2003;25:289-301. Aslani, A., Helo, P., & Naaranoja, M. Role of renewable energy policies in energy dependency in Finland: System dynamics approach. Applied Energy 2014;113:758765. Bulsari, G. P. Neural networks for chemical engineers; Elsevier Science: Amsterdam, The Netherlands 1995. Chen, S.-S., & Hsu, K.-W. Reverse globalization: Does high oil price volatility discourage international trade? Energy Economics 2012;34:1634-1643. Fan, Y., Liang, Q., & Wei, Y.-M. A generalized pattern matching approach for multi-step prediction of crude oil price. Energy Economics 2008;30:889-904. Fan, Y., Zhang, Y.-J., Tsai, H.-T., & Wei, Y.-M. Estimating ‘Value at Risk’ of crude oil price and its spillover effect using the GED-GARCH approach. Energy Economics 2008;30:3156-3171. Forrester, J. W. Industrial Dynamics. Cambridge1961, MA: The MIT Press. Gao, L., Kim, H., & Saba, R. How do oil price shocks affect consumer prices? Energy Economics 2014;45:313-323. Ghaffari, A., & Zare, S. A novel algorithm for prediction of crude oil price variation based on soft computing. Energy Economics 2009; 31:531-536. Gori, F., Ludovisi, D., & Cerritelli, P. F. Forecast of oil price and consumption in the short term under three scenarios: Parabolic, linear and chaotic behaviour. Energy 2007;32:1291-1296. Göthe-Lundgren, M., Lundgren, J. T., & Persson, J. A. An optimization model for refinery production scheduling. International Journal of Production Economics 2002;78(3):255–270. Hellevik, S. G., Langen, I., & Sorensen, J. D. Cost optimal reliability based inspection and replacedment planning of piping subjected to CO2 corrosion. International Journal of Pressure Vessels and Piping 1999; 76: 527-538. Himmelblau, D. Applications of artificial neural networks in chemical engineering. Korean Journal of Chemical Engineering 2000; 17: 373-392. Holland, S. P. Economics of Peak Oil. In J. F. Shogren (Ed.), Encyclopedia of Energy, Waltham: Elsevier, Natural Resource and Environmental Economics; 2013.p.146150. Jeon, C., & Shin, J. Long-term renewable energy technology valuation using system dynamics and Monte Carlo simulation: Photovoltaic technology case. Energy 2014;66:447-457. Julka, N., Srinivasan, R., & Karimi, I. Agent-based supply chain management 1: Framework. Computers & Chemical Engineering 2002a;26(12):1755–1769. Julka, N., Srinivasan, R., & Karimi, I. Agent-based supply chain management 2: A refinery application. Computers & Chemical Engineering 2002b;26(12):1771– 1781. Kang, I.-B. Multi-period forecasting using different models for different horizons: an application to U.S. economic time series data. International Journal of Forecasting 2003;19:387-400.
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Kang, S. H., Kang, S.-M., & Yoon, S.-M. Forecasting volatility of crude oil markets. Energy Economics 2009;31:119-125. Kang, S. H., & Yoon, S.-M. Modeling and forecasting the volatility of petroleum futures prices. Energy Economics 2013;36:354-362. Khashei, M., Bijari, M., & Raissi Ardali, G. A. Improvement of Auto-Regressive Integrated Moving Average models using Fuzzy logic and Artificial Neural Networks (ANNs). Neurocomputing 2009;72:956-967. Lakkhanawat, H., & Bagajewicz, M. J. Financial risk management with product pricing in the planning of refinery operations. Industrial & Engineering Chemistry Research 2008;47(17):6622–6639. Lara, A., Turner, M., Leger, M. W., & Auers, J. AM-07-45 Crude Oil Price Forecasting: A Statistical Approach. 2007. Lee, B.-J., Yang, C. W., & Huang, B.-N. Oil price movements and stock markets revisited: A case of sector stock price indexes in the G-7 countries. Energy Economics 2012;34:1284-1300. Lyu, B., Kwon, H., Lee, J., Yoon, H., Jin, J., & Moon, I. Forecasting of Naphtha Demand and Supply using Time Serial Data Causal Analysis. In P. S. V. Jiří Jaromír Klemeš & L. Peng Yen (Eds.), Elsevier, Computer Aided Chemical Engineering 2014;33:829-834. Lee, H., Pinto, J. M., Grossmann, I. E., & Park, S. Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Industrial & Engineering Chemistry Research 2012; 51: 8453-8464. Masih, A. M. M., Albinali, K., & DeMello, L. Price dynamics of natural gas and the regional methanol markets. Energy Policy 2010;38:1372-1378. Masih, M., Algahtani, I., & De Mello, L. Price dynamics of crude oil and the regional ethylene markets. Energy Economics 2010;32:1435-1444. Montroll, E. W. On some mathematical models of social phenomenon. In V. Lakshmikantham (Ed.), Nonlinear Equations in Abstract Spaces, Academic Press; 1978.p.161-216. Morana, C. A semiparametric approach to short-term oil price forecasting. Energy Economics 2001;23:325-338. Movilla, S., Miguel, L. J., & Blázquez, L. F. A system dynamics approach for the photovoltaic energy market in Spain. Energy Policy 2013;60:142-154. Oddsdottir, T. A., Grunow, M., & Akkerman, R. Procurement planning in oil refining industries considering blending operation. Computer & Chemical Engineering 2013;58:1-13. Pan, M., Li, X., & Qian, Y. New approach for scheduling crude oil operations. Chemical Engineering Science 2009; 64: 965-983. Peng, M., Peng, Y., & Chen, H. Post-seismic supply chain risk management: A system dynamics disruption analysis approach for inventory and logistics planning. Computers & Operations Research2014;42:14-24. Qudrat-Ullah, H. Understanding the dynamics of electricity generation capacity in Canada: A system dynamics approach. Energy 2013;59:285-294. Raida, Z. Modeling EM structures in the neural network toolbox of MATLAB. Antennas and Propagation Magazine, IEEE 2002;44:46-67. Rao, R. D., & Parikh, J. K. Forecast and analysis of demand for petroleum products in India. Energy Policy 1996;24:583-592. Reddy, P. C. P., Kirimi, I. A., & Srinivasan, R. Novel solution approach for optimizing crude oil operations. Americal Institute of Chemical Engineers Journal 2004; 50: 1177-1197. Regnier, E. Oil and energy price volatility. Energy Economics 2007;29:405-427.
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an
us
cr
ip t
Speight, J. G. The Chemistry and Technology of Petroleum (Fourth ed.): CRC Press; 2006. Sung, C., Kwon, H., Lee, J., Yoon, H., & Moon, I. Forecasting Naphtha Price Crack Using Multiple Regression Analysis. In A. K. Iftekhar & S. Rajagopalan (Eds.), Elsevier, Computer Aided Chemical Engineering 2012;31.p. 145-149. Visetsripong, P., Sooraksa, P., Luenam, P., & Chaimongkol, W. Naphtha's price forecasting using Neuro-fuzzy system. In SICE Annual Conference; 2008.p. 659-663. Wei, Y., Wang, Y., & Huang, D. Forecasting crude oil market volatility: Further evidence using GARCH-class models. Energy Economics 2010;32:1477-1484. Wen, X., Guo, Y., Wei, Y., & Huang, D. How do the stock prices of new energy and fossil fuel companies correlate? Evidence from China. Energy Economics 2014;41:63-75. Wong, S. L., Chang, Y., & Chia, W.-M. Energy consumption, energy R&D and real GDP in OECD countries with and without oil reserves. Energy Economics 2013;40:51-60. Ye, M., Zyren, J., & Shore, J. A monthly crude oil spot price forecasting model using relative inventories. International Journal of Forecasting 2005;21:491-501. Zhang, G. P., & Qi, M. Neural network forecasting for seasonal and trend time series. European Journal of Operational Research 2005;160:501-514. Zhang, J., Wen, Y., & Xu, Q. Simultaneous optimization of crude oil blending and purchase planning with delivery uncertainty consideration. Industrial & Engineering Chemistry Research 2012;50(25):8453–8464.
te
d
List of Table
Table 1. Comparative analysis of naphtha price forecasts (this study) and crude oil price
Ac ce p
forecasts (literature)
Table 2. Comparison of optimization and heuristics method results for average purchasing unit price
Page 24 of 39
ip t cr us an
Predication
Training
Horizon
d
Approach
M
Table 1. Comparative analysis of naphtha price forecasting (this study) and crude oil price forecasting (literature) FAP (%)
Reference
2010.05~2012.09
67.86
This study
SM
Monthly
ESM
Monthly
2008.06~2010.04
2010.05~2012.09
75.00
This study
ANN
Monthly
2008.06~2010.04
2010.05~2012.09
85.71
This study
Ac ce p
te
2008.06~2010.04
Prediction
European naphtha price (SD)
Monthly
2008.06~2010.04
2010.05~2012.09
92.28
This study
Asian naphtha price (SD)
Monthly
2008.06~2010.04
2010.05~2012.09
82.29
This study
Semi parametric approach
Daily
-
1998.11.21 ~ 1999.01.21
46.67
(Morana, 2001)
Genetic algorithm
Daily
-
2005.06.27 ~ 2005.07.26
54.58
(Fan, Liang, et al., 2008)
ANFIS
Monthly
-
1999.02 ~ 2003.12
45.76
(Gori et al., 2007)
ANFIS (SP model)
Daily
-
2007.01.05 ~ 2007.05.31
70.09
(Ghaffari & Zare, 2009)
Page 25 of 39
an
us
cr
ip t
2009)
Table 2. Comparison of optimization and heuristics method results for average purchasing
Actual
Heuristics
M
unit price
Optimization
870.78
870.78
784.68
Feb-11
895.14
878.39
824.10
978.95
889.56
1050.64
1056.78
946.61
988.26
1026.16
939.00
Jun-11
939.55
941.90
969.17
Jul-11
974.27
993.34
949.15
Aug-11
946.29
965.84
925.00
Sep-11
947.61
939.27
905.18
Oct-11
883.86
890.08
882.61
Nov-11
878.23
857.30
845.64
Dec-11
902.61
856.84
859.23
Average
938.24
937.97
893.33
Apr-11
Ac ce p
May-11
981.61
te
Mar-11
d
Jan-11
Page 26 of 39
Figure Captions
Figure 2. Flowchart of the forecasting model
cr
Figure 3. Comparison of normalized actual and three forecasting models
us
Figure 4. Three-layer artificial neural network (ANN) Figure 5. Causal loop diagram of naphtha supply
ip t
Figure 1. Crude oil (WTI) and naphtha price trends
an
Figure 6. Comparison of normalized actual and forecast naphtha supply
M
Figure 7. Causal loop diagram of naphtha demand
Figure 8. Comparison of normalized actual and forecast naphtha demand
d
Figure 9. Causal loop diagram of Asian and European naphtha
te
Figure 10. Comparison of normalized actual and forecast European naphtha prices
Ac ce p
Figure 11. Comparison of normalized actual and forecast Asian naphtha prices Figure 12. Branch (indicated by solid line) in the time interval t1 t t3 to be included in the calculation of the newest updated data of optimization model
Page 27 of 39
te
d
M
an
us
cr
ip t
Figure 1. Crude oil (WTI) and naphtha price trends
Ac ce p
Figure 2. Flowchart of the forecasting model
28
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ip t cr us an M Ac ce p
te
d
l
Figure 3. Comparison of normalized actual and three forecasting models
29
Page 29 of 39
ip t cr us an M d te
Ac ce p
Figure 4. Three-layer artificial neural network (ANN)
30
Page 30 of 39
ip t cr us an M d te Ac ce p
Figure 5. Causal loop diagram of naphtha supply
31
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ip t cr us an M d te
Ac ce p
Figure 6. Comparison of normalized actual and forecast naphtha supply
32
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ip t cr us an M Ac ce p
te
d
Figure 7. Causal loop diagram of naphtha demand
33
Page 33 of 39
ip t cr us an M d te Ac ce p
Figure 8. Comparison of normalized actual and forecast naphtha demand
34
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ip t cr us an M d te
Ac ce p
Figure 9. Causal loop diagram of Asian and European naphtha
35
Page 35 of 39
ip t cr us an M d te Ac ce p
Figure 10. Comparison of normalized actual and forecast European naphtha prices
36
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ip t cr us an M d
Ac ce p
te
Figure 11. Comparison of normalized actual and forecast Asian naphtha prices
37
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ip t cr us an M d te
Figure 12. Branch (indicated by solid line) in the time interval t1 t t3 to be included in the
Ac ce p
calculation of the newest updated data of optimization model
38
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39
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d
te
Ac ce p us
an
M
cr
ip t
S0098-1354(15)00273-2 http://dx.doi.org/doi:10.1016/j.compchemeng.2015.08.012 CACE 5263
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
9-12-2014 19-8-2015 22-8-2015
Please cite this article as: Kwon, H., Lyu, B., Tak, K., Lee, J., Cho, J. H., and Moon, I.,Optimization of naphtha purchase price using a price prediction model, Computers and Chemical Engineering (2015), http://dx.doi.org/10.1016/j.compchemeng.2015.08.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights
The average optimization value is approximately 45.07 USD/ton cheaper than
ip t
the actual purchase price.
Nonlinear Programming (NLP) model was developed to optimize the naphtha
cr
purchase price.
us
Proposed SD model give best prediction accuracy for Europe naphtha price (FAP 92.28).
an
Proposed SD and optimization model would be of great significance for industry
Ac ce p
te
d
M
decision-makers.
Page 1 of 39
Optimization of naphtha purchase price using a price prediction
cr
ip t
model
Hweeung Kwona, Byeonggil Lyua, Kyungjae Taka, Jinsuk Leeb, Jae Hyun Choc,
Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei ro,
an
a
us
Il Moona,*
Seodaemun-ku, Seoul 120-749, Korea
Hanwha total Corporation, 411, Dokgot-ri, Daesan-eup Seosan-si, Chungcheongnam-do
356-711, Korea c
M
b
Engineering Development Research Center (EDRC), Seoul National University, 1, Gwanak-
te
d
ro, Gwanak-gu, Seoul 151-744, Korea
*Corresponding author: Il Moon, [email protected]; Tel.: +82 2 2123 2761; Fax: +82 2312-
Ac ce p
6401
Page 2 of 39
Abstract In order to meet company needs, various models of naphtha price forecasting and optimization models of average naphtha purchase price have been developed. However, these
ip t
general models are limited in their ability to predict future trends as they only include quantitative data. Furthermore, naphtha price predictions based on fluctuation trends have not been published in the literature. Thus, we developed a system dynamics (SD) model
cr
considering time-series data, mathematical formulations, and qualitative factors. The results obtained from our model were compared with the published literature. The best result of the
us
SD is the European naphtha forecasting price model, and the forecasting accuracy percentage shows 92.82%. Furthermore, an nonlinear programming (NLP) model was developed to
an
optimize the purchase price by considering the naphtha price of the forecasting models. In addition, the average optimization value was approximately 45.07 USD/ton cheaper than that
M
of the heuristic approach.
Ac ce p
te
dynamics, Heuristics
d
Keywords: Purchase price optimization, Artificial neural network, Forecasting model, System
1. Introduction
Page 3 of 39
Naphtha plays an important role in the world economy as it is used to produce widely used products including ethylene, propylene, and butadiene as well as aromatic products such as benzene, toluene, and xylene through thermal cracking. Naphtha price trends tend to follow that of crude oil (Asche et al., 2003). Fig. 1 shows the trends of West Texas Intermediate
ip t
(WTI) crude oil and naphtha prices from March 1996 to November 2011. This close relationship means that naphtha price forecasting has a great influence on all loss factors in
cr
petrochemical industries. For example, the point of purchase of oil has a significant effect on the total profit of oil refiners. If the oil price falls by $1, oil refiners suffer an operating profit
us
loss of $10 billion.
Naphtha price is also affected by the supply and demand for the product as well as ocean freight costs, both of which have political consequences (Chen & Hsu, 2012; Gao et al.,
an
2014; Holland, 2013; Kang et al., 2014; Lee et al., 2012; Montroll, 1978; Wen et al., 2014; Wong et al., 2013). Therefore, decision makers want to reduce the uncertainty of future prices.
M
However, decisions on the point of purchase of naphtha require the domain knowledge of chemical engineers. General mathematical models including the statistical model (SM), exponential smoothing model (ESM), and artificial neural network (ANN) are well known in
d
the chemical engineering field, but these general models are now being applied to naphtha
te
price forecasting for the first time. In addition, the innovative system dynamics (SD) model is very valuable for determining the point of purchase because it considers integrated data and
Ac ce p
heuristics. These considerations prompted us to predict naphtha price using the SM, ESM, and ANN forecasting models. An SD model based on a causal loop considering human and psychological heuristics was also applied to naphtha price forecasting. Heuristics is a very important approach for producing decisions at the point of purchase, and their efficacy can affect naphtha purchase. The heuristic approach allows us to reach reasonable solutions for planning decisions.
This paper considers short-term planning for the naphtha purchase problem, which includes the number of naphtha purchases, inventory levels, and running capacity for cracking units. We assume that a naphtha purchase plan is determined by petrochemical industry planning, and this research analyzes the optimization problem to minimize the costs included in spot trading to achieve optimal naphtha purchase planning. Furthermore, we developed a general nonlinear programming (NLP) model to optimize the purchasing unit price and compared its results with the heuristic results. The purpose of this research is to develop a reliable forecasting model. Moreover, the average purchase price was minimized by naphtha
Page 4 of 39
procurement planning using the predicted price. The numerical results of this paper verify the effectiveness of the optimization model. In summary, the NLP model can help decision makers to plan purchase opportunities, so naphtha can be bought at an optimal price.
ip t
2. Literature review
Predictions of crude oil prices have been carried out by many investigators all over the
cr
world (Fan et al., 2008; Gori et al., 2007; Kang & Yoon, 2013; Lara et al., 2007; Rao & Parikh, 1996; Regnier, 2007; Wei et al., 2010; Ye et al., 2005, 2006) but studies on naphtha
us
price forecast are scarce (Lyu et al., 2014; Rao & Parikh, 1996; Sung et al., 2012; Visetsripong et al., 2008). Various approaches to forecasting oil price have used both linear
an
and nonlinear models. Lara et al. applied a simple linear regression model to predict crude oil prices and stochastic models to calculate patterns of volatility in oil prices (Lara et al., 2007). Instead of using a single autoregressive model for all horizons, Kang reported a multi-period-
M
ahead forecasting autoregressive model selected separately for each horizon and found that forecast performance depends on optimal order selection criteria, forecast origins, forecast
d
horizons, and the time series to be forecasted (Kang, 2003). Kang and Yoon (2013) studied the forecasting potential of the ARIMA–GARCH,
te
ARFIMA–GARCH, ARFIMA–IGARCH, and ARFIMA–FIGARCH models by using the daily spot prices of WTI crude oil. Their results for unleaded gasoline suggested that the
Ac ce p
ARFIMA–FIGARCH model better captures the long-memory properties of the returns and volatility, even though there was no unique model for all three types of petroleum products. Kang et al. attempted to find the best model to forecast volatility in three crude oil prices (WTI, Brent, and Dubai). They evaluated the volatility of the three crude oil prices using daily spot prices during the period January 6, 1992 to December 29, 2006 by considering the out-of-sample forecasts of the 1, 5, and 20-day forecasting horizons, corresponding to 1-day, 1-week, and 1-month trading periods, respectively. It was found that for Brent and Dubai crude oil, the FIGARCH model was superior to other models (GARCH, IGARCH, and CGARCH) for all three forecast horizons, from 1-day to 1-month. However, in the case of WTI crude oil, the CGARCH model outperformed the other models (Kang et al., 2009). Visetsripong et al. studied naphtha forecasting using the adaptive neuro-fuzzy inference system (ANFIS) and the statistical method for nonlinear time-series data (Visetsripong et al., 2008). It was found that 86% of the comparison tests showed that the ANFIS model
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forecasting power achieved more accurate results than the exponential smoothing method. It was concluded that the neuro-fuzzy system method is more accurate and more reliable than the statistical method when used to forecast nonlinear time-series data. Wei et al. (2010) compared nine linear and nonlinear GARCH-class models: RiskMetrics, GARCH, IGARCH,
ip t
GJR, EGARCH, APARCH, FIGARCH, FIAPARCH and HYGATCH. They concluded that the nonlinear GARCH-class models are capable of capturing long-memory and/or
cr
asymmetric volatility and exhibit greater forecasting accuracy than linear ones, especially in volatility forecasting over longer time horizons, such as five or twenty days, for WTI and
us
Brent crude oil. Masih et al. investigated the impact of ethylene prices in the naphtha intensive ethylene markets of the Far East, North West Europe, and the Mediterranean on WTI crude oil price (Masih et al., 2010). They observed that the ethylene prices in North
an
West Europe and the Mediterranean were weakly endogenous, but the Far East ethylene price was weakly exogenous, both in the short and long term. It was even found that the results
M
were consistent during the period under review, which had a surge in demand for ethylene throughout the Far East, especially in China and South Korea. However, during the postsample forecast period, as evidenced in their variance decomposition analysis, the emergence
d
of WTI as a leading player was found to be consistent with the recent surge in WTI price.
te
This change reflects the growing importance of input costs in determining the dynamic interactions of the input and product prices.
Ac ce p
The results of these studies showed that (a) the time-series model was adequate for forecasting oil prices in the short run but had limited forecasting ability in the medium and long-term, (b) time-series models proved to be accurate forecasts of oil price volatility, but a single model could not be used in every case, and (c) oil prices and their volatility displayed significant nonlinearity, which indicates that small shocks to the economy could have large and unpredictable implications for oil prices and their volatility. Recently, the application of artificial neural networks (ANN) has been reported in many fields. An ANN model is a computational model inspired by the brain’s central nervous system (Raida, 2002). Zhang and Qi (2005) proposed a hybrid model in time series prediction using both the autoregressive integrated moving average (ARIMA) and the ANN models. The hybrid model was able to improve the forecasting accuracy in the time series data. Khashei et al. (2009) integrated the ARIMA and ANN models with fuzzy logic in order to overcome the linear and data limitations of ARIMA models to get more accurate results. The proposed models were more reliable in forecasting future prices. Another approach that is
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used by many researchers in different fields is the system dynamics model (SD) using a causal loop (Aslani et al., 2014; Jeon & Shin, 2014; Mao et al., 2013; Movilla et al., 2013; Peng et al., 2014; Qudrat-Ullah, 2013). Ullah explained the dynamic variables acting in the electricity supply and demand of Canada using a causal loop diagram of SD (Qudrat-Ullah,
ip t
2013). Aslani et al. (2004) developed a system dynamic model with the role of renewable energy resources for energy security investigations in Finland. Jeon and Shin (2014)
cr
proposed a long-term technology valuation method for renewable energy technologies with a system dynamics model combined with the Monte Carlo method. This study considered a
us
causal loop diagram under the 3E framework. Peng et al. (2014) proposed a system dynamics model considering the uncertainties related to forecasting post-seismic road networks and delayed information. Movilla et al. (2013) developed a model based on SD to understand the
an
behavior of the photovoltaic sector in Spain and its expectations under possible scenarios. Decision making on naphtha purchases is very important for petrochemical industries.
M
Numerous important scheduling and planning problems have been analyzed in recent decades. Lakkhanawat and Bagajewicz (2008) addressed how much crude oil has to be purchased. Procurement methods can be very valuable in refineries. However, they do not provide
d
sufficient information to decision makers because it is not important what crude oil is
te
purchased. Their proposed model only considers six crude oil types and three time horizons. In addition, it indicates that the proposed model is not appropriate as a supporting method for
Ac ce p
decision makers. Julka, Srinivasan, and Karimi (2002a, 2002b) developed an agent-based decision support systems (DSSs) framework for a supply chain and a petroleum refinery integrated supply chain modeler and simulator (PRISMS) for a decision-supporting tool for crude oil procurement. These systems facilitate integrated decisions in terms of the refinery business. However, their studies only provide insight into responding to changes in domestic policies and unexpected events in an international environment. Göthe-Lundgren, Lundgren, and Persson (2002) solved the scheduling problem based on the mixed-integer programming (MIP) model, including utilization of the production process. They formulated an optimization model for production scheduling that can support the decisions of procurement planners at the strategic, tactical, and operational planning levels. However, the developed model is only designed to integrate planning with production scheduling and does not focus on support for procurement or purchase plan decisions. Zhang, Wen, and Xu (2012) introduced mixed integer nonlinear programming (MINLP) for optimization of crude oil blending and purchase planning with uncertainty. This is a significant contribution to
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decision support that considers short-term crude oil blending and long-term purchase planning simultaneously. However, it has limitations based on the given information, such as the estimated crude oil price and crude oil type. Most previous work has aimed to develop a rigorous optimization model for short-term
ip t
crude oil unloading, the inventory management of crude charging and mixing tanks, and crude distillation unit (CDU) operation scheduling. The objective of these papers is to
cr
minimize operation costs, which involve inventory costs, crude vessel sea waiting and harboring costs, and changeover costs for each CDU. Lee et al. (1996) developed an
us
optimization model based on the mixed integer linear programming (MILP) model for shortterm refinery scheduling by considering crude oil unloading and inventory management. Oil procurement planning in refineries is addressed with an innovative two-stage solution
an
approach using the MINLP model. The developed model easily handles crude oil types and
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quality parameters compared with existing papers.
3. Data preparation and normalization
d
The current study considers the actual price of naphtha and 37 major factors, such as the naphtha demand, naphtha supply, European naphtha price, and Asian naphtha price. First,
te
naphtha demand takes into consideration downstream products (e.g. ethylene, propylene, butadiene, benzene, toluene, and xylene), the operation rate, and margin in the petrochemical
Ac ce p
industry. Second, naphtha supply includes the production quantities of BTX (benzene, toluene, and xylene), naphtha production of the refinery, T/A of the refinery, operation rate of the refinery, and type of oil. Third, the European naphtha price is assumed to be influenced by the naphtha inventory, oil price, Europe gasoline and propane price, and seasonality. Finally, the Asia naphtha price is assumed to be influenced by the Asian naphtha demand and supply interrelated with the European naphtha price. The naphtha price and the 37 major factors have different values. Therefore, this actual data and the value of the 37 major factors are normalized from 0 to 1.
3.1. Data preparation The naphtha price data (in USD/ton) was obtained from the Mean of Platts Japan (MOPJ) as the representative naphtha price for this analysis. The MOPJ indicates the monthly data on the naphtha price, which is treated as the benchmark naphtha price for the international
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market. The naphtha prices and 37 major factors for the previous trading month were used in the SD model. The datasets consisted of 37 points for the naphtha monthly price from May 2010 to September 2012. The naphtha price is presented for every month, which includes five
ip t
days per week except for weekends (here Fridays and Saturdays) and official holidays.
3.2. Data normalization
cr
Data normalization is the process of removing redundant data from various variable datasets. Data normalization is needed to compare price and other major factors. The following
us
equation is used for data normalization:
X max Maxdata 1.02 ~ 1.07 ,
X i X min . X max X min
M
X i,normalization
an
X min Mindata 1.02 ~ 1.07 ,
(1)
d
where X i is the value of the ith data point, X min is the minimum value among all the data
te
points, and X max is the maximum value among all the data points. The advantages of data normalization include the ability to maintain data integrity, a maximum price correlation with
Ac ce p
the 37 major factors, and a minimum standard deviation. All the major factors in the data were normalized in a range from 0 to 1. 3.3. Proposed forecasting methodology This section describes the three different approaches used for forecasting: (a) The SM, (b) ESM, and (c) ANN models. Another model based on SD was also developed in this study. The methodology was applied to naphtha price forecasting as shown in the flowchart in Fig. 2. This study included 45 data values of actual naphtha price and 37 major factors. Among the four datasets in the SM and ESM models, the first 50% of all the data was used as the training set to find the optimal model parameters, and the remaining 50% was used for verification purposes or prediction ability. The model parameters were obtained through training. The concepts of each approach are detailed in Fig. 2. If the predicted variance of the naphtha price has the same trend as the actual naphtha variance, the predicted value is treated as correct. Otherwise, the predicted value is treated as incorrect. The forecasting accuracy percentage
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(FAP) is computed by dividing the number of correct predictions by total predictions as follows: FAP
Number of correct predictions 100 . Number of total predictions
cr
ip t
(2)
4. Results and discussion
us
4.1. Statistical method model
The statistical method (SM) model was developed using the Statistical Package for the
an
Social Sciences (SPSS) tool. The SM method was used to model the linear relationships between one dependent variable and several independent variables. It is based on multiple linear regressions. The SM equation, with the error term, is defined as follows:
M
f x1 , x2 , , xn Ft 0 1 x1,n 2 x2,n n xn ,t n . (3)
d
where n is the parameter, and xn ,t is each major factor value for a specific time. Each
te
parameter of the SM is estimated such that the sum of the squares of error is minimized.
Ac ce p
Therefore, the forecasting equation is given by
Ft ' 0' 1' x1,n 2' x2,n n' xn,t . (4)
where the symbol (’) denotes the estimated parameter values. The error term includes multiple regression residuals and is defined as follows:
n' Ft Ft ' . (5)
Here, Ft and Ft ' represent the actual value and the predicted value of the nth month, respectively. The regression residuals measure the nearness of the actual and predicted values in the calibration periods.
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The results reported in this section were collected after training the data of the SM model. We used a time-series method for forecasting. In order to carry out the simulation, we divided the data into four datasets (50:50, 60:40, 70:30, and 80:20). The results of the model used for the training and verification steps were compared with the real data of the normalized
ip t
naphtha prices. The naphtha prices for a continuous 29-month (May 2010 to September 2012) period and 37 factor values were selected. The best prediction of these four datasets (i.e.,
cr
50:50) of the normalized naphtha price variance for the 29 months was compared with the normalized actual values of the corresponding months in Fig. 3. The FAP of the normalized
us
SM was 67.86% for this duration of 29 months. The SM model generally has one problem: n data values are contained in the average, and then the n-1 values of the previous data must be included for future forecasts.
M
4.2. Exponential smoothing method model
an
carried forward in order to be combined with the real observation values. The past data was
The exponential smoothing method (ESM) was introduced by Robert G. Brown in 1944. ESM can be applied to time-series data, and it is one of the most efficient forecasting
d
methods when the time-series data has neither seasonality nor trend. ESM assigns weights to
te
past data and adjusts for past inaccuracies in prediction. To achieve this, the ESM model uses a weighting factor in which the weight reflects the most recent values. The time-series data is
Ac ce p
a sequence of observations. The following simple form of ESM is given by F1 x0 ,
F1
Y1 Y2 Yt Y Y Yt 1 t t 1 , t t
F1 xt 1 1 Ft 1 . (6)
where Ft is the forecast value at period t. In this equation, the forecasting value Ft applies the weighting factor of the previous observation data xt 1 . The weighting factor of ESM is , which ranges from 0 to 1. The value of the weighting factor determines the smoothing degree applied to the fluctuations of the data. A small shows a visible ESM trend, and a large provides a quicker response to recent changes in a time series. If the value is close
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to 1, the prediction value will contain an effective adjustment for the error in the preceding forecast whereas when the value is close to 0, the prediction value is similar to the preceding real data. The ESM can quickly produce accurate forecasting values and change the weighting factor value to fit the model adequately in some external environments.
ip t
However, the ESM model often produces forecasts that lag behind the trend of the real values. In addition, the forecasting values considered in the ESM model are very sensitive to the
cr
standard of the smoothing constant.
The ESM model applies the exponential smoothing technique to the existing model. The
us
results reported in this section were collected after training the data of the ESM model. The ESM model simulates the same method as the SM model. Fig. 3 shows the best dataset (50:50) of the normalized naphtha price variance for 29 months compared with the
an
normalized actual price. The forecasting values of the ESM appear as if they were delayed by one month for the normalized actual price. The FAP of the ESM is 75.00 for the total period.
M
This model is usually used for short-term predictions because it does not operate well if the time-series data have seasonal or cyclical variations.
d
4.3. Artificial neural network model
te
A neural network (NN) finds a pattern or correlation with a large amount of data in a very complex structure; therefore, it is useful for future predictions. NNs have many features, such
Ac ce p
as an adaptive system, many simple process elements, and high interconnectivity. The ANN is used for computing nonlinear problems, and it has an enormous number of nonlinear group neurons that fix the input and output signals. The ANN model is a typical method of feedforward network modeling for time-series forecasting, which was proposed by Zhang and Qi (2005). The nonlinear group numbers determine a complex relationship with high prediction between the neurons. Fig. 4 shows a typical ANN model with a three-layer architecture consisting of the following three layers of node: input, hidden, and output. The mathematical relationship between the input and output in the ANN model is as follows: k
n
j 1
i 1
F1 b0 W j tan sig (b0,k Wi , j Ft 1 ) et ,
(7)
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where Wi , j and W j are the connecting weight factors of the model parameters, n is the input node number, and k is the output node number. The hyperbolic tangent transfer function is used as a hidden layer, and the equation is as follows:
e x e x e x e x
ip t
f ( x)
cr
(8)
.
This function has a range from -1 to 1. The ANN model using Eq. (11) is formulated as a
us
nonlinear equation form, taking past-observed data in order to predict a future value. The ANN model is valuable when predicting an output value from many input variables
an
(Bulsari, 1995). It has nonlinear characteristics, and it can be applied to various chemical engineering fields (Himmelblau, 2000). In this study, the values of 37 major factors were used in the input layer of the ANN model and applied to a feedforward back-propagation
M
network system (Fig. 4). The forecast for one output value was calculated through the three hidden layers used for the hyperbolic tangent transfer function. A comparison of the normalized naphtha price forecast by the ANN model for 29 months and the normalized
d
actual values for the corresponding months is shown in Fig. 3. The FAP of the normalized
te
ANN model is 85.71 for the total period.
Ac ce p
4.4. System dynamics model
The system dynamics (SD) model is an appropriate methodology for describing complex behavior, such as forecasting problems, and overcoming the disadvantages of linear models. SD describes the complex mutual interactions between factors and considers many functions, such as the time-delayed relationships of factors, and offers causal loop diagrams. Here, we propose an SD model using Vensim software to forecast naphtha supply, naphtha demand, and naphtha price by employing not only simulation but also optimization. This SD model was divided into three sub-models: Asian naphtha supply, Asian naphtha demand, and Asian naphtha price including European naphtha price.
4.4.1. Naphtha supply sub-model The demand for naphtha is almost the similar as the demand for petrochemical products. Therefore, the capacity of petrochemical plants and their rate of operation are the main factors of demand. The rate of operation is affected by the economic situation and T/A.
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Additionally, the use of liquefied petroleum gas (LPG), an alternative to naphtha, affects the demand for naphtha. If petrochemical plants have a large capacity, the demand for naphtha is high. However, the operation rate of plants is not always 100%. Thus, the main factor in demand for naphtha is the operation rate of a plant. A naphtha demand model considers the
ip t
petrochemical margin, utility operating rate, T/A, and heuristics. The factors governing naphtha supply are shown in a causal loop in Fig. 5. A comparison of the normalized actual
cr
naphtha supply and its supply forecast is shown in Fig. 6, and the FAP of the normalized
us
naphtha supply is 64.29.
4.4.2. Naphtha demand sub-model
While demand for naphtha can be calculated using a petrochemical company’s operation
an
rate, the supply of naphtha can be calculated using the production of an oil company. The amount of naphtha used to make para-xylene (PX) is also an important factor in determining
M
the supply of naphtha. While petrochemical plants need more naphtha when their capacity increases, more naphtha can be obtained at these times. The T/A and margin also affect an oil plant’s rate of operation as economic and non-economic factors. The margin is defined as the
d
difference in the oil price and the product price. The analysis of the relationship between the
te
margin, rate of operation, and T/A enables calculation of the supply of naphtha. Oil plants produce PX, a high-value petrochemical product, from naphtha. Because oil plants do not
Ac ce p
supply naphtha to petrochemical plants, but consume it, the amount of naphtha used to make PX should be excluded from the supply of naphtha. Therefore, production of PX reduces the supply of naphtha. By considering the operation rate of oil plants and the production of PX, the actual supply of naphtha to petrochemical plants can be determined. A naphtha demand causal loop considering all these factors and heuristics is shown in Fig. 7. The normalized naphtha demand forecast from May 2010 to September 2012 is close to the normalized actual demand (Fig. 8). The FAP of the normalized naphtha demand presented in Fig. 8 is 89.29.
4.4.3. Asian naphtha price model including European naphtha price The causal loop diagram (Fig. 9) for this model is divided into two parts: The forecast of the Asian naphtha price model and the European naphtha price model. The Asian naphtha price can be forecast by considering the European naphtha price, Asian supply and demand, export, Brent oil price, and seasonality. The European naphtha price and the Asian naphtha price
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affect each other, and there is a time delay between the two factors. The Asian naphtha price is influenced by the Asian naphtha supply and demand, and the Asian naphtha and European naphtha prices are time delayed. Fig. 9 shows a causal loop diagram of the Asian naphtha price, including the European naphtha price. Comparisons of the normalized European
ip t
naphtha price forecast with actual European prices and the Asian naphtha price forecast with actual Asian prices from May 2010 to September 2012 (29 months) are shown in Figs. 10 and
cr
11, respectively. The FAPs of the normalized European and Asian naphtha prices were found
us
to be 92.28 (Fig. 10) and 82.29 (Fig. 11), respectively.
4.5. Comparison of the proposed models with the published literature
As there are no studies in the literature on naphtha price forecasting, and the trends of the
an
actual prices of crude oil and naphtha are similar, the present forecasting results are compared with the crude oil forecasting results in the literature. Morana (2001) predicted crude oil
M
prices using a semiparametric approach, and the FAP was 46.67. Ghaffari and Zare (2009) forecast WTI crude oil prices through the ANFIS model using the without smoothing procedure (WSP) model and the smoothing procedure (SP) model. The FAPs of the WSP and
d
SP models were 48.33 and 70.09, respectively. Fan et al. (2008) proposed an approach based
te
on a genetic algorithm. The historical time-series data of the Brent and WTI crude oil prices were calculated using GPMGA. The FAP for the WTI crude oil price of their predicted model
Ac ce p
was 62.07. Moreover, Gori et al. (2007) used an ANFIS model to propose a method to predict WTI crude oil prices with a FAP of 46.56. Table 1 summarizes the FAPs of the results of the naphtha price forecasts in the present study along with the crude oil forecasts in the literature.
5. Optimization of the naphtha purchase price using price prediction The entire naphtha trading configuration of planning problems corresponds to the multi-step system, including inventory, amount of naphtha, and running capacity. The existing optimization models in the literature section do not provide decision-making support for product purchases, such as oil and naphtha. Therefore, this study develops practical approaches for formulating and solving the naphtha purchase problem using NLP models and
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connects to the appropriate techniques. For planning periods, this model indicates how much of the available naphtha to purchase and keeps track of the inventory levels per month. The decision variable of the naphtha purchases is future trading for the next three months. The purchase order indicates how much naphtha is needed for the petrochemical industry to
ip t
be able to operate cracking units. Once a purchase order is determined for a planned date, it provides the amount of naphtha trading, the amount of the naphtha purchase, the storage tank
cr
capacity, and the purchasing unit price of the optimal naphtha. This research omitted the naphtha loading and unloading cost because it is relatively small and not sensitive to a given
us
period.
The particular purchase problem used in this study is closely related to the point of purchase of naphtha. The optimization model included the following information. First, the estimated
an
monthly prices for the SD forecasting model were used. Second, the amount of initial inventory in the storage tank and the lower and upper bounds for the naphtha storage tank
M
capacity were given. Finally, the monthly flow rate was specified. In addition, future purchase orders, storage tank inventory, and purchase price were determined by optimization. The initial inventory levels and running capacity were based on real standards from
d
collaborating petrochemical industries. There were three types of storage tanks: Two 60,000-
te
ton, six 33,000-ton, and four 20,000-ton tanks. The overall capacity of each tank was approximately 300,000 tons, and the minimum level of the total tank was 80,000 tons. The
Ac ce p
feed flow rate was set to 300,000 tons per month for the entire period. All storage tanks were available to take the naphtha and feed the cracking unit. The current optimization model was allowed to purchase the naphtha every month under the circumstances of future trading. The optimization approach used is explained by the event tree in Fig. 12 (Hellevik, Langen, and Sorensen, 1999). In addition, the newest monthly updated data was used (e.g., the actual and predicted price information, amount of purchase, and inventory capacity) when the optimization was carried out in the time interval. Generally, future purchases of naphtha are determined by the predicted price. The inventory and storage tank level fluctuates with the predicted price and future purchases of naphtha. The objective function of the optimization is to minimize the average purchase price in this study. The purchase price considers hedge trading and the amount of naphtha purchased. The price is calculated as the finalized procurement plus the hedge cost of the future. Constraints include the capacity limitations of inventory tanks and the amount of naphtha purchased. Eq.
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(9) presents the objective function of the NLP model aimed at minimization of the purchase price.
( HE 2t 1 HE 2t 1 ) Pt 1 HE 3t 2 Pt 1} / ( FN t 1 FN t 2 FN t 3 ) (9)
ip t
MinP {FN d 1 Pd 1 FN d 2 Pd 2 ( HE1t HE 2t HE 3t ) Pt
cr
Eqs. (10), (11), and (12) illustrate the amount of naphtha purchased including hedge trading.
us
FN t 1 FN d 1 HE1t (10)
an
FN t 2 FN d 2 HE 2t HE 2t 1 (11)
M
FN t 3 HE 3t HE 3t 1 HE 3t 2 (12)
d
FN d 1 and FN d 2 are the amounts of naphtha of the finalized procurement. HE1t , HE 2t ,
te
HE 2t 1 , HE 3t , HE 3t 1 and HE 3t 2 are the amounts of naphtha by hedge trading.
Ac ce p
Eq. (13) gives the amount of naphtha procurement constraint at time t. FN tL FN t FN tU , t T
(13)
FN t is the amount of naphtha purchased at time t, and Ft L and FtU are the lower and upper limitations at that time.
Eqs. (14), (15), and (16) indicate the storage tank capacity at each time horizon. FTt 1 FTt FN t 1 RC (14) FTt 2 FTt 1 FN t 2 RC (15)
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FTt 3 FTt 2 FN t 3 RC (16)
Eq. (17) describes the storage capacity constraint of the tank.
cr
FTt L FTt FTtU , t T
ip t
RC is the fixed running capacity of the process.
us
(17)
FTt is the naphtha storage tank at time t. FTt L and FTtU are the lower and upper limitations
an
at that time. Short sales are impossible during hedge trading, as shown in Eqs. (18) to (23). FN t 1 0
M
(18) FN d 2 HE 2t 0
Ac ce p
(20)
te
FN t 1 0
d
(19)
HE 3t 0 (21)
HE 3t HE 3t 1 0 (22)
FN t 2 0 (23)
Table 2 shows the comparative results of the actual and proposed approaches when the best model is selected for forecasting the price based on SD. The procurement planner determines the naphtha purchases after analyzing the future naphtha price. Generally, if the price is predicted to rise in the next month, most buyers will purchase a greater amount of naphtha than they would have already agreed to purchase. Then, in the next month, buyers can sell the
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purchased naphtha by considering the future naphtha forecasting price in case the actual naphtha price increases. However, if the actual price decreases, buyers can purchase more naphtha. Therefore, naphtha price prediction is a very important factor for minimizing the average purchase price. This price is minimized by the naphtha purchase process based on the
ip t
NLP model. The optimized purchase price is affected by the predicted price, amount of naphtha, and future trading. In order to minimize the purchase price, all naphtha purchases
cr
consider the future trading of the next three months.
This study was performed to compare the average purchase units and amount of naphtha
us
purchases for actual trade, the heuristics approach, and the optimization results. The actual trade purchasing method indicates that buyers constantly purchase the same naphtha quantities for one year. Heuristic values depend on the variance of the predicted price using
an
the forecasting model. The heuristics approach applies to multiplying the weighting when purchasing naphtha according to the predicted price variance of the last and current months.
M
The average purchase prices of actual trade, heuristics, and optimization were 938.24, 900.46, and 892.54 USD/ton, respectively. Furthermore, the total quantities of the purchased naphtha for each methodology were 2.40, 2.49, and 2.50 million tons per year. This paper
d
compared their total purchasing costs. The total purchasing cost based on optimization
te
resulted in profit savings of USD 20.50 million per year in petrochemical companies. This saving cost reduced the price by 4.8% in comparison with business profits in 2013. Based on
Ac ce p
these results, it appears that the optimization model is preferable to the heuristic approach. The average purchase price with the heuristic approach was similar to the actual price, but the average optimization value was approximately USD 45.07 cheaper than the actual price.
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ip t
5. Conclusions The point of purchase of naphtha is very important as it is related to business profit in petrochemical industries. In order to prevent companies from having an operating loss, this
cr
research has proposed various models for naphtha price forecasting to predict naphtha price variation, which is of great interest to decision makers, as it would enable them to purchase
us
naphtha at the appropriate time. In addition, an optimization model was developed using naphtha price prediction. The point of purchase of naphtha was determined by the fluctuation
an
trends of the naphtha prediction price and optimization model. The SM, ESM, and ANN models only considered the time-series data, and their FAPs were 67.86%, 75.00%, and 85.71%, respectively. The FAPs of these general models exhibited decreased accuracy for
M
long-term forecasting as they only considered related data. Therefore, the SD model was developed by considering qualitative factors and the existing data, and it was found to show
d
the highest FAP (92.28) for the European naphtha price. The present naphtha forecasting results were also compared with the published crude oil forecasting results. The optimization
te
model of the naphtha average purchase price was found to be superior to the heuristic approach. The average purchase prices of the optimization and heuristic approaches were
Ac ce p
892.54 and 938.24 USD/ton, respectively, and the average optimization value was approximately 45.07 USD/ton cheaper than the heuristic approach. Thus, the SD model developed in this study provided the best forecasts of European naphtha prices, and an optimization model that considers naphtha price prediction can determine the optimal point of purchase of naphtha. This is of great significance for decision makers looking to improve the economic benefits for petrochemical companies.
Acknowledgement Financial support from Samsung Total Petrochemicals Co. Ltd and the BK 21 Program funded by the Ministry of Education (MOE) of Korea are gratefully acknowledged. Also, this
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research was supported by the Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry, and Energy (MOTIE).
ip t
Nomenclature
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FN d 1 , FN d 2 past finalized purchases of naphtha
FTt 1 , FTt 2 , FTt 3
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FN t 1 , FN t 2 , FN t 3 amount of naphtha purchased at time t+1, t+2, and t+3 level of storage tank at time t+1, t+2, and t+3
an
HE1t hedging trading in the first month HE 2t , HE 2t 1 hedging trading in the second month
M
HE 3t , HE 3t 1 , HE 3t 2 hedging trading in the third month
te
Ac ce p
RC running capacity
d
Pt , Pt 1 , Pt 2 naphtha price at time t, t+1, and t+2
Page 21 of 39
References
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ip t
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te
d
List of Table
Table 1. Comparative analysis of naphtha price forecasts (this study) and crude oil price
Ac ce p
forecasts (literature)
Table 2. Comparison of optimization and heuristics method results for average purchasing unit price
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ip t cr us an
Predication
Training
Horizon
d
Approach
M
Table 1. Comparative analysis of naphtha price forecasting (this study) and crude oil price forecasting (literature) FAP (%)
Reference
2010.05~2012.09
67.86
This study
SM
Monthly
ESM
Monthly
2008.06~2010.04
2010.05~2012.09
75.00
This study
ANN
Monthly
2008.06~2010.04
2010.05~2012.09
85.71
This study
Ac ce p
te
2008.06~2010.04
Prediction
European naphtha price (SD)
Monthly
2008.06~2010.04
2010.05~2012.09
92.28
This study
Asian naphtha price (SD)
Monthly
2008.06~2010.04
2010.05~2012.09
82.29
This study
Semi parametric approach
Daily
-
1998.11.21 ~ 1999.01.21
46.67
(Morana, 2001)
Genetic algorithm
Daily
-
2005.06.27 ~ 2005.07.26
54.58
(Fan, Liang, et al., 2008)
ANFIS
Monthly
-
1999.02 ~ 2003.12
45.76
(Gori et al., 2007)
ANFIS (SP model)
Daily
-
2007.01.05 ~ 2007.05.31
70.09
(Ghaffari & Zare, 2009)
Page 25 of 39
an
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cr
ip t
2009)
Table 2. Comparison of optimization and heuristics method results for average purchasing
Actual
Heuristics
M
unit price
Optimization
870.78
870.78
784.68
Feb-11
895.14
878.39
824.10
978.95
889.56
1050.64
1056.78
946.61
988.26
1026.16
939.00
Jun-11
939.55
941.90
969.17
Jul-11
974.27
993.34
949.15
Aug-11
946.29
965.84
925.00
Sep-11
947.61
939.27
905.18
Oct-11
883.86
890.08
882.61
Nov-11
878.23
857.30
845.64
Dec-11
902.61
856.84
859.23
Average
938.24
937.97
893.33
Apr-11
Ac ce p
May-11
981.61
te
Mar-11
d
Jan-11
Page 26 of 39
Figure Captions
Figure 2. Flowchart of the forecasting model
cr
Figure 3. Comparison of normalized actual and three forecasting models
us
Figure 4. Three-layer artificial neural network (ANN) Figure 5. Causal loop diagram of naphtha supply
ip t
Figure 1. Crude oil (WTI) and naphtha price trends
an
Figure 6. Comparison of normalized actual and forecast naphtha supply
M
Figure 7. Causal loop diagram of naphtha demand
Figure 8. Comparison of normalized actual and forecast naphtha demand
d
Figure 9. Causal loop diagram of Asian and European naphtha
te
Figure 10. Comparison of normalized actual and forecast European naphtha prices
Ac ce p
Figure 11. Comparison of normalized actual and forecast Asian naphtha prices Figure 12. Branch (indicated by solid line) in the time interval t1 t t3 to be included in the calculation of the newest updated data of optimization model
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cr
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Figure 1. Crude oil (WTI) and naphtha price trends
Ac ce p
Figure 2. Flowchart of the forecasting model
28
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d
l
Figure 3. Comparison of normalized actual and three forecasting models
29
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Figure 4. Three-layer artificial neural network (ANN)
30
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Figure 5. Causal loop diagram of naphtha supply
31
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Ac ce p
Figure 6. Comparison of normalized actual and forecast naphtha supply
32
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d
Figure 7. Causal loop diagram of naphtha demand
33
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Figure 8. Comparison of normalized actual and forecast naphtha demand
34
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Ac ce p
Figure 9. Causal loop diagram of Asian and European naphtha
35
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Figure 10. Comparison of normalized actual and forecast European naphtha prices
36
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Ac ce p
te
Figure 11. Comparison of normalized actual and forecast Asian naphtha prices
37
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Figure 12. Branch (indicated by solid line) in the time interval t1 t t3 to be included in the
Ac ce p
calculation of the newest updated data of optimization model
38
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39
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