CHEMICAL ENGINEERINGTRANSACTIONS VOL. 51, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors:Tichun Wang, Hongyang Zhang, Lei Tian Copyright © 2016, AIDIC Servizi S.r.l., ISBN978-88-95608-43-3; ISSN 2283-9216 Determination and Evaluation of Affecting Factors of Raw Material Cost Based on Rough Set Theory Yajun Wang*, Zhangxuan Yin, Huijie Yan, Shuangjiao Fan, Junli Shi, Maojun Zhou Department of Industrial Engineering, Dalian Polytechnic University, Dalian wangyajun2004@hotmail.com Effective cost control in electric arc furnace steelmaking relies on accurate analysis of factors that affect raw material cost and the causes of cost variation. This paper proposes a method to evaluate the importance of each factor affecting raw material cost. With the importance of each factor, the deterministic and nondeterministic factors can be identified by solving a minimal reduction of a decision table. Advice on further improvements for steelmaking production can then be provided. The simplicity and effectiveness of this method is illustrated by an example at the end of this paper. This method can be applied to quantitative analysis of factors that affect raw material cost in steelmaking. 1. Introduction In steel production, raw material cost is defined as the amount of iron and ferroalloy required to produce one ton steel, which is the major technical economic index in steelmaking. Approximately 80% of the total cost in steelmaking is raw material cost. This index reflects the effectiveness of cost control in steelmaking. The evaluation method of analyzing the importance of each factor affecting raw material cost is the most critical part of cost control, because it will directly affect production management. Methods based on rough set theory as proposed in references. References (Cheng et al., 2008) are more scientific and objective than conventional methods and more feasible than neural network methods (Zhang and Liu, 2004). To meet the demands for cost control in steelmaking industry, the paper proposes an importance evaluation method from the perspective of knowledge discovery for affecting factors raw material cost in steelmaking based on real production and raw material cost data and it establishes a raw material cost analysis and decision system. By decertification and simplification of real production data, major affecting factors raw material cost and their importance can be determined, revealing the causes of cost variation and providing a basis for cost control decisions. 2. Rough set theory Rough set theory was developed by Polish scientist Pawlak in the 1980s while studying the logical characters of information system, and it is becoming more and more popular in recent times (Pawlak,1991 and 1982). Rough set theory has been applied to areas such as machine learning, knowledge discovery, data mining, decision support and analysis, pattern reorganization, and intelligent control (Pawlak and Miao, 2008 and 2000). Related definitions in rough set theory are listed below: Definition 1: Knowledge representation system and decision making system. In rough set theory, a knowledge representation system can be represented as, where U is a non-empty, finite set of objects called the Universe, A=C∪D is a non-empty finite set of attributes which fulfills C∩D≠Φ, Subsets C and D are sets of conditional attributes and decision attributes, respectively. V=∪a∈A Va is the set of values of the attributes. Va represents the possible values of a∈A which is the range of a. f: U×A→ V is an information function that defines the attribute values of every object in U, i.e., for ∀a∈A, x∈U, and f(x, a) ∈Va. A knowledge representation system can be represented as a 2-dimensional table in which objects are presented in rows and attributes are presented in columns. The attribute value of each object is shown in the corresponding cell f(x,a) to generate a decision table. DOI: 10.3303/CET1651050 Please cite this article as: Wang Y.J., Yin Z.X., Yan H.J., Fan S.J., Shi J.L., Zhou M.J., 2016, Determination and evaluation of affecting factors of raw material cost based on rough set theory, Chemical Engineering Transactions, 51, 295-300 DOI:10.3303/CET1651050 295 Definition 2: Indiscernibility. In the Decision Table T= (U, A), for a subset P ⊆A, indiscernibility is defined as: }),,(),(|),{()( PaayfaxfUUyxPIND  (1) If (x,y)∈IND(P), x and y are indiscernible from each other by P. Indiscernibility is an equivalence relation in U. Thus owing to indiscernibility with respect to P, U can be classified into k equivalent classes, x1,x2,…,xk, which is noted as: U/IND(P)={ x1,x2,…,xk }. Definition 3: Set approximation. For any object set X⊆U and attribute set P⊆A the lower and upper approximations of P are defined, respectively, as: });(/{)( XYPINDUYYXapr p  (2) });(/{)(  XYPINDUYYXapr p  (3) For attribute set P, equation (3) is the complete set of objects that can be unambiguously classified as belonging to X. The equation (4) shows all objects that are possibly in X, which describes the minimum possible range. Definition 4: Attribute dependency, attribute importance, and attribute redundancy. A rough set identifies the importance of an attribute by attribute dependency and filters those redundant attributes according to dependency. For attribute set P, R⊆A, the dependency of P on R is: || |)(| )( U PPOS P R R  (4) )()( )(/ XarpPPOS R PINDUX R    (5) POSR (P) is the positive region (lower approximation) of R in U/IND (P). Definition 5: Core reduction. B⊂C is a reduction of information system S, only if POSB (D) = POSC (D), and every element in B is necessary for D. This reduction is noted as RES (B, D). If ∀X⊆U/IND (D), POSC(X) = POSB(X) and there is no B’ such that B’⊂B and POSC(X) = POSB’(X), then B is a minimal reduction of the information system. The common set of all reductions of C in decision table D is called the core of C, which is denoted as )}()(:{),( }{ DPOSDPOSCaDCCORE aCC   (6) The core can be used as the basis data for finding the minimal reduction. 3. Affecting factors of steelmaking raw material consumption cost 3.1 Production process of steelmaking UHP EAF is a high temperature, multiphase, fast metallurgical process (Zhang,2007), there are many the variables involved in the whole process, so a reasonable cost analysis model for steelmaking to increase productivity, reduce costs and improve product quality has important significance. In order to establish a reasonable cost analysis model, it must be first to analyze the system for the steelmaking process. For example, 3Cr13 stainless steel production process is divided into ingredients, smelting furnace, AOD(Argon- Oxygen Decarburization, AOD) refining, LF(Ladle Furnace, LF) refining, VD(Vacuum Desulphurization, VD) vacuum furnace, 150 square casting, slow cooling, transfer and other operations processes in figure 1. After supplies of raw materials provided by the department entering the steel production process, the planning amount of scrap, pig iron, slag, raw slag, return steel and ferroalloy is initially identified by the ingredient process according to furnace capacity. Such as the EAF has nominal capacity of 30t, the actual amount of steel is 40t, Solid material loading is 45-46t, generally the total planned ingredients is 40t, 35t for chromium stainless steel (scrap 25t, slag 5t and raw slag 5t). The melting furnace smelting process mainly completes steel melting and oxidation stage of steelmaking, adjusts C, P levels and tests the Cu content. In an electric furnace it does not adjust the chemical composition of alloy element content, so it’s kind of the steelmaking is essentially not be impacted, but it has some special requirements: in the end of life of the furnace, due to tap hole becoming large and with slag, the furnace cannot refine stainless steel; after exchanging furnace tap, the first smelting furnace is cleaning furnace steel and special requirements steel grade is not been refined in the first three furnaces; new furnace body and new ladle are not used for the same furnace number; smelting furnace with leaking cannot refine bearing steel, carbon steel can be refined; after high Cr steel , bearing steel 296 smelting furnace is equivalent to cleaning the furnace. AOD is referred to Argon oxygen decarburization, this method is major refining method for smelting low carbon steel, CO is diluted with Ar for decreasing pressure to achieve the effect of a vacuum, so that the carbon can be off to a very low level. AOD furnace tuyere is mounted on the side wall near the bottom of the furnace and the mixed gas of Ar and O2 is blown into furnace. The blowing process is divided into the oxidation period, the reduction of the refining period. AOD is the main production process of stainless steel. LF refining process mainly completes the reduction of steelmaking and adjustment of steel chemical composition. When the temperature appropriate, the laboratory analysis of the chemical composition is conducted, and as a basis to add ferroalloy, up to temperature before testing, substandard then add ferroalloy. And so forth until it reaches the composition and temperature requirements, then hanging steel bag. LF furnace time depends on the furnace conditions (chemical composition). VD requires vacuum tank furnace for mainly removing the gas (H, N, O, etc.), reducing inclusions and improving purity. After ingredients are qualified, the casting is conducted. In molding / casting process, sampling and laboratory analysis ingredients are carried out, and the results can be as the chemical composition of the final steel. The inspector compares the ingredients with the standard. If the ingredients are substandard then the steel is melted down, else turn to next process, fill out the "ingot / billet turn card" transferred together to the next branch. Manufacturing Department Material supply department Steel-making plant Material steel, Ferroalloy and other Ingredients Smelting furnace Sampling for chemical analysisSteel AOD Refining Plan Acceptance Meetting the requirements LF refining Adjust the chemical composition Die-cast/ casting Transfer to the next plant Ingot/billet VD vacuum furnace Figure1: Production process for stainless steel smelting 3.2 Determination effecting factors of steelmaking raw material consumption cost From the steelmaking process, the raw material consumption costs of ingot or billet smelting production process on the one hand depend on the quality and quantity of different raw materials in different ratios, on the other hand depend on the yield of molten steel and molten steel into ingot (billet) rate, here ingot (billet) rate=(weight of qualified ingot) / (pouring molten steel weight), in which pouring molten steel weight = baked steel - steel recycled, the steel recycled is not double counted in the calculation of consumption of raw materials. The main material balance model of electric arc furnace is shown in figure 2. Electric furnace steel-making 1130kg Steel scrap/DRI 10kg Ferro-alloys 40kg Dissolvent Exhaust gas 1t Crude steel Wastewater Solid waste 2.5kgCO 120kgCO2 60gSO2 0.5kgNOx 165g Particulate matter 3m3 Wastewater （SS，Fuel） 146kg slag 19kg Furnace dust 16kg Iron oxide 2.5kg Sludge 17kg Refractory material 0.8kg Fuel 3kg Other materials Figure 2: Main material balance model of Electric Arc Furnace Building the steel metal balance equation j i ijii QrbaPX  (7) 297 Here, Xi indicates raw material number i, Pi means the grade of raw material number i, aij represents the percentage of the j metal in raw material number i, Q represents amount of molten steel, r represents the yield of molten steel, bj represents the percentage of j metal in molten steel and is target of ingredients of production steel. By the material balance model and metal balance equation, when the amount of raw materials and quality indicators are certain, it is must to control waste and burning amount for making the ingot (billet) production as much as possible, and the quality and price of raw materials are comprehensively considered. So the consumption of raw materials can be controlled. 4. Analysis of affecting factors of steelmaking raw material consumption cost based on Rough Set 4.1 Calculation of the important degree of factors The changes of one or several of the factors necessarily lead to changes of steelmaking raw material consumption cost. If one of the factors is ignored, that is the property representing the factor is deleted from the decision-making table, it will certainly undermine the indiscernible relationship between original objects of the decision-making table. Therefore, a condition attribute is removed from the decision table of raw material consumption cost analysis to examine the classification changes of decision table without this attribute. If the attribute will be removed the classification accordingly will changed, then the attribute is the effecting factor on changes of raw materials consumption cost. The larger the degree of change is, the greater intensity of the impact and higher importance this attribute has, and vice versa it illustrates the effect of the strength of the attribute is smaller, the lower importance that is. It can be inferred, all attributes in minimum attribute simplicity of costs analysis decision table of steelmaking raw material consumption may be factors affecting the cost of raw materials consumed. The core attribute must be included in the minimum attribute simplicity, therefore the core attributes is necessarily affecting factors of the consumption cost and are certainty factors. While other attributes excepting the core in the minimum attribute simplicity may be affecting factors of the cost of raw materials consumed, are uncertainty factors.The Pc(D) indicates the quantitative possibility of condition attribute c effecting on the decision-making attribute D. T=(U,A) indicates the cost analysis decision table of raw material consumption, Pc(D)can be expressed as NnDP N i ic /)()( 1    (8) N is the number of all minimum attributes set of decision table, ni indicates whether the condition attribute c is the element of minimum attribute simplicity of decision table. If it is, then ni =1, otherwise ni=0. Obvious 0≤Pc(D)≤1, if Pc(D)=0, then attribute c is not an effecting factor of decision attribute D. If 0