ANALYSIS OF THE COMPLEX MATERIAL FLOW NETWORKS IN TYPICAL STEEL ENTERPRISE

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1 ANALYSIS OF THE COMPLEX MATERIAL FLOW NETWORKS IN TYPICAL STEEL ENTERPRISE 1 YEQING ZHAO, 2 GUIHONG BI 1 School of Computer and Informaton Engneerng, Anyang Normal Unversty, Anyang , Henan, Chna 2 Faculty of Power Engneerng, Kunmng Unversty of Scence and Technology, Kunmng , Yunnan, Chna ABSTRACT The am of ths paper s to present a new modelng method for complex materal flow networks system of typcal steel enterprse. Iron and steel ndustry s one of the most mportant ndustry n the country, especally, have a drect mpact on the whole natonal economy. For the dversty and complexty of the producton technque of the materal flow system n the steel enterprse, the manufacturng process was defned as a complex networks based on complex networks theory and technques, n whch the devces were seen as nodes and the drect relatonshps between the devces were seen as edges. The statstcal analyss of the network model of the producton process n typcal steel enterprse was provded to explore new methods and breakthrough for local path optmzaton and global plannng, and that supply the nstructons of theores and technques for the further mprovng the topology structure of the materal flow networks n steel enterprse. Keywords: Materal Flow System, Complex Networks, Degree Dstrbuton, Shortest Path, Clusterng Coeffcent 1. INTRODUCTION Steel producton s a very long typcal productve process. Because of the hgh temperature and mxed wth dscreteness and contnuty n the manufacturng process, the processes are numerous and the devces are qute complcated. In the steel productve process, the man reacton nvolved n all stages s dfferent as a result of dfferent goals of specfcally phase. For example, n the smeltng stage the chemcal reactons are prmary and the physcal reactons are secondly, however, n the rollng stage, the physcal reactons are promnent roles and the chemcal reactons are subordnate roles. The whole manufacturng process must be a unty of coherence n form and coheson n meanng, and possess the characterstcs of complexty, mutablty and uncertanty. The typcal steel productve process manly ncludes the process of ronmakng, steelmakng and steel rollng. In ronmakng process, ron ore, coke and auxlary materals are mxed together by followng some proportonal relatons and the mxture s fed nto the blast furnace. Once the ngredents of the hot metal meet the standards, the hot metal wll be transported nto the next process such as steelmakng process by car or tran as the raw materals. The hot metal by a seres of pretreatment and steel scrap and other raw materals are fed nto converter to realze heatng, decarburzaton and deoxdzaton treatment on purpose of removng varous mpurtes and satsfyng the standard requrements of steel composton n steelmakng process. Accordng to customer requrements of products, n steel rollng process, steel bllets are nput the heatng furnace to reach the set temperature and that are rolled nto varous types of steel products to meet customer requrements, for specal requrements of steel products, further processng operatons are mplemented, and the fnal products are accessed to markets. At present, due to the polytrope and uncertanty of market, manufacturers must flexbly adapt to changng market condtons n tmely. These result n ncreasng complexty of decson processes, dversfcaton of products and complexty of realworld manufacturng systems. Many domestc and foregn scholars have done a lot of research on the materal flow characterstcs of steel producton systems. Network-based modelng, n partcular, based on complex networks theory and methods n many areas, the research work has made many achevements, such as socal networks[1], the nternet and World Wde Web[2], metabolc, proten, and genetc networks[3], arport networks[4] and author collaboraton networks[5]. 1001

2 However, the model for steel producton system by utlzng complex networks theory and methods was rarely studed at current, especally, on the materal flow system of the steel productve process. In ths paper, n order to realze the goal of energy conservaton and emssons reducton, enhance the compettve ablty and adaptablty, search for new breakthrough for further optmzaton of the materal flow system, the model of steel producton process was bult by complex networks theory and methods n vew of the characterstcs of complex materal flow system of steel enterprse. The research deas of complex system focus on the system structure and functons from the pont of vew of the systematc theory, and the structural propertes of networks topology s the key for us to study by abstractng the real systems. Based on current requrements of energy conservaton and emsson reducton and the productons and materal flow networks of the ron and steel enterprses adaptaton to the changng needs of the market, we should how to gradually ncrease n sze or adust and mprove the structure of producton networks accordng to the complex system theory, further explore the relatonshp between producton networks topology statstcs and producton process materal flow for realzng optmzaton of the system performance n the ron and steel enterprse. The man purpose of ths paper s to establsh the materal flow networks model of producton process of typcal modern ron and steel enterprse, and perform a statstcal analyss on the data of networks model by applyng the complex networks theory and technology. We would explore the nternal relatonshps between the statc structure and dynamc evoluton of the networks model of the producton process and the system optmzaton of materal flow n ron and steel enterprse, more explore new deas, new methods and approaches for further optmzng the materal flow system of producton process. The outlne of ths paper s as follows. In Secton 2 we descrbe emprcal studes of the structure of networks and complex networks, ncludng the common propertes. In Secton 3 we descrbe some of the common propertes of the manufacturng process n steel enterprse, especally, the dynamc and polytrope of the producton technque. The model of complex materal flow networks of the manufacturng process was bult based on complex networks theory and technques. In Secton 4 we provde statstcal analyss of the networks model for typcal complex materal flow of steel enterprse that reveals the performance of the networks model and subnetworks, devces avalablty, materal flow system, and so on. In Secton 5 we gve our conclusons and pont to drecton for future research. 2. COMPLEX NETWORKS A network s a set of tems, whch are known as nodes (vertces), wth connectons between them, called edges, there s a smple network n fgure 1(a), the network s composed of seven nodes and fourteen edges. Based on mathematcal graph theory, the study of networks s one of the fundamental pllars of dscrete mathematcs. Now, the hstory of the networks s summarzed nto three stages, namely: (1) Networks early stage, t s the mportant mark for Euler to solve the Kongsberg brdge problem by the theory of networks n 1736, and durng the twenteth century graph theory has developed nto a substantal body of knowledge. (2) Networks mddle stage, the experment of sx degrees of separaton of Mlgram [6] s the turnng pont to transform network scence from pure graph theory to scentfc research. (3) Networks modern stage, because of propertes of statc and dynamc of networks, network scence must study both statc attrbutes and dynamc attrbutes of networks. Emergence was defned by Holland n the book to descrbe the network evoluton of what happened on detal, and t s playng a crtcal role of explanng the nternal mechansm n modern network scence. Watts and Strogatz [7] stmulated the nterest n small world networks model by llustratng unversalty and practcalty of the small world networks. Barabas and Albert [8] focus partcularly on work on scale-free networks and generatng process of model on scale-free networks. Graph theory s the natural framework of complex networks based on the mathematcal theory and, formally, a complex network can be regarded as a graph. Defne 1 A undrected (drected) graph s a 2- tuple G = ( N, L),where: (1) N = { n, = 1, 2,, m} s a set of nodes of the graph. (2) L = { l, = 0,1, 2,, k} s a set of edges of the graph. Defne 2 A complex networks s a 3-tuple CN = ( N, L, f ),where: (1) ( N, L) s a undrected(drected) graph. 1002

3 (2) f : L N N s the functon to map the edge to nodes A node s usually referred to by ts order n the set N. In undrected graph, each of the lnks s defned by a couple of nodes and, and s denoted as (, ) or l. The lnk s sad to on the two nodes, or to be causal relatonshp n nodes and. Two nodes oned by a lnk are referred to as adacent or neghborng. In a drected graph, the order of the two nodes s mportant: the lnk l stands for a lnk from to, but l means a lnk from to. In fgure 1 (a) and (b), a smple undrected graph and a drected graph wth seven nodes and fourteen edges are shown respectvely. Fgure 1: A Smple Undrected Graph (A) And Drected Graph (B) Shortest paths play an mportant role n realty network envronment, such as transport and communcaton. For such reason, shortest paths have also played an mportant role n the characterzaton of the nternal structure of a graph. So, we can defne the matrx A n whch the entry d s the shortest length of the geodesc from node to node. The dameter of the graph s defned as the maxmum value of d, whch s marked as D= max d. Average shortest path length s a, measure of the typcal separaton between two nodes n the graph, defned as the mean of geodesc lengths over all couples of nodes, namely: 1 L= d (1) N( N+ 1) Where d s the geodesc dstance from node to node, and N s the number of the nodes n the graph. Clusterng, also known as transtvty, s a typcal characterstc of acquantance networks, where two ndvduals are lkely to know each other whle they are a common frend. In a general graph, transtvty represents the presence of a hgh number of trangles. In order to descrbe the degree of aggregaton of nodes n complex networks, clusterng coeffcent C was ntroduced by Watts and Strogatz n the paper [9], and defned as follows. 1 C=< c>= c (2) N N The clusterng coeffcent C of the graph s gven by the average of c over all the nodes n graph. The clusterng coeffcent c represents the local clusterng coeffcent of node and expresses how lkely a m = 1for two neghbors and m of node. The clusterng coeffcent c s defned as the rato between e and the maxmum possble number of edges n subgraph of neghbors of, 1 ( 1) 2 k k, namely: aamam 2 e m, N c = = (3) k( k 1) k( k 1) By defnton, 0 c 1, and 0 C 1,f and only f complex networks s globally coupled, namely any two nodes are drectly connected n complex networks, C= 1. The degree k of a node s the number of edges ncdent wth the node, and s defned as follows: k = a (4) In drected graph, the degree of node ncludes two components: the out-degree and n-degree, the out-degree s defned as k out = a and the number of ngong lnks k n = a. So the total degree of node s defned as k k n k out = +. Average degree, marked for < k>, s defned as the average of all the degree k of nodes n the networks. In a graph G,the most basc topologcal characterzaton can be ganed by analyzng the degree dstrbuton Pk ( ),whch defned as the probablty that a node chosen unformly an random has degree k or, equvalently, as the fracton of nodes n the graph havng degree k. The three statstcal propertes are the bass of studyng complex networks, as research contnues; some other mportant statstcal propertes contnue 1003

4 to be dscovered n real networks, such as network reslence, betweenness and the relatonshp between degree and clusterng coeffcent. The reslence of a network s a measure of ts relablty; t s the expected number of node pars whch can communcate [10]. Betweenness s a measure of the centralty of a node n a network, and s normally calculated as the fracton of shortest paths between node pars that pass through the node of nterest. Betweenness s, n some sense, a measure of the nfluence a node has over the spread of nformaton through the network [11]. 3. THE COMPLEX MATERIAL FLOW NETWORKS MODEL OF TYPICAL STEEL ENTERPRISE Steel enterprse s a process seres-parallel complex system, whch composed of varety of processes and devces wth dfferent functons of nterrelaton, mutual support and suppresson. Accordng to the analyss of typcal steel productve process, we can fnd the features of contnuous and dscrete for the productve actvtes n the ron and steel enterprses, and the whole process shows up as mult-stage producton, mult-segment transport and mult-stage storage large scale hgh temperature producton process, producton materal flow has the characterstcs of dversty, complexty and many perods. Therefore, producton materal flow system of the steel enterprse manfests as multple producton processes seres-parallel materal flow networks n macro, and manfests as contnuous and dscrete tme queue networks n mcro. So, producton materal flow system of the steel enterprse s a complex networks system, we must make use of the theory and methods of complex networks to research on complex materal flow networks system of the steel producton for solvng tme balance and temperature balance n the relatonshp between all aspects of nterrelated and mutually nfluence each other constrants, and even balance problems of resource supply and materal flow capacty. Steel producton s a process of manufacture whch composed of smeltng equpments and ts nterrelatonshps, and realzed the changes from raw materals to the product; and s a process of functons ever-expandng and updatng; and s a complex process of devces growng and relatonshp complcatng. As a whole, the process of manufacture shows the functon devces contnues to add and delete, and the materal networks are huge and complcated n the evolutonary process to meet the requrements of the development of the market and socal envronment. Specfcally, the steel producton process s a complex networks ncludng a number of nodes and lnks. At the ntal stages, steel producton process s comprsed of several dscrete smple processes, and the nternal structure s very smple and the accessory equpment s more lmted n the process. And that, the networks conssted of relatonshps of the staton s uncomplcated n the processes. But, wth the development of technology and market requrements, the processes and statons n the steel producton are more and more sophstcated and cumbersome, and that the relatonshps of devces are usually mscellaneous and tolsome. So, we can defned the steel producton process as a complex networks for descrbng the complex process and complcated relatonshps by utlzng the technology and theory of complex networks. In the complex networks model of the steel manufacture process, the networks are composed of nodes and edges that connected between nodes. Where, the nodes are dentfed by the staton (manufacturng equpment) of the manufacturng process and the staton (transport equpment) of the transport process; the edges manly show the drect contact wth equpments. Wth the development of metallurgcal technology and the acceleratng process of global economc ntegraton, the nodes and the edges are undergong profound changes n the complex networks model of the steel manufacture process. The backward processes and ts statons were elmnated from the networks, the more advanced processes and ts statons are added n the networks. So, the complex networks model of steel manufacturng process shows a complcated process of relatvely stable n specfc perod and contnuous dynamc changes n the process of whole development. In ths paper, based on the above analyss, the complex networks model of steel manufacturng process s dynamc networks along wth the tme changes; of course, ths s relatve to the entre course of development. That s, on the bass of gven ntal network, we can obtan a seres of the process of change of the dynamc network topology for a certan perod of tme through the applcaton of network update rules. The tme of changes of network topology s trggered by an event, and the network topology s called a network scenaro at the moment. Therefore, the complex networks model can be seen as the results of an ntalzaton, growth and cuttng n the development of network system. 1004

5 Step 1 system ntalzaton: accordng to the sze of systems, we establsh the nodes of 2N-1, whch s lnked wth edges of 2(N-1), and represent the manufacturng equpments of N and the transport equpment of N-1. In the networks, the coordnate poston s random; Step 2 growth rules: when the system functon need to add staton, a new node s generated and added to the networks based on the propertes of staton, and the edges s lnked wth the nodes of ts upstream and downstream process; Step 3 cuttng rules: when the system functons need to update or mantan, the nodes and the related edges wth the nodes are removed smultaneously. 4. TOPOLOGY ANALYSIS OF THE COMPLEX MATERIAL FLOW NETWORKS IN TYPICAL STEEL ENTERPRISE In the manufacturng process of steel enterprse, there are knds of devces whch responsble for dfferent tasks. In order to reduce the complexty of the model of the complex materal flow system, some mnor nodes are gnored. So the networks model s a drected networks wth ( N = ) 40 nodes and 140 drected lnks. It s represented by a bnary adacency matrx, AN ( N), whose elements a take value 1 f there s materal flow from devce to devce and 0 otherwse. The asymmetrc adacency matrx A was used to fnd the some propertes of networks whch are senstve to the drecton, other propertes of networks were calculated by symmetry operatons of the adacency matrx. Shortest path analyss s ntended to gve us an ntutve dea on the ease of travel n the network. Shortest path length from node to, L s the number of edges needed to be taken to go from to by the shortest route. We found the average shortest path length of the complex materal flow networks n the typcal steel enterprse to be ( L =) , whch s of the order of that of a random network of same sze and average degree. The average clusterng coeffcent of the complex materal flow networks n the typcal steel enterprse was found to be ( C =) , whch s an order of magntude hgher than that of the comparable random network. Accordng to these two propertes, we can regard the complex materal flow networks s a small world networks. Fgure 1 shows the dstrbuton of the shortest paths n complex materal flow networks of the typcal steel enterprse. Table 1 summarzes the results of shortest paths analyss. Around 80% of paths are reachable by changng maxmum of 3 devces. Around 58% of paths are reachable by changng maxmum of 2 devces. Especally, about 31% paths are connected by drect devces. We also deduce that the dameter of the complex materal flow networks n the steel enterprse s 7, whch means that the raw materal was transformed nto the last product by seven dfferent devces for achevng the physcal and chemcal changes. Degree, as defned n Equaton 4, s one of measure of centralty of a node n the network. Degree symbolzes the mportance of a node n the complex networks, namely, the larger the degree of the node, the more mportant t s. In the complex networks, the degree dstrbuton s an mportant property whch embodes the topology of the network. The topology structure may shed lght on the process by whch the complex networks has come nto exstence. Fgure 2: Shortest Path Dstrbuton In Complex Materal Flow Networks In Steel Enterprse Table 1 Shortest Path And Ther Percentage Of The Network Model Shortest Path No. of Paths Percentage As can be seen from fgure 3, degree dstrbuton n the complex materal flow networks of the typcal steel enterprse shows the centralty of the nodes n the network. The degree changes from 1 to 1005

9, and the value, n the degree K column of the maxmum of the pk ( ) whch defned as the probablty that a node chosen unformly an random has degree k, aganst s 4, whch means these nodes n the network s

By analyss the fgure 4, we can fnd the node 5 and the nodes 6,7,8 are the mportant role n the network, further research the structure of the real steel enterprse, we can fnd the node 5 stands for the

6 9, and the value, n the degree K column of the maxmum of the pk ( ) whch defned as the probablty that a node chosen unformly an random has degree k, aganst s 4, whch means these nodes n the network s mportant for the materal flow system. The dfferent node stands for the devce act as dfferent role n the whole system, the larger the degree of the node, the more mportant t s. By analyss the fgure 4, we can fnd the node 5 and the nodes 6,7,8 are the mportant role n the network, further research the structure of the real steel enterprse, we can fnd the node 5 stands for the process of ronmakng whch receves all raw materal and output the products to other next process. All materal flows pass through ths central hub, so the process of ronmakng s mportant, especally, the processng capacty of ronmakng drectly determne the producton capacty of the whole steel enterprse. By the same token, the nodes 6, 7, 8 stand for the dfferent steelmakng and determne the materal flow speed and rhythm of the systems respectvely. 5. CONCLUSION In ths paper, we have presented a complex networks model of the materal flow system n the typcal steel enterprse by ntroducng the complex networks theory and technques. Accordng to the structure propertes of the materal flow system, the devces were defned as nodes and the drected relatonshps between devces were defned as edges n the complex materal flow networks of the typcal steel enterprse. In order to analyss the topology structure of the complex networks model, we have created the adacent matrx, n whch the 1 means that there s the drect nterrelatonshp between the nodes and 0 otherwse. The average shortest path and the clusterng coeffcent of the complex materal flow networks model n the typcal steel enterprse were solved and the results show that the complex networks model s a smallworld network. Furthermore, the degree and degree dstrbuton were carred out statstcs and further analyze the topologcal propertes of the complex materal flow networks. The statstcal analyss of the network model of the producton process n typcal steel enterprse was provded to explore new methods and breakthrough for local path optmzaton and global plannng, especally, supply the nstructons of theores and technques for the further mprovng the topology structure of the materal flow networks n steel enterprse, moreover, network behavor s the research topcs n the future. ACKNOWLEDGEMENTS Fgure 3: Degree Dstrbuton In The Complex Materal Flow Networks Ths work was supported by the Natonal Natural Scence Foundaton of Chna (Grant No ).The authors would lke to acknowledge Kunmng Iron and Steel Co.Ltd for ther help n collectng producton data. REFERENCES: Fgure 4: Degree Of The Nodes In The Complex Materal Flow Networks [1] J. D. Montgomery, Socal networks and labormarket outcomes: toward and economc analyss, The Amercan Economc Revew, Vol. 81, No. 5, 1991, pp [2] R. Albert, A. L. Barabas, Statstcal mechancs of complex network, Revew of Modern Physcs, Vol. 74, 2002, pp [3] H. Jeong, S. P. Mason, A. L. Barabas, Z. N. Oltva, Lethalty and centralty n proten networks, Nature, Vol. 411, 2001, pp

7 [4] R. Gumera, S. Mossa, A. Turtsch, L. A. N. Amaral, The worldwde ar transportaton network: Anomalous centralty, communty structure, and ctes global roles, Proc Nat Acad Sc USA, Vol. 102, No. 2, 2001, pp [5] M. E. J. Newman, The structure of scentfc collaboraton networks, Proc Nat Acad Sc USA, Vol. 98, No. 22, 2005, pp [6] S. Mlgram, The small world problem, Psychology Today, Vol. 2, 1967, pp [7] D. J. Watts, S. H. Stroatz, Collectve Dynamcs of small world networks, Nature, Vol. 393, No. 6684, 1998, pp [8] A. L. Barabas, R. Albert, Emergence of scalng n random networks, Scence, Vol. 286, No. 5439, 1999, pp [9] F. Ball, D. Mllson, G. S. Tomba, Epdemcs wth two levels of mxng, Annals of Appled Probablty, Vol. 7, 1997, pp [10] C. J. Colbourn, Network reslence, SIAM. J. on Algebrac and Dscrete Methods, Vol. 8, No. 3, 1987, pp [11] M. E. J. Newman, A measure of betweenness centralty based on random walks, Socal Networks, Vol. 27, No. 1, 2005, pp

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