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An integrated methodology for the analysis of collaboration in industry networks

In literature, a large number of studies on the Italian districts exhibit a portrait which points out the Italian economic specificity. A specific feature of the Italian districts is the large number of collaborative actions carried on by the
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  J Intell Manuf (2012) 23:2443–2450DOI 10.1007/s10845-011-0510-z An integrated methodology for the analysis of collaborationin industry networks Dario Antonelli  ·  Brunella Caroleo Received: 29 September 2008 / Accepted: 20 January 2009 / Published online: 15 February 2011© Springer Science+Business Media, LLC 2011 Abstract  In literature, a large number of studies on theItalian districts exhibit a portrait which points out the Italianeconomicspecificity.AspecificfeatureoftheItaliandistrictsis the large number of collaborative actions carried on by theassociatedenterpriseswhicharenotlimitedtothesolutionof the usual supply chain management problems. As not all thecollaborativeactionsbringimmediate(andmeasurable)eco-nomic benefits, there is the need for a reliable and unbiasedmethod aimed at the identification and analysis of the col-laborative patterns inside an industry network, to determinetheir presence and effectiveness. The proposed method usesa graph representation of the inter-firm relationships insidea network and induces the presence of collaborative behav-iours by the analysis of the graph topology. Keywords  Enterprise network   ·  Network topology  · Graph theory  ·  Algorithms  ·  Clique identification Introduction Aiming at avoiding any confusion about the basic terms orconcepts, some widely accepted definitions are reported inthe following.The term ‘industry cluster’ refers to a group of businessenterprises which enhance their individual competitivenessby sharing some enterprise functions (Bergman and Feser1999). Examples are: buyer–supplier relationships, com-mon technologies, common buyers or distribution channels, D. Antonelli ( B )  ·  B. CaroleoDepartment of Manufacturing Systems and Economics, Politecnicodi Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italye-mail: dario.antonelli@polito.itB. Caroleoe-mail: common labor pools (Enright 1996). An industry network is a group of firms which agree expressly to cooperate insome way and to depend on each other (Rosenfeld 1995). Aregional cluster is a socio-territorial entity characterized bythe active presence of a “population of firms” into a boundedgeographical area with specific socio-economic-technicalfeatures.In the last decades there was, at the academic level, anenthusiastic adoption of the regional cluster model as themost effective and stable paradigm to enhance firm-to-firmrelationships. Afterwards, studies of research policy showedthat the impact of innovation on enterprises was scarcelyaffected by their belonging to a cluster. As an example,enterprises belonging to clusters in UK and Germany havecomparable return of investments (ROI) for their innovationactivities with the enterprises which compete on the marketon a stand alone basis (Love and Roper 2001). Nevertheless, the benefits for an enterprise belonging toa cluster cannot be described by economic indices alone.Some studies considered the regional cluster from an evo-lutionary point of view and pointed out the better stabilityof the SMEs belonging to clusters (Beccatini 1990). Thereason is in the collaborative activities performed inside adistrict which cover different aspects of the network exis-tence and which not always have outcomes directly measur-ableintermsofeconomicprofits.Collaborationgoesbeyondthe classic cooperation in the supply chain management butincludescommonmarketingstrategies,sharedtrainingactiv-ities, cooperative design and others. It is apparent that thestudy of only one aspect of the cluster activities can lead tohasty conclusions.Extending to a cluster the value analysis methodology,some studies (Bititci et al. 2004; Lewis 1990) attempted to makeuseofthevaluecreationincollaborativenetworks.Theconcept of value propositions has been applied to different  1 3  2444 J Intell Manuf (2012) 23:2443–2450 forms of enterprise aggregations, including supply chains,extended enterprises, virtual enterprises and clusters. Theirresearch identified different levels of collaboration and cate-gorised each one accordingly, analysing and identifying thevalue transactions in case of each collaborative enterprisemodel. The conclusion is that it is not possible to define asingle criterion to describe the outcomes of collaboration.Nevertheless,theextensiontoregionalclustersofanalysismethods developed for a single enterprise or even a supplychainrunsintothedifficultytoobtainreliabledatabyacam-paign of interviews. There are two reasons underlying thedifficulty: •  each enterprise inside a cluster has a limited visibility of the whole cluster activities and there is an objective dif-ficulty to find a representative actor for each interview; •  there is the actual possibility that the interviewed peo-ple give biased answers based on their expectations morethan on the bare reality (as the questions refer to infor-mal exchanges of information among firms and not onlygoods and money transactions).Therefore, the present study proposes a method for the mea-sure of the collaboration inside industry networks inferringthe results from unbiased data regarding the existence of information flows among enterprises in the cluster. It is pos-sible to represent the net of links among the enterprises of a cluster by means of graphs which are afterward analysedwith the aid of the graph theory.The paper is structured as follows: the inter-firm collabo-rationissueispresentedinthenextsection.Section“Amodelfor the network” deals with a framework for collaboration inindustry networks, leading to a formalization of the prob-lem presented in section “Collaboration and graph theory”.After some applications of the analysis (section “Examplesof applications”), an extension of the model is proposed insection“Miningmultiplegraphs”.Finally,someconclusionsare drawn. Focusing the problem A thorough definition of collaboration was given by thestudies of  Huxham (1996). Collaboration literally means ‘working together’. The collaboration among the differentcompanies belonging to a network, in order to optimize themanagement of the supply chains, leads to recognized stra-tegic assets (Bititci et al. 2004). The successful examples of  collaboration reported in literature regard the collaborationin the implementation of business processes related to thesupply chain management: planning, sourcing, productionand delivery (as defined by the Supply Chain Council).IntheframeworkoftheCollaborativePlanning,Forecast-ing & Replenishment (CPFR) Committee a white paper waswrote (Nix et al. 2004) which identifies the requirements fora successful collaboration among independent firms: •  jointly managed business processes; •  standards for the sharing of information (data formats); •  methods of integrating the results of this collaborationinto the operational systems of both the distributors andsuppliers; •  key performance measures for joint supply chain activi-ties.The importance of the information sharing for collaborationand cooperation is stressed also in Gavirneni et al. (1999). The study developed and exercised a minimal cost model tocompare three levels of information sharing:1. decentralized control: there is no information sharing;2. coordinatedcontrol:twoadjacentnodessharetheirinfor-mation about customer demand;3. centralized control: total information sharing exists.The study results show a steady improvement in value for allmembers of the industry network as the level of informationsharing increases. A model for the network The description of the organization of a network cannotleave out of consideration an architecture framework whichincludes all the network activities. Though it should be pos-sible to relate to similar contexts, this reference model is notdefined yet.Reference models are Generalised Enterprise ReferenceArchitecture and Methodology (GERAM) project, which isageneralisationoftheenterprisearchitectureprojectscarriedon by IFIP-IFAC (Bernus and Nemes 1997). The work had strong impact on enterprise integration projects world-wide,for example the Globemen consortium specialised it for thecase of developing Enterprise Networks and Virtual ProjectEnterprises (VERAM) (Zwegers et al. 2002). Another reference model which is taken into account isthe supply chain model adopted by the SCC (Supply ChainCouncil 2006) to describe the activities of a supply chainfrom the point of view of performance evaluation.For the sake of attempting a preliminary analysis of thenetworkorganization,itispossibletoproposeforitsdescrip-tion the following general framework: •  a conceptual model which decompose the network in itskey sub-systems:  1 3  J Intell Manuf (2012) 23:2443–2450 2445 Fig. 1  Graphical representation of the modeling framework for ageneric network  ◦  Operative system: the production and delivery of goods and services; ◦  Decision system: the management of actions whichimpact on the whole network; ◦  Information system: the exchange of informationamong the firms of the network. •  amodellingframework:anintegratednetworkmodellingspace which has at least two dimensions (Fig. 1): ◦  Abstraction level: operative, tactical and strategic; ◦  Viewpoint:function,information,resource,organiza-tion •  a modelling formalism: in this case the graph appears themost appropriate language in order to describe links andflows among different nodes of the network.As regards the collaboration among enterprises in a clus-ter, it could be described by a number of graphs, correspond-ing to the intersections of the paradigms on the two axisin Fig. 1. As an example, in the paper of  Goyal and Joshi (2003)eachlinkrepresentscommercialagreementsbetweentwo enterprises (circle), in the paper of  Albino et al. (2002) links indicate the existence of flows of goods between twoenterprises(triangle).Inthepresentstudythelinkshaveinter-pretations focused on every level of information exchange(oval): •  at the operative level when internet tools like web por-tals or virtual private networks (VPN) are implementedto ease information exchanges; •  atthetacticallevelwhenproceduresofdataexchangearemutually applied to supply management and other oper-ational activities; •  at the strategic level when there is an agreement betweentwo firms to jointly manage their processes.The scope of this study and its peculiar usefulness for a net-work analyst is to show that it is possible to identify thecollaborative patterns inside a cluster, by the analysis of theinformation exchange structures, represented by a graph.All the graphs have  n  vertices, in a one-to-one correspon-dence with the enterprises of the cluster. Each node is linkedto another one in the graph if a relationship between thetwo corresponding companies exists, in particular if the twoenterprises share some kind of information or if there is anyinformation flow between them.Theadjacencymatrixcorrespondingtotheserelationshipsis a matrix with rows and columns labeled by graph vertices,witha1or0inposition ( i ,  j ) accordingtowhethertheenter-prises  i  and  j  are related or not,  i ,  j  =  1 ,..., n . The graphis undirected, leading to a symmetric matrix.In the next section some basic concepts of graph theoryare summoned up. Collaboration and graph theory Introducing the clique problemLet  G  =  ( V  ,  E  )  be an undirected graph, where  V   is the setof vertices and  E   is the set of edges in  G . We denote by n  = | V  ( G ) |  the order of the graph and by  m  = |  E  ( G ) |  thenumberofedges.Inthefollowing,wewrite G ( n , m ) tomeana graph  G  with order  n  and number of edges  m .For a subset  S   ⊆  V  ( G ) , we let  G S   denote the subgraphinduced by  S  .In order to deal with collaboration, one should handlecomplete graphs. Definition 1  An undirected graph  G  =  ( V  ,  E  )  is said to bea  complete  graph if: (v,w)  ∈  E  ,  ∀ v,w  ∈  V  , v  =  w The complete graph on  n  vertices is denoted by  K  n .In other words,  K  n is the graph  K  n =  G  n ,  n 2  ,where the notation  nk    =  n ! k  ! ( n − k  ) !  stays for the binomialcoefficient.The basic idea is that a complete graph (Bollobás 1978) is synonym of network collaboration. In fact, since in a com-plete graph all the vertices are linked each other, it meansthat in this context each enterprise shares information withalltheothercompaniesofthecluster.Thisisastronghypoth-esis (supported by the literature, e.g., DeCanio and Watkins1998), that has some limits: as an example, the presentedmodel considers a complete graph as the best topology of anetwork (as concerns the information exchanges), not tak-ing into account the additional costs of creating links in thecluster.Inthefollowingtheanalysisisfocusedontheinvesti-gationofacompletegraphinordertodealwithcollaborativenetworks; the authors will consider a possible relaxation of this assumption in their further research.  1 3  2446 J Intell Manuf (2012) 23:2443–2450 Fig. 2  The problem of identification of a complete subgraph  S   = ( V   ,  E   )  ⊆  G  =  ( V  ,  E  ) Therefore, we would like the graph to be complete, so asto achieve the maximum collaboration: if this is the case, thenetwork taken into account will be collaborative. Unfortu-nately, in an actual cluster of enterprises it is unlikely thateach firm is able to communicate each other.Inthelattercase,onecould beanyway interestedindeter-mining if some collaborative subnetworks exist, in order tobetter comprehend the behaviors of the actors of the net andto recognize possible collaborative patterns. According tothe concept of collaboration in terms of a graph, this issueis equivalent to the problem of identifying a complete sub-graph  S   of a given graph  G . Figure 2 shows an example of thisconcept:givenagraph G  (input),wewouldliketoextracta complete subgraph  S   (output).The problem can be summarized as follows: how tofind a complete subgraph of a given undirected graph? Inmathematical terms, this question corresponds to the  clique problem . Definition 2  A  clique  of an undirected graph  G  =  ( V  ,  E  ) is a set of vertices  C   ⊆  V   such that the subgraph induced by C   is complete, that is, such that: (v,w)  ∈  E  ,  ∀ v,w  ∈  C  ,v  =  w A clique  C   of an undirected graph  G  =  ( V  ,  E  )  is  maximal if there is no clique  D  of   G  such that  C   ⊂  D , and it is  max-imum  if there is no clique of   G  with more vertices than  C  .The  clique number   of   G , denoted by  ω( G ) , is the cardinalityof a maximum clique of   G .Some authors define the clique of a graph as its maximalcomplete subgraph (Gross and Yellen 1998), but others pre-fertodefineacliqueasanycompletesubgraphandthenreferto maximal cliques (Valiente 2002); the latter definition has been adopted in this study.The  clique problem  (or  k  -clique problem) is the prob-lem of determining whether a graph contains a clique of atleast a given size  k  ( k   ∈  N  ) : it is a graph-theoretical NP-completeproblem.Thecorrespondingoptimizationproblem,the  maximum clique problem , consists in finding the maxi-mum clique in a graph.In spite of the inherent difficulty present in NP-completeproblems, many algorithms (that perform well in practice)have been developed for the clique problem. As an example,abruteforcealgorithm(enumerativeapproach,notheuristic)tofinda k  -cliqueinagraphistoexamineeachsubgraphwithatleast k   verticesandchecktoseeifitformsaclique.Anotheralgorithm consists in generating all the cliques of a graph  G by backtracking (Kreher and Stinson 1998); the backtrack  algorithm generates each clique exactly once (without repe-tition) and identifies the maximal cliques.But what happens if no cliques (of order greater thana fixed threshold) are present in the graph  G ? We shouldconcludethatthereisnocollaborationatallamongtheenter-prises in the network. This is not true, some kind of collabo-ration is probably present: we will deal with this problem inthe next subsection.An index of network collaborationGiven a graph  G , if no complete subgraphs are present, wecouldbeinterestedtoidentifythesubnetworksinwhichsomeenterprises of the cluster collaborate each other, that is, thesubgraphs that are as close as possible to a clique. To do this,we first need to measure the distance between two graphs; infact, if it is found, one could measure the distance between agiven graph and the corresponding clique of the same order.First of all, let us consider a global measure of deviationof a graph  G  from the corresponding complete graph: Definition 3  the deviation  d  G  of an undirected graph G ( n , m )  from the complete graph  K  n is given by: d  G  =  n 2  − m  n 2   (1)The numerator corresponds to the number of missing edgesof   G  to get the complete graph  K  n . The denominator cor-responds to the size of a complete graph of order  n , so thatwe have 0  ≤  d  G  ≤  1. In other words, Eq. (1) defines the deviation of a graph from the corresponding complete graphas the number of edges missing to obtain a complete graph,opportunely normalized.Then, we can define a  global index of collaboration c G  of a given graph  G  as a decreasing monotonic function of   d  G ;the basic idea is that  c G  should satisfy: c G  =  1 if   d  G  =  00 if   d  G  =  1 (2)sothatnetworkcollaboration c G  ismaximumwhenthegraphis complete, and minimum when all the enterprises of thecluster are isolated, 0  ≤  c G  ≤  1.  1 3  J Intell Manuf (2012) 23:2443–2450 2447 Fig. 3  Some possible trends of   c G Figure 3 shows some examples of   c G  =  c G ( d  G ) ; the eas-iest case is the linear one, where  c G  =  1 − d  G .Note that the global degree of collaboration is an exten-sion of the definition of   γ  -density proposed by Abello et al.(2002); in particular, the two quantities coincide in the linearcase.The degree of network collaboration defined in (2) could be low, but anyway some enterprises of the network couldbe very collaborative. So, our intent becomes now that of extracting a subgraph as close as possible to a clique, that is,with the highest possible degree of collaboration.Itisclearthatifaclique  S   of  G  exists,itwillbetheanswerto this problem  c S   =  1; but in general, if it does not, the aimis to find:  D  =  argmax c S  , that means, among all the subgraphs  S   of   G ,  D  is the onethat has a degree of collaboration as close as possible to 1;in case the maximum is reached at many values, argmax canbe extended to value a set of solutions.The idea of finding sub-graphs with the highest degreeof collaboration is very related to the concepts of   γ  -quasi-complete graph and  γ  -quasi-clique (Pei et al. 2004) Definition 4  A connected graph  G  is a  γ  -quasi-completegraph (0  < γ   ≤  1 )  if every vertex in the graph has a degreeat least  γ   ·  ( n  − 1 ) : δ(  x  )  ≥  γ   ·  ( n  − 1 ),  ∀  x   ∈  V  ( G ). Definition 5  In a graph  G , a subset of vertices  S   ⊆  V  ( G )  isa  γ  -quasi-clique (0  < γ   ≤  1) if   G S   is a  γ  -quasi-completegraph.Clearly, a 1-quasi-complete graph is a complete graph,and a 1-quasi-clique is a clique.If the  γ  -quasi-complete graph  G  is connected, γ   · ( n  −  1 )  ≥  1, necessarily. Hence, we have: γ   ≥ 1 n  −  1 . In order to find  γ  , one can use the following formula: γ   = δ min n  − 1 , where  δ min  =  min δ(  x  )  is the minimum degree of the nodes  x   ∈  V  ( G )  of the graph  G .As an example, the value of   γ   in the graph  G  of Fig. 4ais 0.4, since all the vertices of   G  have at least a degree of 2  =  ( 6  − 1 ) ×  0 . 4.The parameter  γ   controls the compactness of the graph:the larger  γ  , the higher the compactness. In order to havecollaborative networks we look for quasi-cliques with a rea-sonablylargevalueof  γ  ,suchas γ   ≈  0 . 5orlarger.Itisappro-priate to specify a minimum number of vertices  min s  of a γ  -quasi-clique, so that only quasi-cliques large enough arereturned by the algorithms adopted to find  γ  -quasi-cliques(Abello et al. 2002; Pei et al. 2004). The problem can be summarized as follows: The  γ  -quasi-clique problem : given a graph  G  =  ( V  ,  E  ) ,a parameter  γ   (0  < γ   ≤  1) and a minimum size threshold min s , the  γ  -quasi-clique problem consists in finding the setof   γ  -quasi-cliques that have at least  min s  vertices each.The problem is NP-complete; its complexity derives fromthe NP-completeness of the clique problem. So, the problemof enumerating the complete set of quasi-cliques is NP-hardin the worst case.Nevertheless algorithms for finding quasi-cliques exist:for example, Abello et al. (2002) propose a greedy random- izedadaptivesearchprocedure(GRASP)forfinding γ  -quasi-cliques. These algorithms are better suitable to the case of massive quasi-cliques, when the number of nodes is veryhigh.The enumerative approach is heavy from the computa-tionalpointofviewbutitismoreappropriatefortheboundednumber of enterprises usually present in a network. It has Fig. 4 a  An example of a cluster  G  and  b  of an induced subgraph G S  ,  S   = {  A ,  B , C  ,  D ,  E  }  1 3
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