(1) Business Administration Department. University of Illinois at Urbana Champaign. Illinois, USAEmail : [email protected]. Address: 363, Wohlers hall, S sixth street, Champaign. Phone: +1-217-265-0654
Complex products are typically considered as a network ofcomponents that share interfaces in order to function as awhole (Ulrich, 1995; Suh 2001). Two studies provide the inspi-ration for the current paper. Herbert Simon posits in his de-lightful book (Simon,1981) the need for design to balance theinternal and external environments (like a clock on a ship –which shows exact time in spite of the pitching and rolling ofthe ship in a storm). Recent literature (Gershenson et al, 2004)has highlighted the present inconsistencies in the field of mod-ular product design and put forward some critical questions.The current paper is focused on developing and analyzing thestream of research as recommended by Gershenson et al andin the spirit noted by Simon. The paper develops product rep-resentations as component networks that evolve from sharingof interfaces with other components in a product and linksthem to the external world of sourcing. It draws on the branchof mathematics known as 'Graph Theory' to develop measuresthat quantify the relative degree of modularity of componentsin complex products, basing it on the patterns of design inter-faces of each component.
What makes the study of component modularity interesting? Inestablished firms, organizational subsystems continuously im-prove particular technological subsystems (modules). This typeof innovation can be linked to a stable environment and estab-lished firms excel in it. However, architectural innovation oran innovation between the modules may require an adjustmentin the relationship between modules. Henderson and Clark(1990) posited that established firms are notoriously bad at ar-chitectural innovations. These firms have difficulty managingthe inter dependencies between modules. This usually happenssince existing organizational structures – which get developedbased on the dominant design of the product that is successfulfor the focal firm - interfere with architectural innovation. Newfirms or firms entering an industry without pre-existing, mod-ule-specific organizational structures have competitive advan-tage over existing firms since they can align the organizationstructure along the paths of architecture needed in the market.Therefore, understanding architectural properties, such as com-ponent modularity, is particularly important for establishedfirms at the strategic level.
Component modularity is also important at the operationallevel because it can provide indication to designers about im-portant parameters relating to component performance met-rics, such as design rework, or to sourcing managers about keydecisions, such as make or buy (Novak and Eppinger, 2001).Understanding of such parameters can lead to better decisionson operational and strategic parameters.
A key feature of product architecture is the level to which it ismodular or integral. In the engineering design field, a largestream of research has focused on methods and rules to mapfunctional models to physical components (Kirschman andFedel, 1998; Newman, 2001; Suh, 2001; Eckert et al, 2004; Jarattet al, 2004). However, as Ulrich and Eppinger (2004) have sug-gested, product architecture study involves mapping of func-tional elements to physical components as well as thespecification of the interfaces among interacting components.Hence it is necessary to have tools for measuring the effect ofsuch interfaces among interacting components.
There have been many studies which suggest how to measurewhether a product or a subsystem is integral or modular (seefor example Ulrich 1995, Sosa et al 2003; Mikkola andGassmann 2003; Sharman and Yassine, 2004). Gershenson et al(1999) develop product modularity measures which are appli-cable at any life cycle of the product. In a similar vein, Newcombet al (1998) discuss modularity at a module level of the prod-uct. However previous research has not focused on the meas-urement and usage of modularity at a component level, todevelop operational and strategic plans (see the literature re-view section for a more detailed review of the modularitymeasurement literature).
We believe that component level modularity measurement isextremely important. On one hand, component modularitymeasures provide design and sourcing engineers with a basictool for assisting in the day-to-day operational work, while onthe other hand, these measures provide supply chain managerswith a base-level tool that they can use to develop long termrecommendations for sourcing.
Thus, our proposed network representation of products, fo-cusing on component level modularity, can augment the way ar-chitectural properties of product components are defined inthe literature and the way in which operational and strategicdecisions are taken by practitioners.
This paper is structured as follows. First, the relevant literaturein the product architecture and sourcing domain is reviewed.Next, some basic tenets of graph theory are presented and re-sults are used to develop network representation of productsleading to definition and development of component level mod-ularity measures. This section is the heart of the paper. In thenext section, these definitions are applied to determine themodularity of the components of an automobile subsystem(dataset described as in Pimmler and Eppinger (1994)) and aDelta Jigsaw (dataset available at the Design Repository of theDesign Engineering Lab at University of Missouri-Rolla). Next,the Modularity Sourcing Framework is developed, taking com-ponent obsolescence as a policy decision variable. Effects of
modularity on sourcing for the two products are discussed. Thepaper concludes with a discussion of the results and commentsfor future work.
2. Literature Review
This section builds upon two streams of research. The first isthe body of work dedicated to product architecture represen-tations, and the second is the established stream of work fo-cused on sourcing.
2.1 Product Architecture and Modularity
The literature on product decomposition and product archi-tecture goes a long way back. Simon (1981, first edition of thebook was in 1969) suggested that a product is a complex sys-tem, which is made up of many interacting parts. Each part issubordinated to the product system hierarchically. To simplifythe complexity of the system, the product should be designedas a set of sub-assemblies (sub-systems) so that their assemblyconstitutes a new product. Through product modularization,the manufacturer can create many products by assembling dif-ferent sub-assemblies within a short product development leadtime. Alexander (1965) described the design process as abreakdown of designs into smaller subsystems that are mini-mally or loosely coupled. When the product sub-systems aresignificantly independent, the product redesign is limited to themodification of a set of related sub-systems, which could bedone independently. This helps in improving the agility of thechange management processes and overall reduction in designcycle time. Suh (1990;2001) builds upon these concepts bymodeling the functional requirements of product design interms of exchanges of energy, materials, and signals betweenfunctional elements organized in hierarchical function struc-tures. Products have been considered as graphs of connectedcomponents and component connectivity is a central conceptwhen studying engineering changes and design propagation dur-ing the development of complex products (Clarkson et al,2004).
A key feature of product architecture is the level to which it ismodular or integral. In the engineering design field, a largestream of research has focused on methods and rules to mapfunctional models to physical components (Kirschman andFedel, 1998; Newman, 2001; Suh, 2001; Eckert et al, 2004; Jarattet al, 2004). However, as Ulrich and Eppinger (2004) have sug-gested, product architecture study involves mapping of func-tional elements to physical components as well as thespecification of the interfaces among interacting components.
The Design structure matrix (DSM) is the basic tool for study-ing the structure of product architectures in terms of subsys-
tem and component interactions. The DSM is a graphicalmethod introduced by Steward (1981) and used by many re-searchers (see Eppinger et al, 1994 for example) to study in-terdependence between product development activities.Pimmler and Eppinger (1994) also used the DSM to illustrateproduct design decompositions. They posited that by using theDSM, development teams can better understand the complexinteractions within the product system, thus simplifying the de-velopment process for large and complex projects. The DSMrepresentations of complex products have also been extendedto analyze the model design change propagation (Clarkson etal, 2004; Eckert et al, 2004; Jaratt et al, 2004). These papersspecifically focus on the modes by which component level in-teractions impact the effect of any design change in any com-ponent.
Modularity is usually defined in the literature as an efficient wayof organizing complex products and processes , by decompos-ing complex tasks into simpler portions so they can be man-aged independently and yet operate together as a whole(Baldwin and Clark, 2000). When designing complex products,modularity is considered an important product characteristicthat results from directly mapping the functional and physicalcomponents of the product (Ulrich and Eppinger, 2004). Froma systems perspective, modularity can be viewed as a continuumdescribing the degree to which a system’s components can beseparated and recombined, and it refers both to the tightnessof coupling between components and the degree to which the“rules” of the system architecture enable (or prohibit) the mix-ing-and-matching of components (Schilling, 2000). Modularitypermits components to be produced separately, or ‘loosely cou-pled’ (Orton and Weick, 1990; Sanchez and Mahoney, 1996), andused interchangeably in different configurations with very littleeffect on the overall system level performance or quality(Garud and Kumaraswamy, 1993).
How does one measure modularity? Ulrich and Eppinger (2003)propose that “Modularity is a relative property of a product ar-chitecture. Products are rarely strictly modular or integral.Rather, we can say that they exhibit either more or less mod-ularity than a comparative product. (Page 166)) . They also pro-pose three types of modular architecture :
(a) Slot-modular - where each of the interfaces between themajor building blocks (called chunks) of the product are of a dif-ferent type - so that various blocks cannot interact for exam-ple an automobile radio.
(b) Bus -Modular - Here there is a common bus to which otherchunks connect via the same type of interface for example inan expansion card for a PC .
(c) Sectional-modular - where all interfaces are of the sametype, but there is no single element to which all other chunksattach - example would be office partitions.
There have been various measures developed for describingthe product architecture and its modularity. Gershenson et al(2004) provide a recent review of the measures developed inthe literature for modularity. While mostly the measures de-veloped resemble the DSM concept, there are two studieswhich offer new interpretations for modularity measurement.Newcomb et al (1996) use a multiplicative measure of modu-larity. The inter module connections are multiplied with the av-erage correspondence between modules to arrive at a singlenumber. This measure precisely links the material compatibilityissues related to modules. Gershenson et al (1999) proposed anadditive measure of modularity – they focused on developing ameasure which can be applied during the complete product lifecycle. Their measure consists of the addition of two ratios –the first ratio is the ratio of intra module similarities to thoseof all the similarities in the product (ie. both intra and intermodule similarities). The second ratio is the ratio of of intramodule dependencies to all the dependencies in the product.
A recent paper by Mikkola (2006) focuses on developing a newmeasure for the degree of modularization embedded in prod-uct architectures. This paper is in line with that of Mikkola andGassman (2003) and develops a firm level view of modularity –The author takes four different factors that contribute to mod-ularity: components (standard and new-to-the-firm), interfaces(standardization and specification), degree of coupling, and sub-stitutability. A modularization function is developed to capturethe effects of these four factor – the paper also describes howthis measure can be used to elicit the opportunities for modu-larization of products.
2.2 Modularity and Sourcing
Aligning the decisions on modular product design and sourcingas well as overall supply chain design and coordination can notonly save production costs (Ernst and Kamrad, 2000), but alsoimprove supply chain performance (Fine, 1998). There are manypapers focused on the integration of product modularizationand supply chain design and coordination to optimize both op-erational and supply chain performance (Krishnan and Ulrich,2001). This review is focused on the literature that integratesthe concepts of design capabilities and design details like mod-ularity with sourcing policies and supplier development routines.
Novak and Eppinger (2001) focus on how product architecture(specifically modularity) of components affects sourcing deci-sions. They use an original dataset and an interesting method-ology. For simultaneously determining Product Complexity and
Vertical Integration factors, they treat these two variables asjointly endogenous. Their main results show that complex prod-ucts (say an engine) have interfaces that need coordination fordevelopment of design. It may require much more time to co-ordinate the sourcing with suppliers outside the firm thanwithin. Therefore, in-house development of complex productsrequires less effort in coordination and redesign. Their resultsalso show that
i. As product complexity increases, firms tend to vertically in-tegrate
ii. Product quality can be ensured when manufacturers designsimpler products for outsourcing to module suppliers.
iii. Product design and supply chain design both need to be har-monized for superior performance. This indicates that productdesign engineers and supply chain executives need to work inclose coordination within the firm to effect optimal decisionmaking.
Sanchez and Mahoney (1996) posit that an increase in modu-larity leads to more outsourcing. They reason that this effectis induced because the standardized component interfaces in amodular product architecture reduce the coordination cost oftrading at arm’s length. Schilling (2000) links modularity to in-dustry standards. She argues that industry-wide standardization— de facto as well as regulatory — makes the interrelation be-tween components very generic, which leads to an increase inmodularity and incentivizes outsourcing policies.
Ulrich and Ellison (2005) focus on the motives for internalizingan activity within a firm and posit that decisions about inter-nalizing design and internalizing production cannot be fully un-derstood in isolation. They conclude that design and productionactivities can only be disintegrated when production processeshave matured to the point where there are explicit design rulesthat express the constraints and capabilities of the productionprocess. Fine (1998) suggests that module suppliers havegreater autonomy and need lower proximity to improve supplychain performance. As each product module is independent ofthe others, the supplier is only required to conform to the pre-defined module specifications, but not to consider the modifi-cations of other modules. Schilling (2000) notes thatmodularized components allow suppliers to work on particu-lar modules by themselves and still assure that the modules willinteract effectively in the product development process.Therefore the problem of iterative communication and coor-dination between suppliers and manufacturers in product de-velopment modification and engineering change managementis reduced (Ulrich and Eppinger, 2004). Fine (1998) also sug-gests that a modular supply chain can result from developing
modular products. This may have effects on the physical loca-tion of the suppliers from the core assembly plants easing trans-action costs and permitting interchangeable arrangements formajor components. The effect of collocation was also focusedon by Dyer (1996) in an interesting paper on the differences be-tween asset specialization of US and Japanese firms. He findsthat firms which have tightly integrated production networkhave better performance. An interesting part of Dyer’s paperlooks at the configuration of Japanese automotive plants andtheir suppliers. He documents that all Toyota’s plants are within32 kms of each other and affiliated supplier plants are 30.7 milesaway (on average) with independent supplier's average distancebeing 86.6 miles. Nissan’s suppliers are 53 kms (affiliated) and172 miles (independent) away from its main plants. For GeneralMotors (GM), the plants are scattered around US and primaryGM suppliers are 350 miles away on an average. He posits thatgeographic proximity is one of the reasons of higher asset speci-ficity of Toyota. The advantage of close supply chain design withmanufacturers and suppliers (e.g. physical collocation) improvesthe chances of face-to-face communication and joint productdevelopment between them, leading to better tacit knowledgesharing which is vital for product innovation.
The concept of better knowledge sharing leading to bettersourcing, and its link to component modularity has been ex-plored in a paper by Gerwin (2004) who posits that, in the con-tractual relationship between buyers and suppliers, coordinationrequirement (referring to the total intensity of information pro-cessing needed in product development) and the ability of co-ordination (defined by the number of available coordinationmethods) in modular product development are lower than thatin integrated product development. Similarly, In their case studyof product modularization on supply chain design and coordi-nation in Hong Kong and China, Lau and Yam (2005) show thatproduct modularization reduces product development time, andimproves product quality and inventory levels. They furtherposit that supply chain design is greatly affected by product mod-ularization while supply chain coordination is affected bywhether the product is innovative or conventional.
Overall, the current literature links modularity to sourcing de-cisions and we can conclude that modular products are bettercandidates for outsourcing. This literature takes as given theconcept of ‘core competencies’, first forwarded by Prahlad andHamel (1994). At a strategic level, a firm can focus on its knit-ting and outsource the operations which are not in its core do-main. The modularity and sourcing literature focuses on thedetail of operationalizing the ‘non-core’ operations. But arethere other variables which affect this conclusion? How canmanagers operationalize the impact of other variables that mod-erate the decision of outsourcing? In section 5, We look at a mod-erating variable of obsolescence for enriching this discussion.
3. Graph Theory and Network Representation ofProducts
In this section, a product network representation based upongraph theory is developed using the foundations to define prop-erties of products when considered as graphs of connectednodes.
3.1 Graph Theory
For a detailed discussion on graph theory and its applicationto network concepts, the reader is referred to Harary (1994)and Diestel (2005). Some basic graph theoretic concepts arepresented below which will help build the connections to prod-uct networks literature.
A graph is a symbolic representation of a network and of itsconnectivity. The fundamental mathematical entity is the binarydirected graph or digraph. A digraph is a set of nodes and a setof links which connect pairs of nodes. The basic units of analy-sis under our approach consist of these nodes and links. Nodesare the junctions that represent the critical points of origin,routing, and termination. Links are any type of connection be-tween nodes. The adjective binary represents the added con-straint that we do not allow the links to have strengths or thatthe links may be of different types. Thus the digraph is a math-ematical representation of the simplest form of choice data –unranked choices on a single criterion.
A basic network configuration can be one that directly linksevery pair of nodes. Such a network is called a complete graph(Figure 1). If a network consists of n nodes, then its completegraph will have (1/2) n (n – 1) links. A complete graph also cor-responds to a point-to-point network. A prominent feature ofpoint-to-point networks is that they contain numerous cycles,which are paths along which it is possible to pass through asuccession of links and eventually return to the original nodewithout crossing any link more than once. A cycle is thus aclosed path, with no other repeated nodes than the startingand ending nodes. (This is often related to what is known asthe first problem of graph theory. Euler studied whether it waspossible to cross each of the seven bridges interconnecting thetwo banks of the Pregel River and the island of Kneiphof, lo-cated within the city of Königsberg, without crossing any bridgemore than once. Euler posited that every node except for thebeginning and ending nodes of the path must necessarily havean even number of links leading away from it if the type of paththat Euler sought were to exist. Because the network createdby the Königsberg bridges contained four nodes with an oddnumber of links, no such path existed. This description is inBarabási (2002), note on page 12).
The network architecture that minimizes the number of linksis a tree, which is a graph that connects nodes without creat-ing any cycles. A tree that connects all of the nodes in a net-work is known as a spanning tree. In a network with n nodes,such a spanning tree would consist of n – 1 links. According toCayley’s Formula (Harary, 1994), the number of spanning treesin a graph with n nodes is nn–2.
Another fundamental concept in graph theory is the geodesic,or the shortest path of nodes and links that connect two givennodes. There may not be a unique geodesic between two nodes:there may be two or more shortest paths, which may or maynot share some nodes. An Algorithm to calculate geodesics hasbeen given by Newman (2001).
3.1.1 Network Adjacency Matrix, X
Let us denote the number of nodes in a graph as g – the sizeof the group. If the nodes are numbered arbitrarily from 1 tog, then we may construct a useful matrix representation of the
digraph as below. Let X be a g*g matrix whose (i,j) entry is
Note that i -> j means that there is a directed link from nodei to node j. There may also be a directed line from node j tonode i, but this possibility is neither implied nor denied by thenotation . The link (i , j) is of initial extremity i and of terminalextremity j. The matrix X is called the Adjacency Matrix in graphtheory.
A weighted graph is an extension of digraph where we relaxthe assumption of the links having no strengths. A weightedgraph has a number associated with each link. The numbersare called link weights and the graph is said to have weightedlinks. Like links, nodes may also be weighted. A graph in whichevery node is associated with one or more numbers, callednode weights, is referred to as a graph with weighted nodes.
Link weights are often used to represent some physical pa-rameter of interest in applications of graph theory. For exam-ple, a graph may represent a system of roads between fivenodes A, B, C, D, and E, where the numbers attached to eachlink, the link weights, can represent the length in kilometers ofthat link.
A network is a graph with particular numerical values, such ascost or capacity or strength of relationship between the nodes,assigned to the links. Thus, a network is an extension of the di-graph and the matrix X associated with a network is called theNetwork Adjacency Matrix. The architecture of a networkrefers to the set of nodes and the pattern of the links that con-nects them.
3.1.2 Degree and Bridge of X
In graph theory the degree or valency of a node i is the num-ber of links incident to i. Let deg(i) denote the degree of i. Thevariable deg(i) therefore ranges from a minimum of 0 to a max-imum of (n-1) if there are n nodes in a graph.
In a directed graph the indegree of a node v is the number ofedges terminating at i and the outdegree is the number of edgesoriginating at i. Let deg + (i) and deg − (i) denote the indegreeand outdegree of node i. The degree of a node deg (i) is thesum of its deg+(i) and deg- (i). Note that the sum of deg+(i)over all nodes equals the sum of deg -(i) (and both are equal ton for a digraph). Individual nodes may show imbalances in theirindegree and outdegree.
A node with deg(i) = 0 is called isolated. A node with deg(i) =1 is called a leaf. If each node of the graph has the same degreek the graph is called a k-regular graph and the graph itself issaid to have degree k. A node with deg + (i) = 0 is called asource and a node with deg − (i) = 0 is called a sink.
For a weighted graph or a Network, the calculation of indegreeand outdegree is moderated by the weights of the links. Ourvariable Xij then is no longer binary but can have a value greaterthan 1 also. The indegree will then be defined as
where Xmax is the maximum strength of any of the links andtherefore the maximum value of Xij.We divide by Xmax tomake sure the degree measure is homogeneous across all
nodes of the graph.
The outdegree is defined similarly as
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where the only change on the right hand side is that the sub-scripts of X have changed to indicate the outgoing direction ofthe links at node i.
A useful definition in graph theory for developing connectionsto the product architecture is that of a bridge. The bridges ofa connected graph are the graph links whose removal dis-
connects the graph . Harary states ‘ A bridge is an edge of agraph G whose removal increases the number of componentsof the graph G’ (1994, p. 26). (An edge is a link, I use the termlink throughout to maintain homogeneity). We can note thatevery link of a tree is a bridge. Figure 2 shows an example ofa graph with five nodes. The links which are not at the end arebridges.
Figure 2. The three middle nodes are bridges
As we had noted before, a geodesic is the shortest path ofnodes and links that connect two given nodes. If we calculatethe ratio of all geodesics between two nodes, a and b, whichcontain our focal node i (ndab(i)) to the number of total geo-desics between a and b (ndab) we will get a measure of howmuch bridging is being done by node i – that is we will get a
measure of how much ‘in between’ a and b the node i is. Herend is not the geodesic distance d but the total number of thesegeodesics between a and b. Summing over all such pairs of aand b components in the product give us a measure of thebridging strength of node i.
3.2 Product Architecture and the Design StructureMatrix
We will use the standard tool of product architecture, theDSM or the design structure matrix, (Eppinger et al, 1994;Sharman and Yassine, 2004) for developing the link to productarchitecture literature. Let us denote the DSM by Y. Y is asquare matrix whose columns and rows are identically labeledwith the components of the product. It is the matrix of designdependencies for any type of design dependency - Previouswork in engineering design has identified various types of de-sign dependencies between components such as spatial, struc-tural, material, energy, and information (Pimmler and Eppinger,1994). Hence, Y captures the dependency between compo-nents for any given design domain. Y has non-zero elements,Yij, if component i depends for functionality on component j.The value of Yij indicates the strength of the design depend-ency.
We immediately see the parallel between the NetworkAdjacency Matrix defined in graph theory and the DesignStructure Matrix defined in Product Architecture literature.Matrices X and Y are similar in their representation : X is a groupof nodes and links and Y is a group of components and their de-pendencies. These two representations – from two different researchstreams - are similar in their nature. It is proposed that graphtheoretic formulations can aid the DSM formulations by help-ing the practitioners via the network representation of com-plex products. Such a representation helps to identify modularcomponents which can aid policy decision on design andsourcing.
3.3 DSM and Network Representations – An illustra-tive view
To further illustrate the parallel between the Network rep-resentations and the DSM representations, we take an exam-ple of a product called the Delta Jigsaw. Table 1 shows theDSM of the Delta Jigsaw. This is a 41*41 matrix and repre-sents the design dependencies of all the 41 components ofthe Delta Jigsaw with each other. Treating this matrix as aNetwork Adjacency Matrix, we can identify each componentas a node and the design dependencies as links of a graph. Thenetwork representation of such a graph is shown in figure 4(drawn with UCINET). This network representation helps usin identifying the modular and integral parts of the Network(at a component level) by detailing the interconnectivity ofthe network. For example, figure 4 details that a component'switch' has a lot of direct design dependencies with othercomponents and thus represents a component that is veryembedded in the overall design of Delta Jigsaw. If there arechanges in the design of switch, there may be associated de-sign changes in other linked components. We can then thinkof the switch as a component that is very integral to the design ofa Delta Jigsaw or alternatively has very low modularity for the DeltaJigsaw. Such a representation then gives us inspiration to de-fine modularity of the components in terms of their depend-encies on other components. There may be other ways inwhich components could affect each other and these differentways help us in developing different measures of componentmodularity.
Such representations have gained popularity in understandingthe product architecture.
What does this matrix represent? The 41* 41 matrix is a matrix of0’s and 1’s.
The first column has the names of the 41 components that makeup the product called “Delta Jigsaw”. The first row also has these 41
components, however for representation the product names havebeen replaced by their component numbers (1 to 41). If there is 1in a particular cell, this means that the row component and the col-umn component have a dependency with each other.
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Table 1 : Design Structure Matrix of the Delta Jigsaw (Equivalent to Network Adjacency Matrix) .
What does this representation show ? In essence, there is the sameinformation as that in matrix of figure 1. However, we see that thisnetwork representation gives us a much better appreciation of thelinks between components. As discussed in the text, the componentcalled switch ( see arrow) seems to have a lot of dependencies withother components, indicating that it may not be modular.
(For clarity, components which do not have links to other compo-nents are not shown – they are isolates in graph theory parlance)
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Figure 4 : Product Network Representation of the Delta Jigsaw.
In this section, we develop formal measures of componentmodularity based on the discussions of graph theory and thesimilarity of representations of the Network Adjacency Matrixand the Design Structure Matrix, which we developed in section3. We link the proposed measures to graph theory and prod-uct architecture literature.
4.1 Degree Modularity
The most fundamental measure of modularity that we proposeis the answer to the question: “how many other components
depend on the design of this component?” The larger the num-ber of components that affect, or are affected by, the design ofcomponent i, the less modular component i is. It is clear then,that the modularity of a component can be defined precisely asan inverse of the definition of degree of a node as detailedabove from graph theoretic considerations.
Similar to graph theory definitions given above, the In-Degree ofa component i is equal to the number of other componentsthat i depends on for functionality, whereas Out-Degree is equalto the number of other components that depend on compo-nent i. Thus we define, for a product with n components, theIn-Degree Modularity of component i, M(ID)i, as
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where Ymax is the maximum value that Yji can take. Similarly, the Out-Degree Modularity of component i, M(OD)i, canbe defined as
where again, Ymax is the maximum value that Yij can take. Thusthe degree modularity of a component will be the sum of the
above and will be given by
We see that this definition is probably inadequate for productnetwork representation from the view of a firm, since the ab-solute values that the above definitions will give will not be in-terpretable across products. Hence we need to standardizethe above definitions so that degree modularity of a compo-nent is an interpretable value across products. One way to dothis would be to introduce the number of components we wantto measure (n) in the definition. We can also constrain the
measures so that the value obtained is between 0 and 1.Applying these modifications, we get the standardized meas-ures of indegree modularity, outdegree modularity and the de-gree modularity of a component. The standardized measuresthen become
A high value of any of the modularity measures indicates thatthere are fewer and/or weaker design dependencies andtherefore the component is more modular. The maximumvalue of degree modularity is 2, which corresponds to a com-ponent that has zero design dependencies with all other (n-1) components of the product. Hence, such a componentwould be highly modular. In graph theory terms, this compo-nent is an isolate node that has no links to any other node inthe graph.
4.2 Bridge Modularity
A second way of measuring modularity is akin to the definitionof a bridge in graph theory. Here we can focus on those com-ponents that link two highly integral components. We can viewthese bridge components as having control over the design de-pendency flow since information about the design dependencymust propagate through them. In this sense, these componentscan be considered as information valves that regulate theamount of information transmitted in the product network forsome dependencies. The more a component is “linked to” otherintegral components, the more integral it is – thus a less mod-ular component is less related to integral components. Whatis meant is that even if a component has only two links, if thecomponents at the other ends of these two links have a very
low modularity, the modularity of our focal component shouldalso be low.
As noted in the previous section, graph theory definition of abridge is a line such that the graph containing the line has fewercomponents than the subgraph that is obtained after the line isremoved. In product representation domain, we can then thinkof components becoming more integral as their bridging posi-tion increases. As a result we define bridge modularity of com-ponent i based on the number of times it is on the path of twoother components. We can assume that components lying onmost geodesics will be the one bridging most components andtherefore the least modular. This assumption makes sense inthe product domain if a design dependency between two com-ponents propagates through the minimum number of parts (i.e.the geodesic). Thus the bridge modularity of a component canbe defined precisely as an inverse of the definition of bridges ofa node as detailed from graph theoretic considerations. Hence,if we calculate the ratio of all geodesics between two compo-nents, a and b, which contain our focal component i (ndab(i)) tothe number of total geodesics between a and b (ndab) we willget a measure of how “in the middle” (between a and b) com-ponent i is. Summing over all such pairs of a and b componentsin the product give us a measure of the bridging potential ofcomponent i. Our measure M(B) then takes the form
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so that the standardized degree modularity measure for a com-ponent is
Similar to the degree modularity measure, the maximum valueof this index is 2, which is reached for a perfectly modular com-ponent that is not on the geodesic of any other pair of com-ponents – then our focal component i does not bridge any twoother components in the product for that particular type ofdesign dependency. An Algorithm to calculate geodesics is givenby Newman (16) and is also available in commercial softwarepackages like Mathematica.
Bridge modularity measure is quite different from the degreemodularity measure in its focus of measurement. Since bridgesare nodes that disconnect the network if removed, a low bridgemodularity measure would mean that the particular compo-nent is one which is critical – if such a component malfunctions,the product network will disconnect – the product cannotfunction. Thus, while degree modularity measures the directeffect of design dependencies, bridge modularity measures thesensitivity of these dependencies as they are propagatingthrough the product network. Bridge modularity is thus a rep-resentative measure of the critical and sensitive areas in theproduct network.
I consider the two proposed measures of component modu-larity to be complementary of each other because they em-phasize related but distinct features about the patterns ofdesign interfaces between product components. Degree modu-larity only takes into account the effects of immediate neigh-bors neglecting the connections beyond adjacent components.In addition, it captures the strength of the design dependency.Since the design structure matrix need not be symmetric, wedefine In-Degree and Out-Degree modularity. Bridge modularityis based on the component’s role in bridging other componentsand therefore its sensitivity with regards to the overall func-tioning of the product. Thus bridge modularity does take intoaccount the effect of components which may not be its imme-diate neighbors. The less bridging role a component has, themore modular it is.
Both these measures are based on the underlying argument
that the more independent the components are from othercomponents, the more modular they become. Less modularcomponents are components with many interfaces and/or oc-cupying bridging positions in the product. We therefore for-mally define component modularity. Component modularity isdefined as the level of independence of a component from sharedinterfaces in a product. This definition implies a range of modu-larity at the component level. This definition also entails thatconstraints on components due to their interactions with othercomponents define their modularity.
In the next sections, this understanding of component modu-larity and the modularity formulations are applied to two dif-ferent products for which design structure matrices have beendeveloped. We will then explore how we can build on the mod-ularity knowledge of the components to evolve sourcing deci-sions.
5. Sourcing Policy Development
In this section, I develop a theoretical policy decision frame-work linking sourcing of components to component level mod-ularity. While one can focus on a number of parameters forsourcing, I focus on a single parameter - the obsolescence of theproduct. In today's automotives, which are having large inter-faces with electronics, there is an increasing degree of obso-lescence built in. Some components may have a longer lifecycle (example castings and forgings) while others may have ashorter life cycle (example electronic chips – faster chips maycome in very soon ). In an interesting essay, Saleh (38) givesthe example of the obsolescence of the flight management sys-tem of the Boeing B-777 airplane. The Boeing 777 relies on theIntel 80486 chip for its Flight Management System. The airplanewas designed to be in use for approximately 30 years. Theproblem is that Intel will withdraw support to 486 chips by nextyear. Saleh notes “The Flight Management system must be (orshould have been) designed to accommodate flexibility (Saleh,2005).” The upgrade costs have been estimated to be close to$250,000 per circuit redesign.
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Once again, we see that this measure will give us different val-ues for different products depending on number of compo-nents. We can standardize this measure by taking into accountall pairs of components excluding component i. There can be (n-1) components not including i, which can have geodesics with(n-2) other components. Note that the fewer geodesics com-
ponent i is on, the higher the value of M(B)i, and the more mod-ular component i is. To have measure which is similar to our de-gree modularity standard measure, we constrain our bridgemeasure to lie between 0 and 2. Our standard measure ofbridge modularity then becomes
Component obsolescence can be mitigated in many ways :
• By arranging for alternate or substitute parts• By Cannibalizing from product returns• By procuring from Grey Market or After market • By having a Lifetime buy – Firms can stock the lesser lifetimepart for the life of the product/system !• By Reverse engineering or Process emulation• But in a proactive way – by Sourcing decisions based on mod-ular and integrative component detailing.
In this section we explore the last alternative - How can com-ponent level modularity be applied to design/sourcing decisionsso as to obviate the risks of obsolescence? The guidelines wedevelop can be used for improving component level sourcing ata firm level. At the sourcing level, the steps related to this de-cision may be the following
1. The network of components for the complex products canbe explored using the DSM and the product representationsto measure component level modularity. The degree and thebridge modularity values of all components can be then com-puted.
2. Component obsolescence can be measured by evaluatingindustry trends and product life cycle estimates.
3. Finally, the procurement policy for each component can bedeveloped to evolve a coherent sourcing policy.
We develop below the sourcing policy framework on the twinparameters of obsolescence and component modularity. Formodular components that also have a high obsolescence pro-file, the policy decisions can focus on outsourcing. Since theproduct clockspeed (Fine, 1998) is fast, firms who are OEM's(and their product obsolescence rate is lower than the focalcomponent) may ideally not invest in the technology requiredfor upgrading the components. Thus, a highly modular compo-nent with a high obsolescence rate is a candidate for the “buy”process within the make-buy sourcing decision process. Onthe other hand, a component that has a very low modularity(and is therefore integral to the product) but also has a highobsolescence rate is a candidate for maintaining technologicaledge. This can be done either by developing very strong sup-plier relationships, or by developing the component in-house –in either case, the firm has to continue investing in competen-cies to ensure that the design dependencies that the focal com-ponent has with other components does not affect the productperformance, service levels and warranty commitments, evenafter the product has been introduced.
For the products which have a high modularity but a low ob-solescence rate, the decision is not so complex. Such compo-nents are ideally purchased from the market as per the needs.For the last remaining combination of a component with lowmodularity and low obsolescence, the firms will normally de-velop these components in-house or have strong processesbuilt around these components by virtue of previous associa-tions. The above discussion is summarized on the two axes ofmodularity and obsolescence in figure 5.
So, can the above discussion lead a manager to a simplistic ar-gument – “If a component is of low modularity then we shoulddevelop the component in house, and if it is of high modularity- buy it off the shelf? – I am not too sure how obsolescencecomes in? “ 1
The reasoning is slightly more involved. We propose that theobsolescence variable is a moderator between sourcing andmodularity. A highly integral component may be a good candi-date to produce inhouse - however, obsolescence considera-tions can dictate that the product designers go back to thedrawing board and redesign the components so that a modu-lar architecture results. Such architecture will then dictate out-sourcing - which is a different decision than that taken inabsence of figure 5. This is what we mean by a moderator vari-able - obsolescence affects the strength of the relationship be-tween sourcing and modularity. We can also understand themoderating relationship as an interaction. The relationship be-tween the sourcing and modularity variables depends on thelevel of obsolescence.
How is this discussion of obsolescence linked to componentmodularity? Having a value of modularity at the componentlevel allows the designers to experiment on components andmodules that have the most potential for altering the value of thesystem. Performing many experiments on the componentsmost critical to overall system performance maximizes theoverall value. Because of the computation of modularity at thecomponent level, the designer now has the option to pick thebest outcome from many trials.
6. Applications
6.1 Applications I - Delta Jigsaw
We use the dataset available at the Design Repository of theDesign Engineering Lab at University of Missouri-Rolla. TheDSM is shown in figure 3 and the Network Representation inFigure 4. As discussed earlier, the network representation letsus visually analyze the interconnections between the compo-nents. The component modularity definitions developed in theprevious sections are used to confirm the intuition developedvia the product network representations. Both the modularitymeasures are calculated for all the components of the DeltaJigsaw. Table 2 shows the results of the modularity calculations.The most modular components can be identified easily usingthe modularity values. Since we had standardized our meas-ures, these values are also comparable with other products to
get a sense of the level of modularity of components within aproduct.
Analysis of Delta Jigsaw Modularity Values
The data values are aligned with the primary intuition devel-oped via the network representation. The basic measure of de-gree modularity is what corresponds to the network graphs,and we see that two components - switch and system - showhigh integral values. The bridge modularity values provideadded information, needed for day-to-day operations and pol-icy level decisions. We recollect that a bridge represents a nodethat. if removed, will disconnect the network. Thus, the bridgemodularity values provide us with the 'sensitive' components –those whose operation is critical to the functioning of the net-work as a whole, even though they may not be highly integralfrom a degree perspective.
We see that the battery and its contacts have the lowest val-ues of bridge modularity. These then, are the sensitive spots foroperation of the Jigsaw as a product. If one of these compo-nents fail, the Jigsaw fails. This provides the designers withadded information about the needed performance parameters.
Overall, we can interpret that components with low degreemodularity values provide direct information about the mod-ularity or integrality of that component while the low bridgemodularity values provide information about the sensitive spotsin the product. These results can then be applied on theModularity Sourcing Matrix (Figure 5) to develop sourcing rec-ommendations. For example, we can recommend that the com-ponent switch is a component whose design dependencies arethe strongest. It is the most integral component of the DeltaJigsaw. If the product life cycle of the switch is such that its ob-solescence is high, then the firm producing the Delta Jigsaw maylike to either produce the switch in-house or develop strongtechnical competencies around the switch production. On theother hand, there needs to be enhanced quality control and de-sign processes developed for the battery, the contacts and thewires to ensure that their design and production (either in-house or outsourced) is robust. There may be inventory rec-ommendations developed for both in-house production as wellas service related issues. For example, service centers may beadvised to treat the switch, the system, the battery and batterycontacts as critical items, items which must never be allowed tobe out of stock, so that customer service satisfaction is high.
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1 We are grateful to one of the referees for pointing this out.
We use the dataset published by Pimmler and Eppinger (1994)describing the climate control system of an automobile. TheDSM is shown in Table 3. We divide the DSM into four differ-ent design dependency matrices to distinguish the four types of
design dependencies between the physical components -Material, Spatial, Energy and Information. We note that thisDSM uses a three-point scale to capture the level of criticalityof each dependency for the overall functionality of the compo-nent in question – for all four dependencies. These metrics arediscussed at length in Pimmler and Eppinger (1994).
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Table 2 : Degree and Bridge Modularity values for Delta Jigsaw
There are therefore four design dependency matrices that re-sult from the original DSM (Table 3). One of the resulting ma-trices – the Energy design dependency matrix is shown in Table4 – it is basically a subset of table 3. The design dependency ma-trix in this case is similar to the network adjacency matrix andcan be used instead of the DSM as the input for developing themodularity measures. I develop network representations forthe four types of design interfaces between the components.Figure 6 shows the network representation for the materialdesign interfaces while Figure 7 shows the same representa-tion for the energy dependencies. These diagrams help us in vi-sually analyzing the interconnections between the components.
The component modularity definitions developed in the sec-tion 4 are used to calculate modularity measures for all thecomponents of the Climate Control System for all the four de-pendencies. Table 5 shows the results of the modularity calcu-lations. The most modular and integral components can beidentified easily using the modularity values, however the analy-sis is more complicated and therefore more insightful since wehave four types of design dependencies identified. Since we hadstandardized our measures, these values are also comparablewith other products to get a sense of the level of modularity ofcomponents within a product.
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Table 3 : DSM of the Climate Control System (from Pimmler and Eppinger ,1994)
There are four design dependencies – Spatial , Energy, Informationand Material. These are denoted by S,E,I and M respectively. Againsteach part, these dependencies are denoted in a 2*2 matrix. The keyof these four dependencies is at the upper right corner of the table.
This DSM table thus gives information about four separate de-pendencies. It can be broken up into four different matrices, each forone dependency. Table 4 gives an example of this breakup – the e-nergy dependency matrix.
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Table 4 : Design Dependency Matrix for ENERGY dependency for the Climate Control System . (This table is a subset of Table 3. There are total 4 such matrices for four design dependencies.)
Figure 6 : Network Representation of Material design dependency. Components not shown have no links with any other component.
Figure 7 : Network Representation of Energy design dependency. Components not shown have no links with any other component for this dependency. See Table 3.
Table 5 shows that the data values are aligned with the primaryintuition developed via the network representations in Figure6 and Figure 7. We see that partitioning the DSM into variousdesign dependencies enriches the content and provides criticalinformation regarding the overall product network. We alsosee that different components can be classified as more mod-ular or less modular depending upon the design dependencybeing investigated. So, for information dependencies, the EATCcontrols are the most integral component, while for materialdependencies, evaporator core and blower motor are the mostintegral (they have the lowest degree modularity values). Onceagain we see that the bridge modularity values provide addedinformation, needed for day-to-day operations and policy leveldecisions. The bridge modularity values provide us with the'sensitive' components – the compressor is a sensitive compo-nent from the material point of view, even though it is modu-lar from a degree point of view. Hence, while the compressormaterial design is perhaps not critical, its operations affect theclimate control system the most – therefore the performanceparameters of the compressor are the most critical. TheCompressor is our material 'hot-spot' - while condenser andheater hoses are similarly sensitive components with respect toenergy and spatial dependencies.
Overall, we can interpret that components with low degreemodularity values provide direct information about the mod-ularity or integrality of that component while the low bridgemodularity values provide information about the sensitive spotsin the product. These results can then be applied on theModularity Sourcing Matrix (Figure 5) to develop sourcing rec-ommendations. For example, we can recommend that fourcomponents - evaporator core, blower motor, heater hosesand EATC controls are components which form the most in-tegral components of the Climate Control System. The ClimateControl unit firm may like to develop strong technical compe-tencies on these four components, even if it does not wish toproduce them in-house. Again, if the product life cycle of EATCcontrol system is such that its obsolescence is high, then thefocal firm may like to develop strong competencies around theEATC control system production. Additionally, we can recom-mend that enhanced quality control and design processes needto be deployed for the compressor, condenser, heater hosesand EATC controls, to ensure that their design and production(either in-house or outsourced) is robust. Inventory recom-mendations for production and service related issues can alsobe developed. For example, service centers may be advised totreat the compressor, the condenser, heater hoses and EATCcontrols as critical service items, items which must never be al-lowed to be out of stock. These four components, along with
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Table 5 : The Modularity values for Climate Control System
evaporator core and blower motor are also the items whichmust be high on the training agenda of service personnel at theservice centers of the automobile firm.
7. Conclusions and Future Work
This paper makes two important contributions. First, it en-riches the product architecture literature by providing formaldefinitions and measures of modularity at the component level.It shows that the Network Adjacency Matrix as understood in graphtheory literature and the Design Structure Matrix as understood inthe Product Architecture literature are similar in their treatment. Thepaper takes a network approach based on graph theory to de-fine two measures of component modularity. The two defini-tions of component modularity emphasize two different andvital aspects of modularity relevant at the component level.Degree modularity is related to the strength of design depend-encies with adjacent components. Bridge modularity is the indi-cator of sensitivity of components. These measures arequantified and interpreted for two different products and thepaper shows how design dependencies data can provide infor-mation about component modularity.
Second, the paper also illustrates how to use component modularitymeasures to develop day-to-day operational level as well as strate-gic level sourcing related recommendations by taking a moderatingvariable into consideration. The paper takes the variable of com-ponent obsolescence and develops the modularity sourcing ma-trix depending upon the level of obsolescence. Similar sourcingmatrices can be developed for other procurement parameters.The paper also discusses how some of these parameters like in-ventory and after sales service can be related to modularity ofcomponents. The easy computation and use of modularitymeasures at the component level may make it easier for man-agers to develop sourcing recommendations.
Although the two proposed measures of component modular-ity enrich our understanding and are relatively simple to calcu-late (once the network of component design interfaces hasbeen documented), future research may concentrate on the dy-namic effects of these and alternative measures that capturearchitectural properties of components. How do these mod-ularity measures change over time and as technologies change?An interesting question can also be related to fact of multipleuse of same component. A component is modular or integralwith respect to a product. But the same component may havea different modularity measure if it is also used in another prod-uct procured by the same firm. How can the sourcing decisionmatrix be developed for such a scenario? These and associatedqueries form future research questions for us.
8. Acknowledgments
I am grateful to Dr. Robert Stone for giving me permission touse the data available at the Design Engineering Lab. I am alsograteful to Dr. Steven Eppinger for giving me permission to usethe dataset described in Pimmler and Eppinger (1994). I ap-preciate the helpful comments provided by Dr. Manuel Sosaduring the early parts of this research.
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