Designing Supply Networks in Manufacturing Industries

Read Sections 1 and 2 of this article. The study investigates how automotive original equipment manufacturers (OEMs) design supply networks. In Table 2, notice how personal ties and contractual, transactional, and professional network ties play a role.

Theoretical Background and Hypotheses

Indices for Network Characterization

To demonstrate different supply network architectures consisting of the four aforementioned heterogeneous supply network ties (i.e., contractual, transactional, professional, and personal ties), this study adopts social network analysis (SNA), which has long been used in analyzing any social network as a set of interrelated actors and ties. The field of SCM has stressed the potential applicability of SNA in a supply network context. For instance, Carter et al. proposed SNA as a valuable complement to traditional methodologies which may be used to advance current knowledge on various relationships existing within and beyond the supply chain. This view was echoed by Borgatti and Li who pointed out that supply chain settings are particularly suitable for SNA indices, which have proven "highly portable" across other disciplines from economics to physics. More recently, Galaskiewicz also noted that SCM theories mostly captured at the local level (e.g., dyad or triad) can be tested by using a supply network as the primary unit of analysis.

Despite repeated calls for such approach, there are still very few SCM studies that use SNA. Moreover, the vast majority of existing studies on supply network are case-based research that uses SNA measures defined for binary (i.e., "1" if a tie exists between two supply network entities, "0" otherwise) and non-directional ties (i.e., if one supply network entity perceives a tie, its counterpart's perception of the existence of the tie is automatically assumed). This is commonly referred to as the binary network approach, and most of the existing SNA indices have been devised solely based on this approach. The binary network approach specified by a symmetric adjacency matrix is conceptually and computationally straightforward and especially appropriate when a researcher focuses on cognitive ties (e.g., who knows whom). An important limitation of this approach, however, is that it involves an unrealistic premise - all ties are completely homogeneous and symmetrical - which contradicts previous findings in the literature. For instance, strong social ties strengthen interpersonal obligations, facilitate change in the face of uncertainty, and help to develop relationship-specific heuristics. Therefore, by using the binary network approach, network researchers can inevitably overlook important information about network properties embedded in network ties and consequently arrive at limited or even misleading implications for network architecture.

We thus adopted a directed valued network approach represented by an asymmetric adjacency matrix to overcome the aforementioned shortcomings of the binary network approach. This approach takes into account the direction and strength (or magnitude) of each tie between different network entities. In network terms, a directed valued network consists of a set of actors (or nodes) ${n_1, n_2, ⋯, n_g}$ , a set of arcs (i.e., directional ties or links) ${l_1, l_2, ⋯, l_L}$ , and a set of values ${v_1, v_2, ⋯, v_L}$ attached to the arcs, subject to $l_k=≠l_m=$ where $v_k$ is not necessarily equal to $v_m$ . This is a more useful and realistic approach for exploring supply network phenomena since it allows for the possibility that a focal firm and its suppliers may view the strength (or even the existence) of their ties differently. In this sense, there has been a growing need for SNA indices that can be used in the directed valued network setting when it is based on a different adjacency matrix.

More specifically, this study focuses on four socio-centric network indices (i.e., betweenness centralization, in-degree centralization, out-degree centralization, and global clustering coefficient), which describe the overall pattern of multiple actors within a single, bounded network. While ego-centric indices, such as centralities, deal with a particular actor's (i.e., ego's) position within the network, they provide a better understanding of the directed valued network in that the network architecture from one ego's viewpoint can be markedly different from those of others linked directly or indirectly. They also fit perfectly with the purpose of this study to explore the association between an OEM's strategic orientation and the supply network architectures it creates based on different types of supply network ties. Table 2 proposes a new framework for the supply network implications of the socio-centric SNA indices for the directed valued networks used in this study for four types of supply network ties.

Table 2. Socio-centric indices, conceptual definitions, and interpretations by supply network tie.

Socio-Centric SNA Index	Conceptual Definition	Tie Type	Implications for Directed Valued Supply Network
Betweenness centralization (BTC)	The extent to which particular network actors serve as hubs relative to the rest of the network	Contractual	The extent to which there exist particular focal firms that have more or less complete (or specific) contract terms than other supply network members. - The lower the index, the more firms there are which have more equally complete contract terms with their supply network counterparts. - The higher the index, the more firms there are which have more unequally complete contract terms with their supply network counterparts.
		Transactional	The extent to which there exist particular focal firms that have a higher or lower percentage of monetary exchanges than other supply network members (i.e. distribution of sales and spending in the network). - The lower the index, the more firms there are which have equal percentages of monetary exchanges with their supply network counterparts. - The higher the index, the more firms there are which have higher or lower percentages of monetary exchange with their supply network counterparts.
		Professional	The extent to which there exist particular focal firms that have more or less work-related interactions than other supply network members. - The lower the index, the more firms there are which have an equal amount of work-related interactions with their supply network counterparts. - The higher the index, the more firms there are which have more or less work-related interactions with their supply network counterparts.
		Personal	The extent to which there exist particular focal firms that have more or less non-work-related interactions than other supply network members. - The lower the index, the more firms there are which have an equal amount of non-work-related interactions with their supply network counterparts. - The higher the index, the more firms there are which have more or less non-work-related interactions with their supply network counterparts.
In-degree centralization (IDC)	The extent to which network resources are converged on particular network actors	Contractual	The extent to which particular focal firms obtain more complete (i.e. less favorable) contract terms from the other supply network members. - The lower the index, the more firms there are which have fair contract terms with their supply network counterparts. - The higher the index, the fewer particular focal firms possess less favorable contract terms with their supply network counterparts.
		Transactional	The extent to which particular focal firms take up a greater percentage of the monetary exchanges occurring inside the supply network than others. - The lower the index, the more firms there are which have equal percentages of the monetary exchanges. - The higher the index, the fewer particular focal firms account for higher percentages of the monetary exchanges than the others.
		Professional	The extent to which particular focal firms obtain more incoming work-related interactions from the rest of the supply network members. - The lower the index, the more equal the amount of work-related interactions between supply network members. - The higher the index, the more work-related interactions among supply network members is focused on fewer particular focal firms.
		Personal	The extent to which particular focal firms obtain more incoming non-work-related interactions from the rest of the supply network members. - The lower the index, then each of the supply network members has a more equal amount of non-work-related interactions with one another. - The higher the index, the more non-work-related interactions among supply network members is focused on fewer particular focal firms.
Out-degree centralization (ODC)	The extent to which particular actors disseminate network resources to others	Contractual	The extent to which particular focal firms provide more complete (i.e. less favorable) contract terms for the rest of the supply network members. - The lower the index, the more firms there are which have fair contract terms with their supply network counterparts. - The higher the index, the fewer particular focal firms yield less favorable contract terms for their supply network counterparts.
		Transactional	The extent to which particular focal firms generate higher percentages of the monetary exchanges occurring inside the supply network than others. - The lower the index, the more firms there are which have equal percentages of the monetary exchanges. - The higher the index, the fewer particular focal firms send out higher percentages of the monetary exchanges for the rest of the supply network members.
		Professional	The extent to which particular focal firms have more outgoing work-related interactions to the rest of the supply network members - The lower the index, the more equal the amount of work-related interactions between each of the supply network members and the others. - The higher the index, the fewer particular focal firms initiate most of the work-related interactions with the rest of the supply network members.
		Personal	The extent to which particular focal firms generate more outgoing non-work-related interactions for the rest of the supply network members - The lower the index, then each of the supply network members has more equal amount of non-work-related interactions with one another. - The higher the index, the fewer particular focal firms make more non-work-related interactions for the rest of the supply network members.
Global clustering coefficient (GCC)	The extent to which the network as a whole is cliquish (or tightly knit) (i.e. the degree to which all the network actors tend to cluster together)	Contractual	The extent to which members of the entire supply network are directly connected by contract relations - The lower the index, the lower the proportion of all supply network members that are directly connected by contract relations (i.e. the supply network has a more ‘hierarchical’ architecture as a whole). - The higher the index, the higher the proportion of supply network members that are directly connected by contract relations (i.e. the supply network has a more ‘lateral’ architecture as a whole).
		Transactional	The extent to which the members of the entire supply network are directly connected by monetary exchanges - The lower the index, the more the supply network as a whole has a “hierarchical” architecture in the monetary exchanges among supply network members. - The higher the index, the more the supply network as a whole has a “lateral” architecture in the monetary exchanges among supply network members.
		Professional	The extent to which all the supply network members freely communicate work-related subjects across firm boundaries - The lower the index, the more “hierarchical” the architecture of non-work-related interactions among members in the supply network as a whole. - The higher the index, the more the supply network as a whole has a “lateral” architecture for work-related interactions among supply network members.
		Personal	The extent to which all the supply network members freely communicate non-work-related subjects across firm boundaries - The lower the index, the supply network as a whole has a more ‘hierarchical’ architecture of non-work-related interactions among supply network members. - The higher the index, the more “lateral” the architecture of non-work-related interactions among members in the supply network as a whole.

First, betweenness centralization (BTC) represents whether most network actors are equally central, or some actors (i.e., hubs) are much more central than others. This index can be calculated by dividing the variation in the betweenness centrality by the maximum variation in betweenness centrality scores possible in a network of the same size. Betweenness centrality is an ego-centric index indicating how often an actor lies on the shortest path between all combinations of pairs of other actors. The higher an actor's betweenness centrality, the more its immediate counterparts depend on this actor to reach out to the rest of the network. This index focuses on the role of an actor as an intermediary and posits that the dependence of others makes the actor central in the network. BTC, a socio-centric version of betweenness centrality, ranges from 0 where all network actors have the same betweenness centrality, to 1, where there exists one single actor connecting all the other actors. This study calculates the BTC of a directed valued supply network by adopting the formula suggested by Opsahl et al. for betweenness centrality (

$C^{wα}_{B}(n_i)$ ) for network actor

$n_i$ , defined as:

$C^{wα}_{B}(n_i)=\dfrac{g^{wα}_{n_jn_k}(n_i)}{g^{wα}_{n_jn_k}}$

where

$g^{wα}_{n_jn_k}$ is the total number of geodesics between two actors (

$n_j$ and

$n_k$ ),

$g^{wα}_{n_jn_k}(n_i)$ is the number of geodesics passing through actor

$n_i$ ,and

$α$ is a positive tuning parameter that is set to the benchmark value of 0.5 to equally value both the number of ties and their strengths (

$w$ ). Thus, BTC can be formally expressed as:

$C_B=\dfrac{∑_{i∈G}{C^{wα}_{B}(n^∗)−C^{wα}_{B}(n_i)}}{max∑_{i∈G}{C^{wα}_{B}(n^∗)−C^{wα}_{B}(n_i)}}$

where

$C^wα_{B}(n^∗)$ is the largest value of the betweenness centrality that occurs across the network

$G$ ; that is,

$C_{B}^{w \alpha}\left(n^{*}\right)=\max _{i} C_{B}^{w \alpha}\left(n_{i}\right)$ .

In the case of a directed network, two additional degree indices are defined: in-degree, or the number of links terminating at the actor

$(k^{in}_{n_i})$ , and out-degree, or the number of ties originating from the actor

$(k^{out}_{n_i)}$ . In-degree centralization (IDC) calculates the dispersion of or variation in in-degree centrality, and the extent of an individual actor's influence on other actors; thus, high IDC indicates the incoming flows of different network resources are focused on a small group of actors in the overall network. In the same sense, high out-degree centralization (ODC) indicates that a small number of actors send out most of the network resources to the rest of the network actors. This study derives IDC and ODC of a supply network from in-degree centrality (

$C^{wα}_{D-in}(n_i)$ ) and out-degree centrality (

$C^{wα}_{D-out}(n_i)$ ) for actor ni of a directed valued network using the following equations:

$C^{wα}_{D-in}(n_i)=k^{in}_{n_i}×(\dfrac{s^{in}_{n_i}}{k^{in}n_i})^α$

$C^{wα}_{D-out}(n_i)=k^{out}_{n_i}×(\dfrac{s^{out}_{n_i}}{k^{out}_{n_i}})^α$

where

$s^{in}$ and

$s_{out}$ are the total strengths attached to the incoming and outgoing ties, respectively. Therefore, the general IDC and ODC ranging from 0 to 1 are respectively defined as:

$C_{D-in}=\dfrac{∑_{i∈G}{C^{wα}_{D-i_n}(n^∗)−C^{wα}_{D-in}(n_i)}}{max∑_{i∈G}{C^{wα}_{D-in}(n^∗)−C^{wα}_{D-in}(n_i)}}$

$C_{D-out}=\dfrac{∑_{i∈G}{C^{wα}_{D-out}(n^∗)−C^{wα}_{D-out}(n_i)}}{max∑_{i∈G}{C^{wα}_{D-out}(n^∗)−C^{wα}_{D-out}(n_i)}}$

where

$C^{wα}_{D-in}(n^∗)$ and

$C^{wα}_{D-out}(n^∗)$ are the largest in-degree and out-degree centrality values in the network

$G$ .

Lastly, this study uses a global clustering coefficient (GCC) varying from 0 to 1 to measure the overall level of cohesion among network actors. In social network terms, this indicates the probability that network actors

$n_j$ and

$n_k$ are also connected to each other when

$n_i$ is connected to both of them, collectively represented as

$(n_i;n_j,n_k)$ . In a directed valued network setting, this socio-centric index is defined as the total value of closed triplets (i.e., triples of network actors where each actor is connected to the other two;

$τ_Δ$ ) divided by the total value of triplets (i.e., triples where at least one actor is connected to the other two;

$τ$ ). Triplet value (

$ω$ ) calculation is based on the geometric mean of the tie values for the nodes comprising the triplet in that it: (1) Captures differences between tie strengths, and (2) is robust to extreme tie strength. Thus, the general GCC (

$C_g$ ) can be formally stated as:

$C_g=\dfrac{1}{N}∑_{i,j,k∈G}\dfrac{{∑_{(ni;nj,nk)∈{τ_Δ}}ω_{τ_Δ}(ni;nj,nk)}}{{∑(_{ni;nj,nk)∈{τ}}ω_τ(ni;nj,nk)}}$

where

$N$ is the number of possible triplets in network G. Readers can refer to the recent study of Opsahl and Panzarasa for more details on this technique.

Because SNA indices have been developed and used within a sociological context, they cannot be directly applied and interpreted within an interfirm supply network context. Table 2, consequently, proposes a new framework for the supply network implications of the socio-centric SNA indices for directed valued networks used in this study for each of the four tie types previously defined in Table 1.