27th Annual INCOSE International Symposium (IS 2017) Adelaide, Australia, July 15-20, 2017
A Hybrid Approach for Supply Chain Analysis: An Application of Network and Cluster Analysis Li Qiao School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT, Australia, 2600 +61 2 62688639
[email protected]
Michael Ryan School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT, Australia, 2600 +61 2 62688200
[email protected]
Copyright © 2017 by Li Qiao and Michael Ryan. Published and used by INCOSE with permission .
Abstract. This study presents a quantitative method for investigating the network characteristics of supply chain management with the help of methodologies derived from the network analysis, which offers many techniques and indicators through measuring the links among nodes to demonstrate the structural patterns of connected systems. More precisely, this investigation derives the structural configuration of each function component within the supply chain by measuring the indicators of network analysis, including degree centrality, closeness centrality, betweenness centrality and PageRank centrality. This study empirically tests an example of supply chain taken from 22 functional organizations based on supply chain operations reference (SCOR) model. The results suggest the proposed method provides an appropriate understanding of each function organization in the supply chain model based on the structural characteristics relating to its network position on informational, material and functional flows. A number of recommendations are made regarding the role of importance be to understand based on the results of the network analysis.
Introduction In today’s global marketplace, the efficiency of supply chain management (SCM) is the key to survive in competitive markets. A supply chain is not only a chain but a complex network that involves many system components from various fundamental facilities (Srinivasan and Moon 1999). Lambert defines SCM as the “cross functional integration within the firm and across the network of firms that comprise the supply chain” (Lambert 2008). Therefore, a supply chain contains fundamental stages/groups such as plan, procurement, production and distribution where each facility has its detailed functional components, e.g. production consists of product design, individual parts processing, coordination etc. These functional components are dependent and cooperate with each other through material, information and/or functional flows in and between stages. Historically, the stages have been managed independently, ignoring the component dependencies between stages and making effective decisions locally (Thomas and Griffin 1996). However, this will have some costly consequences that become increasingly apparent with market globalization. Rather than de-coupling decisions, it is beneficial to consider all the functional components of all stages, in order to provide more systematic view of the supply chain, eventually provide better services to the customer. SCM exists for the management of various flows both in and between facilities (Thomas and Griffin 1996). The performance of a supply chain heavily depends on the effectiveness of communications and coordination among the chain’s functional components within the context of the process or process
being executed. Power stated that “recognition of the inter-dependence of all partners in a supply network appears to be an important precursor of effective integration”(Power 2005). Therefore, it is vital to explore the interactions between the functional components, as these interactions are critical in explaining why inter-organizational networks are formed, disintegrate, and succeed or fail. If we consider each functional component as a setting comprising resource such as personnel, ideally every functional component in the supply chain network should be configured with appropriate resources according to the network characteristics relating to its location respects to the entire supply chain network on various interactions (e.g. the entrance of the network). Due to the increasing size of supply chain, the supply chain network may comprise more functional components and each component in a network may become more and more complex and interrelated (Surana, Kumara et al. 2005). The failure of a functional component may lead to the fragility of the whole supply chain network. Therefore, each component should assign optimal and appropriate resources that ensure every functional component works well accordingly ensure the healthiness of the entire supply chain network. In order to improve the efficiency of SCM, it is necessary to obtain more insights into the supply networks. Specifically, how influential are specific functional components in a supply chain network, and what is relative importance of each function element in the network? This paper argues that one practical method of answering the above questions is via an investigation of the characteristics of supply chain networks by applying network analysis. Network analysis has a well-developed set of methods for systematically studying social structures (Scott 2000). Although primarily developed for the study of social systems, the indicators and techniques of network analysis are highly suitable for application to examine the structural features of the functional components for supply chain management (Ahuja, Magnanti et al. 1993). To illustrate the effectiveness of network analysis, this study introduces the techniques and indicator of network analysis, which our preliminary research indicates may be appropriate for examining the structural characteristics of supply chain. Then to verify the proposed method, we conduct a case study of a supply chain network consisting of 22 functional components. The rest of the paper is organized as follows. Section 2 reviews the related work on supply chain network management and network based analysis methods. Section 3 introduces network analysis techniques and a set of indicators we believe that are appropriate for supply chain application. Section 4 presents the results with colour-coded graphs using an example of supply chain network. Finally, Section 5 briefly discusses our conclusion and plans for future work.
Supply Chain Management A supply chain is defined as a set of three or more entities (organizations or individuals) directly involved in the upstream and downstream flows of products, services, finances, and/or information from a source to a customer (Mentzer, DeWitt et al. 2001). With the current development of supply chain and the increasing complexity in supply chain network, researchers realized the need to study the interaction of more dimensions of supply chain from a more systematic perspective (Chen and Huang 2007). An important current trend in supply chain modelling focuses on adding dimensions. stages or levels rather than discrete business functions (Min and Zhou 2002). For instance, a supply chain network may contains critical enterprises, distributors, retailers, as well as primary suppliers and secondary suppliers. From the functional point of view, the traditional supply chain has three fundamental stages that are procurement, production and distribution (Thomas and Griffin 1996). The new model includes more dimension of the logistics stages: e.g. the supply chain operations reference (SCOR) model released by supply chain council (SCC) has four distinct processes that are source, make, deliver and plan (Huan, Sheoran et al. 2004). The SCOR model is firmly rooted in industrial practices and is widely acknowledged as the quasi-industry standard for SCM (Georgise, Thoben et al. 2012). In addition to having more stages, SCOR model contains three levels of process details. Level 1 is top level that deals with process types; Level 2 is the configuration level and deals with process categories; Level 3 is process element level and is the lowest level in the scope of the model.
SCOR model can support the SCM operational, design and strategic research (Huan, Sheoran et al. 2004) SCM emphasize a systems approach to viewing the supply chain as a single entity, rather than as a set of fragmented parts (Mentzer, DeWitt et al. 2001). Accordingly, the quantity of data and the complexity can challenge the formulation of the supply chain problem. Thus, the research community has spent effort on modelling supply chain network and systematic approaches for SCM. Defee reviewed literatures in SCM research and found the vast majority of theories used in recent logistics and SCM research originated in other disciplines (Defee, Williams et al. 2010). Among various methods that are available for modelling and management of supply chain systems, social network analysis methods are considered useful (Borgatti and Li 2009). Stefan et al. noted that a supply chain can be viewed as a social network comprising interrelated organisations whose success depends on the systematic integration of business processes and collaborative performance of supply chain entities (Stefan Schaltegger, Varsei et al. 2014). Network analysis draws on theories from the social, organizational, and complexity sciences and leverages graph theoretic methods to model, analyse, and visualize the structure, dynamics and strategies that shape supply chain (Carter, Ellram et al. 2007, Bellamy and Basole 2013). Many papers have demonstrated the applicability of network analysis to a wide variety of supply chain problems. Carter proved network analysis are effective tools to capture the structural characteristics of supply chain (Carter, Ellram et al. 2007). Borgatti provides an overview of network analysis and its potential network mechanisms and properties that can be implemented by supply chain researchers (Borgatti and Li 2009). Scholz-Reiter proposed the application of the PageRank algorithm for ranking locations of a production network (Scholz-Reiter, Wirth et al. 2009). Bernardes explored factors associated with the relational embeddedness of social capital from a social network perspective (Bernardes 2010). Kim demonstrated network application to investigate buyers and suppliers in the context of supply chain (Kim, Choi et al. 2011). It can be seen that there is rapidly growing interest in the application of network analysis on the supply chain problems. This study aims to illustrate the value in adopting the network lens to better understand, plan and design the supply chain. The supply chain is constructed using SCOR model, which consists of business processes. In addition, cluster analysis is employed to help classify the functional elements according to the network analysis results, in particularly, the indicator of network such as various centralities. The practical implication of the study is that, appropriate resources coordinated among these various functional components in terms of their network features should be allocated by each department/stage ensure the efficiency of the entire supply chain.
Network Analysis Network analysis, derived from graph theory, attempts to describe the structure of links between given nodes, and applies quantitative techniques to produce relevant indicators and results for studying the characteristics of a whole network and the position of individuals in the network structure (Granovetter, Wellman et al. 1994). Network analysis has been applied to many domains such as anthropology, biology, economics, social psychology (Scott 2000, Knoke and Yang 2008). The supply chain system under the background of global economic integration has a characteristic of complex network. There is growing recognition by the supply chain community of the significant benefits a network analytic lens can provide to understand, design, and manage supply chain systems (Bellamy and Basole 2013). Galaskiewicz et al. proposed that supply chain management problems are especially fruitful for study from a network perspective (Galaskiewicz 2011). Network analysis was applied to improve knowledge management in supply chains (Capó-Vicedo, Mula et al. 2011), to reveal invulnerability mechanism of supply chain network (Li 2014), to investigate the structural characteristics of supply networks with key social network analysis metric (Kim, Choi et al. 2011)
One main network analysis in this study is the identification of the “important” nodes in the network. The most prominent nodes generally occupy strategic locations within a network. One possible reflection of importance is indicators of centrality which idea comes from social networks literature (Scott 2000). Centrality deals with the roles of individuals in a network. The presumption is that nodes or edges that are (in some sense) in the middle of a network are important for the network’s function. The idea is to use the centrality of individuals in their network to acquire the positional features of individual nodes within networks. The study is empirically based; not attempt to include a comprehensive set of network analysis methods but rather, focused on a number of applicable indicators. In this study, we apply classic importance measures of degree centrality, closeness centrality, betweenness centrality and PageRank to the supply chain network.
Notation for Graphs and Matrices Mathematically, a network is marked as a directed graph 𝐺 = (𝑉, 𝐸), with vertices 𝑉 = {1, ⋯ , 𝑛}, and edges 𝐸, where 𝐸 is a subset of 𝑉 × 𝑉. For example, a simple case (in Figure 1 a)) is shown for a network with four components. Based on the graph, the asymmetric matrix of this network (see Figure 1 b)) can be built, where the rows and columns index elements in the graph. In the matrix, if there is a directed flow from 𝑖 to 𝑗, there is a positive integer in the (𝑖, 𝑗)𝑡ℎ cell (row 𝑖, column 𝑗), and a 0 in the cell otherwise. The value in the matrix or the weight of the edge, presents the strengths of interactions such as frequency, effect or magnitude of dependencies. The notion of the weight can be defined flexibly according to the target problem. Each interaction is assigned a strength ranging (e.g. from 0 to 10) by managers and/or experts based on their experience and expertise of the related elements. The scaling values in Figure 2 help managers and experts to determine the ratings. A strong interaction is considered important or critical between the two-related components, while a weak interaction may be considered optional. The benefit of matrix is that matrix can handle large networks through the application of mathematical and computer tools to locate and summarize patterns. In contrast, when a large number of destinations exist, graphs may become visually complex to the point that pattern discernment becomes difficult.
①②③④ ① 0 0 4 ② 2 0 0 0 ③ 3 2 0 0 ④ 0 0 1 0 a) Network graph
b) Network adjacency matrix
Figure 1. A simple graph and matrix
Figure 2. Scales for determine the interaction strength
We next present the indicators and techniques of network analysis that are appropriate for examining the network characteristics of elements. The word "importance" has a wide number of meanings, leading to many different definitions of centrality. In this study, six centralities are opted to measure the importance of nodes: in- and out-degree centrality, in- and out-closeness centrality and betweenness centrality, as well as PageRank. The brief introduction of the centralities is given as follows.
Degree Centrality Degree centrality, proposed by Freeman (Freeman, Roeder et al. 1979), is the simplest and most intuitive. It measures the centrality of an individual in terms of the number of nodes to which a particular node connects. A node with high degree centrality may function as a leader in the network. In directed networks, degree centrality can distinguish between the in-degree (dependence) and the out-degree(conductivity) of each node respectively (Knoke and Burt 1983). The in-degree centrality and out-degree centrality of a given node are formally defined as 𝑛
𝐶𝐷𝑒𝑔𝑟𝑒𝑒,𝑖𝑛 (𝑉𝑖 ) = ∑ 𝑟𝑖𝑗,𝑖𝑛
(1)
𝑗=1 𝑛
𝐶𝐷𝑒𝑔𝑟𝑒𝑒,𝑜𝑢𝑡 (𝑉𝑖 ) = ∑ 𝑟𝑖𝑗,𝑜𝑢𝑡
(2)
𝑗=1
where 𝑟𝑖𝑛 and 𝑟𝑜𝑢𝑡 denote one of the inward and outward connections of node 𝑖, and 𝑛 is the number of nodes within the network. In-degree centrality of a node 𝑖 is the sum of the number of nodes 𝑗 in the network 1 to 𝑛 that connect inwardly from node 𝑗 to node 𝑖; out-degree centrality of a node 𝑖 is the sum of the number of nodes 𝑗 in the network that connect outwardly from node 𝑖 to node 𝑗.
Closeness Centrality Closeness, proposed by Freeman(Freeman, Roeder et al. 1979), is based on distance or path length. The measure focuses on how close a node is to all the other nodes in the set of nodes(Wasserman and Faust 1994). This is a global measurement that brings into play the closeness to all network members, not just connections to immediate neighbours as in degree centrality (Degenne and Forsé1999). It measures how easily accessible the node is to all other nodes in the graph. The closeness centrality of a node is defined as 𝐶𝐶𝑙𝑜𝑠𝑒𝑛𝑒𝑠𝑠 (𝑉𝑖 ) =
1 ∑𝑛𝑗=1 𝑑(𝑉𝑖 , 𝑉𝑗 )
(3)
where 𝑑(𝑉𝑖 , 𝑉𝑗 ) is defined as the length of the shortest path between node 𝑖 and 𝑗. Closeness centrality of a node 𝑖 is the inverse of the sum of the distances from node 𝑖 to all the other nodes in the network (1 to 𝑛). In a directed network, closeness centrality can be seen in terms of what might be termed ‘‘incloseness’’ and ‘‘out-closeness’’, respectively, but both formulas are the same as Equation (3). This indicator reflects the idea that a node is central if it can quickly interact with all other nodes based on inward and outward connections. A node that has high closeness centrality is likely to receive information/infections more quickly than other nodes.
Betweenness Betweenness measures the extent to which a particular node lies between the various other nodes in the set of nodes (Freeman, Roeder et al. 1979). Betweenness centrality is another global measurement that elaborates the ability of a given node to control interactions between pairs of other nodes in the network. If the quickest way between any two nodes on a network disproportionately involves certain nodes, then they are ‘important’ in terms of global cohesion. A node with high betweenness may be
a “key players” in the network. Nodes with high betweenness are structurally important to the economy itself, because if they disappear or slow production, they will affect more other nodes than if they had lower betweenness(Borgatti and Li 2009). The betweenness centrality of a node is defined as 𝑙
𝑙
𝐶𝐵𝑒𝑡𝑤𝑒𝑒𝑛𝑛𝑒𝑠𝑠 (𝑉𝑖 ) = ∑ ∑ 𝑗
𝑘
𝑔𝑗𝑘 (𝑉𝑖 ) 𝑔𝑗𝑘
𝑗≠𝑘≠𝑖
(4)
Where 𝑔𝑗𝑘 denotes the number of distance between node 𝑗 and 𝑘, and 𝑔𝑗𝑘 (𝑉𝑖 ) denotes the number of short distance linking the two nodes that contain node 𝑖. Betweenness centrality of a node 𝑖 is the sum of the node 𝑖’s estimated probabilities of standing along any distance that all pairs of nodes (nodes 𝑗 and 𝑘, excluding node 𝑖) in the network have selected. The betweenness of a node measures the extent to which it can play the role of a broker or gatekeeper with a potential for control over others. A particular node with high betweenness centrality means that it is a highly critical intermediary between pairs of other nodes, since most flows will pass through this node while traveling between other various nodes. Betweenness centrality is an appropriate indicator for measuring the extent to which nodes broker indirect connections between all other nodes in a network.
PageRank PageRank is named after Larry Page, its inventor. RageRank associates a numerical value to every web page to represent its relative importance within the Internet. The objective is to assign a numerical rank for priority to each web page by exploiting the link structure of the web (Getoor and Diehl 2005). PageRank estimates a page’s authority by taking into account the link structure of the web. Thus, PageRank is an enhanced version of in-degree centrality. When one vertex links to another, it casts a vote for that other vertex. The higher the number of votes that are cast for a vertex, the higher the importance of the vertex. Moreover, the importance of the vertex casting the vote determines how important the vote itself is, and this information is taken into account by the ranking model. Hence, the score associated with a vertex is determined based on the votes that are cast for it, and the score of the vertices casting these votes. The PageRank Centrality is defined as (Langville and Meyer 2004) 𝐶𝑃𝑎𝑔𝑒𝑅𝑎𝑛𝑘 (𝑉𝑖 ) = (1 − 𝑑) + 𝑑 × ∑ 𝑗∈𝐼𝑛(𝑉𝑖 )
𝐶𝑃𝑎𝑔𝑒𝑅𝑎𝑛𝑘 (𝑉𝑗 ) |𝑟𝑖𝑗,𝑜𝑢𝑡 |
(5)
Where 𝑑 is a damping factor that can be set between 0 and 1. Starting from arbitrary values assigned to each node in the graph, the PageRank computation iterates until convergence below a given threshold is achieved. PageRank is employed there to find which function has the most votes from the rest of the network.
Cluster Analysis with Centralities Overall, the centralities were strongly correlated (Bolland 1988). When they are not or weakly correlated, there is likely something interesting about the network. For instance, nodes with high betweenness and low degree are crucial for network flow. We employ cluster analysis to classify the nodes according to their centrality scores. Specifically, given two centrality values, Centrality A and B, we group the nodes to four clusters using k-means clustering algorithm. The resulting four groups are nodes with high A and high B, high A and low B, low A and high B, low A and low B, respectively. To display the results, we plot the four cluster regions with different colours. Cluster analysis has been defined as the application of techniques that partition a set of objects into two or more groups based on the similarity of the objects for a set of specified characteristics (Romesburg 1990, Kaufman and Rousseeuw 2009). Methods of cluster analysis fall into two main
groups: hierarchical and partitioning(Jain 2010). K-means is the simplest partitioning algorithm. Mathematically, it takes as input a set of 𝑛 objects 𝑆 and an integer 𝑘 (the number of clusters), and output a partition of 𝑆. The resulting partitions are represented as a set of subsets 𝑆 = 𝑆1 , ⋯ , 𝑆𝑘 such that 𝑆 = ⋃𝑘𝑖 𝑆𝑖 and 𝑆𝑖 ⋂ 𝑆𝑗 = ∅ for 𝑖 ≠ 𝑗. It starts with 𝑘 initial seeds of clustering, where 𝑘 is chosen a priori. All the 𝑛 objects are compared with each seed by a measure of distance such as Euclidean, and are assigned to the closest cluster seed. The procedure is then repeated, using the sum of squares of distances as the optimization criterion. Let 𝑥𝑟𝑖 be the rth element of 𝑆𝑖 , |𝑆𝑖 | be the number of elements in 𝑆𝑖 , and 𝑑(𝑥𝑟𝑖 , 𝑥𝑠𝑖 ) be the distance between 𝑥𝑟𝑖 and 𝑥𝑠𝑖 . In particular, k-means works by calculating the centroid of each cluster 𝑆𝑖 , denoted 𝑥̅ 𝑖 , and optimizing the function 𝑐(𝑆𝑖 ) = |𝑆𝑖 | ∑𝑟=1 𝑑(𝑥𝑟𝑖 , 𝑥𝑠𝑖 ) 2 . The goal of the algorithm is to minimize the objective function 𝑐(𝑆1 ) + ⋯ + 𝑐(𝑆𝑘 ). The algorithm stops when the changes in the cluster seeds from one stage to the next are smaller than a pre-specified value. Clustering membership is determined by calculating the centroid for each group and assigning each object to the group with the closest centroid. For more details about k-means refer to (Everitt 1977, Hartigan and Wong 1979).
Study Case We use the supply chain network example from (Chen and Huang 2007). The example is a functional structure constructed with SCOR models. In this example (illustrated in Figure 3), there are 22 functional components spread across seven stages. Each stage has several sub-level functional components, e.g. the Plan has three components: 1) Business Strategy, 2) Resource Allocation and 3) Coordination and Communication.
Figure 3 Supply chain structure
The system components interact within each other to facilitate the flows. Three important types of flows are accounted in the example: information, material and functional. Information interactions specify customer needs, pricing information, system status, and/or other information that is required to maintain the functionality of a supply chain element. Material interactions are the physical flows and processes from raw materials to finished parts/products.
Functional interactions are the communication and coordination flows among different functional departments (e.g., to determine or change task due date, supplier, quality requirements, product design, material usage or other specifications). Functional interactions can be as general as setting a strategic goal for business or as detailed as making a slight change to product design.
The value of the weight, i.e. the correspondent adjacency matrix of the supply chain network, is originally taken from of Figure 7 of (Chen and Huang 2007). The new adjacency matrix is developed from the original matrix, with each value being ten times the corresponding values in the original one. According to the new matrix, the corresponding network graph is shown in Figure 4. This graph is a preliminary visual evaluation of the entire network, where the nodes represent the 22 functional components and 87 arcs directed between pairs of nodes represent the directional flow between elements. The edges are labelled with the weights and the width of the edges are proportional to the weights.
Results and Discussion The indicators of network analysis for the 22 functional components are calculated by Matlab Graph and Network Algorithms toolbox, shown in Table 1. Since the data of different centralities are on a very different scale, the data are scaled for easy comparison of the distribution. The scaled data are centred to have mean 0 and standard deviation 1. The data distribution is presented in Figure 5. We can see that the distribution of the nodes is not even which suggests the existence of something interesting. Degree centrality identifies the critical and non-critical nodes. The node with higher out-degree is more central/conductive, and the node with higher in-degree is more prestigious/dependent. The indegree and out-degree of 22 nodes are illustrated in Figure 6 and Figure 7, respectively. We highlight the node with maximum value with biggest size node. Seen from Figure 6, Node 9 (Produce Subsystem coordination) has the highest in-degree, which suggests it receives the most choices and gets the most support from other nodes. Node 4 (Source Delivery scheduling), 5 (Source Supplier Selection), 10 (Produce WIP/FG Inventory Management), 8 (Produce Individual Parts Processing), 11 (Warehouse Capacity and Operation) also have high in-degree. These nodes belong to Source, Produce and Warehouse stages. Seen from Figure 7, Node 2 (Plan Resource Allocation) is the highest out-degree node, which implies it plays the role of choice maker. From another perspective, a highest degree indicates the most vulnerable nodes, as its failure will inactivate the maximum number of links, such as Node 2 and 9. Information alignment and sharing are proper for these high degree nodes. Comparing the in-degree and out-degree of each node (shown in Figure 8) reveals nodes that function as beginning or terminal node, respectively. Node 1(Plan Business Strategy) is low in-degree but high out-degree, which means Node 1 is the typical beginning nodes of the entire network. The beginning nodes should be provided with appropriate introductory resources, such as sales related information (e.g. customer survey, market investigation) for making right business strategy. Node 9 (Subsystem coordination) is low out-degree and high in-degree, which is typical terminal node.
Figure 4 Network graph for the supply chain functional structure with 22 nodes
Table 1: Centrality values of the supply chain network Components Degree
Closeness
Betweenness PageRank
In-degree Out-degree In-closeness Out-closeness 1
4.0
57.4
0.0073
0.0087
104.0
0.0255
2
10.0
94.7
0.0056
0.0115
85.0
0.0221
3
10.0
20.3
0.0078
0.0068
26.0
0.0190
4
28.0
20.4
0.0056
0.0055
6.0
0.0832
5
25.0
10.0
0.0065
0.0069
10.5
0.0677
6
22.0
14.0
0.0029
0.0047
0
0.0434
7
15.0
21.5
0.0060
0.0094
96.0
0.0623
8
23.4
12.0
0.0057
0.0086
83.0
0.1189
9
32.6
5.0
0.0040
0.0046
0
0.0547
10
23.7
20.1
0.0040
0.0101
5.5
0.0482
11
23.4
15.0
0.0055
0.0053
15.0
0.0644
12
17.8
5.50
0.0068
0.0090
79.0
0.0527
13
15.0
5.4
0.0054
0.0055
3.5
0.0522
14
20.0
20.3
0.0057
0.0106
71.0
0.0466
15
15.3
11.7
0.0037
0.0106
1.0
0.0190
16
13.0
3.0
0.0059
0.0040
25.0
0.0420
17
11.0
0.0
0.0076
0
0
0.0285
18
11.0
22.5
0.0075
0.0012
0
0.0285
19
16.6
5.0
0.0075
0.0005
16.0
0.0366
20
15.0
0.0
0.0042
0
0
0.0499
21
5.0
9.0
0.0037
0.0003
0
0.0124
22
16.0
0.0
0.0030
0
0
0.0222
Mean
16.9
16.9
0.0055
0.0056
28.5
0.0454
STD
7.3
21.3
0.0015
0.0039
37.5
0.0247
Min
4
0
0.0029
0.0000
0.0
0.0124
96.7
0.0078
0.0114
104.0
0.1189
Max 32.6 STD: Standard deviation
Figure 5 Different centralities distribution
Figure 6 In-degree centrality
Figure 7 Out-degree centrality
Figure 8 In-degree vs. Out-degree
The betweenness centrality measures the extent to which a node lies on the paths between others. It measures how much flow will pass through that particular node indicating the node’s prominence according to its position in the network. The rating of betweenness ranges between 0 and 104, causing deviation (37.5) exceeding their mean (28.5). Thus, considerable variation exists in the betweenness of this network. In Figure 9, Node 1 (Plan Business strategy), 2 (Plan Resource Allocation), 7 (Produce Production design), 8 (Produce Individual parts processing), 12 (Warehouse Procurement), and 14 (Warehouse capacity and Operation) have high betweenness, acting as critical intermediates. Services to control the flows are appropriate for these nodes. For instance, advanced planning modes are needed for Node 1.In addition, as they have the potential to influence others near them, through both direct and indirect pathways, these intermediates need resources that can mitigate the negative influence happed in these intermediates. For instance, a dissatisfaction of customers called “warehouse explosion”(Yao and Gu 2015) in which a company’s ability to handle logistics cannot keep up with its customers’ orders is possible to happen in Node 12 and 14. Therefore, mitigating warehouse explosion related service should be placed here. Compare the betweenness with in-degree in Figure 10 and out-degree in Figure 11, respectively. The nodes with high betweenness and low degree mean their few ties are crucial for network flow. These nodes are Node 1, 2, 7, 8, 12, 14, belong to Plan, Produce and Warehouse stages.
Figure 9 Betweenness centrality
Figure 10 Betweenness vs. In-degree
Figure 11 Betweenness vs. out-degree
Figure 12 In-closeness centrality
Figure 13 Out-closeness centrality
Figure 14. In-closeness vs. in-degree
Figure 15. Out-closeness vs. in-degree
Figure 16 PageRank centrality
Assessing the indicators of in-closeness (in Figure 12) and out-closeness (in Figure 13) scores reveals the extent to which a particular node is reachable from and to other nodes, respectively. Think of closeness in terms of a node’s ability to spread energy to all other nodes in a network (Russell 2013). Figure 12, Node 3 (Plan Coordination & Communication) has the highest in-closeness. Node 17 (Order Quotes), 18 (Order Processing Orders), and 19 (Order Back Orders) also have high incloseness, and all of them belongs to Order Department. They are so accessible and popular that many flows always include these nodes. The resources that can improve the responsiveness of the supply chain to meet the customers’ requirement are proper for these nodes. For instance, regarding the three Order stage nodes, build-to-order strategy had success of its implementation in Dell Computers, BMU and Compaq (Gunasekaran and Ngai 2005). As for out-closeness centrality (in Figure 13), Node 2 (Plan Resource Allocation) has the highest rating which means it is a gateway in the network. Node 15 (Deliver Distribution channel), 14 (Warehouse Capacity and Operation), 10 (Produce WIP/FG Inventory Management) also have high out-closeness. Resources to facilitate the downstream flows are proper for these nodes, such as advanced warehouse operation systems for Node 14. Nodes with high closeness and low degree, normally are key players tied to important nodes. We compare in-closeness and out-closeness with in-degree in Figure 14 and Figure 15, respectively. The nodes in top left region are high closeness and low degree. These nodes are Node 1, 2, 3 belong to Plan; Node 17, 18 and 19 belong to Order. Node 6 (Source Inventory Management) is low incloseness and high in-degree, which means it is far from the rest of the network. If the designers plan to increase the importance of inventory management, they must check and adjust the flows connected to Node 6. This node brings the opportunities for improvement. For instance, we can develop new inventory management models to increase the network competitiveness. Consider the nodes whose degree (in Figure 6 and Figure 7), betweenness (Figure 9), and closeness (Figure 12 and Figure 13) scores are low, such as Node 20 (Order Invoice), 21 (Return Receive and Verify), 22 (Return Defective Rework/Dispose), 17 (Order Quotes), 18 (Order Processing orders). They have few connections with adjacent nodes, are relatively inaccessible, and act less as intermediates between other nodes due to being located near the border of the network. The position of border provides opportunities to bring potentially valuable information from outside the network. These nodes belong to Order and Return stages, which connect to real customers; consequently, it is proper to develop promotion-related information in these border nodes. For example, for Node 20 (Order Invoice), information such as “goods that you might be also interested” should be put here to attract the customers return to the network again. The distribution of PageRank is depicted in Figure 16. Nodes that have high in-degrees tend to have high PageRank values, as well as nodes that are linked to by other nodes with high PageRank values.
In our example, Node 9 (Produce Subsystem coordination) has the highest in-degree, and Node 8 (Produce Individual Parts Processing) has the highest PageRank centrality. In addition, Node 4 (Source Delivery Scheduling) and 5 (Source Supply Selection) have high PageRank centrality. Node 8 and 9 belong to Produce strategy and Node 4 and 5 belong to Source strategy, as these two strategies are vital for high quality product. Nodes with high PageRank scores are most frequently crossed in the network, thus customer fulfilment related resources are proper here. Based on the analysis results of the example network constructed with SCOR model, Table 2 summarise the network characteristics, its interpretation, resources recommendations as well as some example nodes (functional components).
Table 2: Network characteristics, interpretation, resources recommendations and example nodes Network characteristics
Network interpretation Resource recommendations
High in-degree
Prestigious/dependent, Upstream information alignment 9, 4, 5,10,8,11 critical and vulnerable and sharing service
High out-degree
Conductive, critical Downstream information 2, 1,18,7 and vulnerable alignment and sharing service
High out-degree, A beginning low in-degree High in-closeness
High closeness
Introductory resources, such as 1 sales oriented information
Highly accessible Regulation to improve the access 3,17,19,18,1 from all other nodes efficiency, such as new coordination and communication model
out- Highly accessible to Resources to facilitate all other nodes, downstream flows outbound, gateway
High betweenness
Example nodes
Critical intermediate
the 2,15,14,10,7,12,
Service to control the flows 1,7,2,8,12,14 across the network Service to effects
mitigate
negative
Low closeness, Far from the rest of the Opportunities for improvement high in-degree network
6
Low degree, low Border closeness, low betweenness
Promotion-related information
20,21,22,17,18
High PageRank
Customer fulfilment information
Influential nodes
related 8,4,5,11,7,9
Conclusions and Future Work The one, who can better understand the network, may be able to develop meaningful ways to enhance it. Therefore, a systematic and analytical tool is needed to gain important insights into the supply chain network. As the supply chain network becomes increasingly larger and complex, it may be important to understand what network structure characteristics of network, for better planning where to locate resources such as what kind of services to promote. A growing number of firms have begun to realize the strategic importance of planning, controlling and designing a supply chain a s whole (Min and Zhou 2002). SCOR model can support the supply chain management operational, design and strategic research as it integrates a complete business process from various stages such as plan, source, produce, etc. Thus, we used the supply chain network example constructed with SCOR model as a case study in this paper. This case study offers offered an illustration of this investigation with the help of network analysis based data mining. Network analysis employs graphs and matrices to show the flows among components. The advantage of network analysis is that it offers numerous techniques and indicators by measuring the importance of nodes to demonstrate the structural patterns of connected network. Each functional possesses development opportunities and constraints resulting from the influence of other functional components in the network. The practical implication of the study is that this network analysis would assist the supply chain planners to make decision such as locating resources in the following steps. First, the structural characteristic of network could be examined by measuring the structural configuration of each node depending on various centrality scores of network analysis. Second, clustering the nodes according to the centrality scores obtained, and then finds the nodes which indicators are not positively correlated. Table 2 lists the network characteristics, its interpretation and resource recommendations. In industry, we can use these to build a catalogue of behaviours, which would serve as a guide for resource allocation for different business processes. This is one of the future work of this paper. The future work also consists of sensitivity analysis, for instance, what is the effect on the SCM performance if we adjust the weights of flows. In addition, our current discussion focus on the supply chain architecture in the functional process domain. The future work is to investigate the numerical mapping from functional process domain to other domains such as organization/personnel or activities.
References Ahuja, R. K., T. L. Magnanti and J. B. Orlin, 1993. Network flows: theory, algorithms, and applications. Upper Saddle River, New Jersey: Prentice Hall. Upper Saddle River, New Jersey. Bellamy, M. A. and R. C. Basole, 2013. Network analysis of supply chain systems: A systematic review and future research. Systems Engineering, 16(2), 235-249. Bernardes, E. S., 2010. The effect of supply management on aspects of social capital and the impact on performance: A social network perspective. Journal of Supply Chain Management, 46(1), 45-55. Bolland, J. M., 1988. Sorting out centrality: An analysis of the performance of four centrality models in real and simulated networks. Social networks, 10(3), 233-253. Borgatti, S. P. and X. Li, 2009. On social network analysis in a supply chain context. Journal of Supply Chain Management, 45(2), 5-22. Capó-Vicedo, J., J. Mula and J. Capó, 2011. A social network-based organizational model for improving knowledge management in supply chains. Supply Chain Management: An International Journal, 16(4), 284-293. Carter, C. R., L. M. Ellram and W. Tate, 2007. The use of social network analysis in logistics research. Journal of Business Logistics, 28(1), 137-168.
Chen, S.-J. G. and E. Huang, 2007. A systematic approach for supply chain improvement using design structure matrix. Journal of Intelligent Manufacturing, 18(2), 285-299. Defee, C., B. Williams, W. S. Randall and R. Thomas, 2010. An inventory of theory in logistics and SCM research. The International Journal of Logistics Management, 21(3), 404-489. Degenne, A. and M. Forsé, 1999. Introducing social networks. London, UK: Sage Publications. London, UK. Everitt, B., 1977. Cluster analysis. London: Heinemann Educ. Books Ltd. London. Freeman, L. C., D. Roeder and R. R. Mulholland, 1979. Centrality in social networks: II. Experimental results. Social networks, 2(2), 119-141. Galaskiewicz, J., 2011. Studying supply chains from a social network perspective. Journal of Supply Chain Management, 47(1), 4-8. Georgise, F. B., K.-D. Thoben and M. Seifert, 2012. Adapting the SCOR model to suit the different scenarios: a literature review & research agenda. International Journal of Business and Management, 7(6), 2-17. Getoor, L. and C. P. Diehl, 2005. Link mining: a survey. ACM SIGKDD Explorations Newsletter, 7(2), 3-12. Granovetter, M., B. Wellman, S. Berkowitz, R. L. Breiger, J. L. Campbell, J. R. Hollingsworth and L. N. Lindberg, 1994. Structural analysis in the social sciences. Cambrigde: Cambridge University. Gunasekaran, A. and E. W. Ngai, 2005. Build-to-order supply chain management: a literature review and framework for development. Journal of operations management, 23(5), 423-451. Hartigan, J. A. and M. A. Wong, 1979. Algorithm AS 136: A k-means clustering algorithm. Journal of the Royal Statistical Society. Series C (Applied Statistics), 28(1), 100-108. Huan, S. H., S. K. Sheoran and G. Wang, 2004. A review and analysis of supply chain operations reference (SCOR) model. Supply Chain Management: An International Journal, 9(1), 2329. Jain, A. K., 2010. Data clustering: 50 years beyond K-means. Pattern recognition letters, 31(8), 651-666. Kaufman, L. and P. J. Rousseeuw, 2009. Finding groups in data: an introduction to cluster analysis: John Wiley & Sons. Kim, Y., T. Y. Choi, T. Yan and K. Dooley, 2011. Structural investigation of supply networks: A social network analysis approach. Journal of Operations Management, 29(3), 194-211. Knoke, D. and R. S. Burt, 1983. Prominence. Applied network analysis, 195-222. Knoke, D. and S. Yang, 2008. Social network analysis: Sage. Lambert, D. M., 2008. Supply chain management: processes, partnerships, performance: Supply Chain Management Inst. Langville, A. N. and C. D. Meyer, 2004. Deeper inside pagerank. Internet Mathematics, 1(3), 335380. Li, Y., 2014. Networked Analysis Approach of Supply Chain Network. JNW, 9(3), 777-784. Mentzer, J. T., W. DeWitt, J. S. Keebler, S. Min, N. W. Nix, C. D. Smith and Z. G. Zacharia, 2001. Defining supply chain management. Journal of Business logistics, 22(2), 1-25. Min, H. and G. Zhou, 2002. Supply chain modeling: past, present and future. Computers & Industrial Engineering, 43(1–2), 231-249. Power, D., 2005. Supply chain management integration and implementation: a literature review. Supply chain management: an International journal, 10(4), 252-263. Romesburg, C., 1990. Cluster analysis for researchers. London: Robert E. Krieger. London. Russell, M. A., 2013. Mining the Social Web: Data Mining Facebook, Twitter, LinkedIn, Google+, GitHub, and More: " O'Reilly Media, Inc.". Scholz-Reiter, B., F. Wirth, S. Dashkovskiy, T. Makuschewitz, M. Kosmykov and M. Schönlein, 2009. Application of the PageRank algorithm for ranking locations of a production network. Proceedings of 42nd CIRP Conference on Manufacturing Systems, June 3-5, Grenoble, France.
Scott, J., 2000. Social network analysis: A handbook: Sage, London. Srinivasan, M. and Y. B. Moon, 1999. A comprehensive clustering algorithm for strategic analysis of supply chain networks. Computers & industrial engineering, 36(3), 615-633. Stefan Schaltegger, P. R. B., Dr, M. Varsei, C. Soosay, B. Fahimnia and J. Sarkis, 2014. Framing sustainability performance of supply chains with multidimensional indicators. Supply Chain Management: An International Journal, 19(3), 242-257. Surana, A., S. Kumara, M. Greaves and U. N. Raghavan, 2005. Supply-chain networks: a complex adaptive systems perspective. International Journal of Production Research, 43(20), 42354265. Thomas, D. J. and P. M. Griffin, 1996. Coordinated supply chain management. European journal of operational research, 94(1), 1-15. Wasserman, S. and K. Faust, 1994. Social network analysis: Methods and applications: Cambridge university press. Yao, J. and M. Gu, 2015. Optimization analysis of supply chain resource allocation in customized online shopping service mode. Mathematical Problems in Engineering, 2015.
Biography Dr Li Qiao is a researcher at the School of Engineering and Information Technology, University of New South Wales, Canberra, at the Australian Defence Force Academy. She received her B.E. in Electrical Engineering in 2004 and Ph.D. degree in Guidance, Navigation and Control engineering in 2011 from the Nanjing University of Aeronautics and Astronautics, Nanjing, China. Her research interests include spacecraft system engineering, autonomous orbit determination and control, and attitude determination and control. She is author of more than 40 journal papers, and refereed conference papers. Dr Mike Ryan is the Director of the Capability Systems Centre, University of New South Wales, Canberra. He holds Bachelor, Masters, and Doctor of Philosophy degrees in electrical engineering as well as a Graduate Diploma in Management Studies. He lectures and regularly consults in communications and information systems, systems engineering, requirements engineering, and project management. He is the conference chair of two annual international conferences, editor-in-chief of the Journal of Battlefield Technology, and chair of the Requirements Working Group in INCOSE. He is the author or co-author of eleven books, three book chapters, and over 160 technical papers and reports.
