Introduction
From complex systems theory to network science
Complex systems theory
Complex system characteristics of modern supply chain networks
Network modelling of supply chains
Basic network models
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Nodes are randomly connected to each other.
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Modelled using the Erdös-Rényi model (Erdȍs and Rényi, 1959).
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Most nodes are not neighbours of one another, but can be reached from every other node by a small number of steps.
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Modelled using the Watts–Strogatz model (Watts and Strogatz, 1998).
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The degree distribution follows power-law, at least asymptotically.
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Modelled using the Barabasi-Albert (BA) model (Barabási and Albert, 1999).
Modelling network topology
Fitness based network models
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Growth – At each time step, a new node j with m links and fitness ϕ j is added to the network. In generating an ensemble of networks, ϕ j is sampled from a fitness distribution. Once assigned, the fitness of a node remains constant.
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Preferential Attachment – the probability of a new node connecting to node i is proportional to the product of node i’s degree k i and its fitness ϕ i ;
Generating null models using configuration model
Network science approach to modelling the topology and robustness of SCNs
Modelling SCN topologies through growth models
Limitation | SCN modelling implication |
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Does not account for internal link formations (Barabasi, 2014) | In a SCN, new links may not only arrive with new firms but can be created between the pre-existing firms. |
Cannot account for node deletion (Barabasi, 2014) | Firms may exit a given SCN over time. |
An isolated node is unable to acquire any links since according to preferential attachment, the probability of a new node connecting to an isolated node is strictly zero (since the connection probability is governed by the existing number of connections). | In reality, any firm has a certain level of initial attractiveness. |
Assumes that all firms within the supply network are homogeneous in nature with no differentiation other than the topological aspects (Hearnshaw and Wilson, 2013). | Real SCNs include firms with high levels of heterogeneity beyond the number of dealings or connections with other firms. |
The key requirement of the preferential attachment rule is that every new node joining the network must possess complete and up-to-date information about the degrees of every existing node in the network. | Such information is unlikely to be readily available in a real world setting – for example, when considering a manufacturer for a new partnership, full information about the number of their current suppliers and clients is unlikely to be available (Smolyarenko, 2014). Therefore, an algorithm which relies on local information is deemed more suitable. For example, see Vázquez (2003). |
Network growth by preferential attachment produces a decaying clustering coefficient as the network expands. | May not be a realistic representation of exchange relationships and concentration of power in firms within the real SCNs (Hearnshaw and Wilson, 2013). |
Customised attachment Rule | Key features |
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Ad hoc attachment rules based on the military supply chain example, used by Thadakamalla et al. (2004) | Three types of nodes can enter the system in a pre-specified ratio. Each type of node has a specific number of links. Attachment rule depends on the type of node entering the system. The first link of a new node entering the system attaches to an existing node preferentially, based on the degree. The subsequent links, entering the system with each new node, attach randomly to a node at a pre-specified topological distance (also referred to as the ‘hop count’, which denotes the least number of links required to be traversed in order to reach a given node from another). |
Degree and Locality based Attachment (DLA), used by Zhao et al. (2011a). | A node entering the system considers both the degree and the distance of an existing node, when establishing connections. In particular, attachment preference for the first link arriving with each new node is calculated preferentially based on the degree of the existing nodes. If the node is allowed to initiate more than one link, the subsequent links will attach preferentially to existing nodes based on topological distance. Tunable parameters are used to control the responsiveness of attachment preference to both the degree and the topological distance. |
Randomised Local Rewiring (RLR), used by Zhao et al. (2011b) | This model is applied to an existing network, by iterating through all links and considering the nodes at either end of each link. With a predetermined rewiring probability, to control the extent of rewiring, each link will disconnect from the highest degree node it is currently connected with and reconnect with a randomly chosen node within a pre-specified maximum radius (which can either be geographical or topological). |
Start with a random network that consists of a pre-specified number of supply nodes with randomly assigned (x, y) coordinates. Supply and demand nodes are sequentially added to the system, according to a pre-specified supply-demand ratio. If the new node is a supply node, the first link will connect to an existing supply node in the system while other links are connected randomly to existing nodes. If the new node is a demand node, all links will connect with existing supply nodes in the system, with connection probability based on the product of degree and the geographical distance. Similar to DLA discussed above, tunable parameters are used to control the responsiveness of attachment preference to both the degree and the geographical distance. |
Concept of SCN robustness
Analytical measurements of SCN topological robustness
Using simulations to determine the topological robustness of SCNs
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Supply availability rate is represented as the percentage of demand nodes that have access to supplies from at least one supply node.
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The network connectivity is determined through the size of the largest functional sub-network (LFSN), namely the number of nodes in the LFSN in which there is a path between any pair of nodes and there exists at least one supply node.
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Accessibility is determined by;
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○ Average supply path lengths in the LFSN, i.e. the average shortest supply path length between all pairs of supply and demand nodes in the LFSN.
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○ Maximum supply path lengths in the LFSN, i.e. the maximum shortest path length between any pair of supply and demand nodes in the LFSN.
Empirical studies on SCN topologies
Study | Data source and SCNs considered | Key findings |
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Parhi (2008) | Customer-supplier linkage network in the Indian auto component industry has been considered (618 firms), using the data from the Auto Component Manufacturers Association of India. | The Indian auto component industry SCN was found to be scale free in topology, with a power-law exponent, γ = 2.52a. |
Keqiang et al. (2008) | Guangzhou automotive industry supply chain network has been investigated. Data has been collected from 94 manufacturers, between November 2007 and January 2008. | Guangzhou automotive industry SCN was found to be scale-free in topology. Based on the data presented by the authors, we have calculated the power-law exponent of the degree distribution, γ to be 2.02. |
Kim et al. (2011) | Three case studies of automotive supply networks (namely, Honda Accord, Acura CL/TL, and Daimler Chrysler Grand Cherokee) presented by Choi and Hong (2002). | This study has developed SCN constructs based on a number of key network and node level analysis metrics. In particular, the roles played by central firms, as identified by various network centrality measures, have been outlined in the context of SCNs. |
Büttner et al. (2013) | Present network analysis results for a pork supply chain of a producer community in Northern Germany. Data has been obtained by the producer community for a period of 3 years. | Reports that the degree distribution of the SCN follows power law (in and out degree distributions follow power-law with power-law exponents, γ = 1.50 and γ = 1.00, respectively). Disassortative mixingb has been observed in terms of node degree. |
Kito et al. (2014) | A SCN for Toyota has been constructed using the data available within an online database operated by Marklines Automotive Information Platform. | The authors have identified the tier structure of Toyota to be barrel-shaped, in contrast to the previously hypothesized pyramidal structure. Another fundamental observation reported in this study is that Toyota SCN topology was found to be not scale free. |
Brintrup et al. (2015) | Airbus SCN data obtained from Bloomberg database. | Reports that the Airbus SCN illustrates power-law degree distribution, i.e. scale free topology, with a power-law exponent, γ = 2.25a. Assortative mixing was observed based on node degree and community structures were found based on geographic locations of the firms. |
Gang et al. (2015) | Authors have investigated the urban SCN of agricultural products in mainland China. Data collection is based on author observations over 2 years. | The SCN of agricultural products was found to be scale free in topology, with a power-law exponent, γ = 2.75. High levels of disassortative mixingb has been observed in terms of node degree. |
Orenstein (2016) | SCN data for food (General Mills, Kellogg’s and Mondelez) and retail (Nike, Lowes and Home Depot) industries have been obtained from Bloomberg database. | The SCNs considered in this study were found to have scale free topologies with γ < 2. In particular, for the food industry SCNs for General Mills, Kellogg’s and Mondelez were found to have γ = 1.25, 1.47 and 1.56, respectively. For the retail industry, the SCNs for Nike, Lowes and Home Depot were found to have γ = 1.83, 1.73 and 1.67, respectively. |
Perera et al. (2016b) | Analysis has been undertaken for 26 SCNs (which include more than 100 firms) out of 38 multi echelon SCNs presented in Willems (2008) for various manufacturing sector industries. | 22 out of the 26 SCNs analysed display 80% or higher correlation with a power-law fit, with power-law exponent γ = 2.4 (on average). Furthermore, these SCNs were found to be highly modularb and robust against random failures. Also, disassortative mixingb was observed on these SCNs. |
Sun et al. (2017) | A GIS based SCN structure has been simulated for the automobile industry using the data of top twelve car brands of Chinese market in recent five years as basic parameters. | The Chinese automobile SCN simulated using real world data as basic parameters, indicates that the degree distribution conforms to the power-law, with a power-law exponent, γ = 3.32. |