- Research
- Open Access
Modeling topologically resilient supply chain networks
- Viplove Arora^{1}View ORCID ID profile and
- Mario Ventresca^{1}Email author
- Received: 18 February 2018
- Accepted: 13 June 2018
- Published: 9 July 2018
Abstract
The ubiquity of supply chains along with their increasingly interconnected structure has ignited interest in studying supply chain networks through the lens of complex adaptive systems. A particularly important characteristic of supply chains is the desirable goal of sustaining their operation when exposed to unexpected perturbations. Applied network science methods can be used to analyze topological properties of supply chains and propose models for their growth. Network models focusing on the critical aspect of supply chain resilience may provide insights into the design of supply networks that may quickly recover from disruptions. This is vital for understanding both static and dynamic structures of complex supply networks, and enabling management to make informed decisions and prioritizing particular operations. This paper proposes an action-based perspective for creating a compact probabilistic model for a given real-world supply network. The action-based model consists of a set of rules (actions) that a firm may use to connect with other firms, such that the synthesized networks are topologically resilient. Additionally, it captures the heterogeneous roles of different firms by incorporating domain specific constraints. Results analyzing the resilience of networks subjected to node disruptions show that networks synthesized using the proposed model can generally outperform its real-world counterpart.
Keywords
- Network modeling
- Supply chains
- Topological resilience
Introduction
Present day supply chain networks (SCNs) are profoundly interconnected structures that emerge from a largely downstream exchange of goods between firms (manufacturers, distributors, retailers, etc.) that are involved in creating a set of final products. Connections are formed or removed as firms use information from a local neighborhood to increase the value they derive from the supply chain without any knowledge of the interconnection structure of the whole supply network. That is, the network itself emerges through the local decisions of firms (Brintrup et al. 2016). Despite this realization, most industrial operations are still built upon overly simplified (often highly linear) models (Brintrup et al. 2015). Other gaps were identified in (Bellamy and Basole 2013) that suggest a focus on supply chain structure, dynamics and design strategy. Subsequently, there might be a tremendous unlocked potential in supply network efficiency that can be achieved through a complex systems/networks perspective (Choi et al. 2001; Surana et al. 2005). Additionally, three other major challenges have been identified as critical to the study of supply networks through the lens of complex networks (Pathak et al. 2007): (i) Researchers’ ability to comprehend the complex interactive nature of supply chain formation is limited, especially as the network size increases; (ii) Effective metrics for the dynamic nature of supply chain evolution are lacking; and (iii) developing theories to support supply chain design principles in the presence of network adaptation is nontrivial.
Utilizing the knowledge of network science to study supply chain networks was first suggested in (Choi et al. 2001), where various recommendations for future research directions on bridging the two research areas were laid out. Subsequent examinations of supply chain networks through the lens of network science have primarily focused on analyzing topological characteristics of supply chains and providing summary statistics for describing particular features. This is particularly useful since analysis of topological characteristics of the interconnection structure of firms in a supply chain enables managers to reflect on various aspects of the supply chain. For instance, (Kim et al. 2011; Borgatti and Li 2009) investigated automobile manufacturer supply networks with the aim of understanding the implications of using well known social network measures in the context of supply chains. Similarly, (Lomi and Pattison 2006) examined the network of automotive firms in southern Italy and discovered high local clustering, while (Keqiang et al. 2008) had very similar observations for the Guangzhou automotive network. Though an assortment of comparative investigations have been performed in other industry settings revealing fascinating properties of the networks themselves, consensus on a standard approach for designing supply networks remains generally elusive (Bellamy and Basole 2013). Though these surveys of real-world supply networks and their reported summary statistics provide insights into predominant characteristics of supply chains, they provide limited insight into the mechanisms by which these networks grow and evolve. A major reason for this stagnation has been a lack of availability of real-world supply network data to study, leading to a significant need for generators (algorithms for creating networks with specific topological properties) capable of synthesizing realistic supply networks that can be utilized to derive deeper insight into their best design principles. The ability of a network generator to synthesize networks with similar underlying summary statistics can help us understand the result of natural and deliberate perturbations on the overall functionality of the supply chain.
Network generators provide a platform for deriving deeper insights into complex networks and the processes that give rise to their observed structures. Their origins can be traced to random graphs (Erdös and Rényi 1959), which assume a constant number of nodes and edge existence with uniform probability. Random graphs are unlikely to be representative models of real-world systems, but a variety of better approaches have since been proposed that define network growth dynamics and non-uniform edge existence (see (Fienberg 2012; Goldenberg et al. 2010; Barthélemy 2011; Newman 2003) for a more comprehensive overview). Other popular network generators include the small-wold model (Watts and Strogatz 1998) (i.e. a network in which nodes can reach other nodes in a small number of steps), and scale-free model (Barabási and Albert 1999) (i.e., the probability P(k)≈k^{−α}, for degree k with usually α∈(2,3)). One of the most popular statistical network models are the exponential random graphs (Strauss 1986; Wasserman and Pattison 1996; Anderson et al. 1999). These models deal with link formation mechanisms using conditional dependence, which states that the existence of links in a network is shaped by the presence or absence of other links (and possibly node-level attributes) (Robins et al. 2007). These models have limited utility for synthesizing supply chain networks due to the absence of mechanisms to incorporate real-world supply chain constraints. These methods have been shown to be highly unlikely to synthesize networks that share a strong structural resemblance to actual supply networks and are woefully insufficient to study the intricate nature of supply chains, therefore being unsuitable for discovering new design principles (Bellamy and Basole 2013; Kim et al. 2011). Incorporating constraints on nodes (i.e., firms) is generally outside the capabilities of most existing network generators, which is why most existing studies have concentrated on general analyses with limited insight into new design principles (Bellamy and Basole 2013).
A particularly important characteristic of dynamic supply chains is the desirable goal of sustaining their operation when exposed to unexpected disruptions. The goal of supply chain robustness is to sustain operation during such disruptions, whereas the goal of supply chain resilience focuses on designing systems that quickly recover from these disruptions. (Perera et al. 2015) suggests that the definition of resilience and robustness should be established in parallel with the definition of disruption, and shows how some of the important research in supply chains have accomplished this. These terms are often used interchangeably in the literature, but in either case the impact may be significant. For instance, according to a 2017 report by the Business Continuity Institute (Alcantara et al. 2017) 75% of businesses experience at least one supply chain disruption every 12 months (although they suggest the value is likely higher due to underreporting), 22% report cumulative losses of at least $1 million over this time, with 34% reporting at least $270,000. Additionally, 55% reported a loss in productivity, 34% reported that their service was impaired, and 32% reported a loss in revenue. These trends have led to a shift in focus of research from supply chain efficiency to supply chain resilience (Perera et al. 2015).
(Klibi et al. 2010) suggested that topological resilience should be assessed when designing supply chains to ensure sustainable value creation. Robustness and resilience have thus become important areas of study (for simplicity we refer to both as resilience). While (Thadakamalla et al. 2004) was the first to use topology of SCNs for studying resilience, subsequent papers like (Zhao et al. 2011b; Wang et al. 2015) provide supply chain design insights by examining resilience against both random and targeted attacks. Numerous specialized measures of resilience have also been proposed for supply chains (Barroso et al. 2015), but most analyses concentrate on empirical studies from a centralized context. Outside of the supply chain network community, resilience has also attracted significant attention (see for example (Gao et al. 2016)). A resilient supply chain should rapidly and effectively respond to perturbations such as supply or demand fluctuations, or to complete or partial failure of a subset of firms. However, being a complex system, adaptation to changes in the supply chain cannot be dictated by those overseeing or relying upon it. Instead, structural resilience should exist as an outcome of the local linking decisions of various firms within a supply chain without explicit awareness of the overall structure.
A significant amount of research examining complex network models for supply chain networks has focused on using straightforward and conventional strategies as models for SCN evolution. To understand these network models, we first need to introduce two concepts that are essential ingredients of any such approach: (i) each firm belongs to a unique tier, which corresponds to its distance (number of hops in the networks) from the consumer in the final supply chain with a restriction that supply-demand relations occur only between firms in adjacent tiers; (ii) every firm has a fixed role in the network, i.e. it is a supplier, manufacturer, consumer etc. Most supply chain models categorize nodes based on their tiers and roles, and then use these attributes to define attachment rules, for example (Thadakamalla et al. 2004; Wang et al. 2015) use a heterogeneous preferential linking mechanism that varies based on role of the firm, (Nair and Vidal 2011) proposes an agent-based model that uses firm role and demands to form links, (Wen et al. 2012; Mari et al. 2015) use restricted preferential attachment mechanism based on firm tiers. Others use more complicated linking mechanisms such as, local selection and preferential attachment (Li et al. 2013; Zhao et al. 2011b), random, preferential attachment and similarity (Xuan et al. 2011), and fitness based attachment (Perera et al. 2017b). Though these models incorporate basic features for modeling SCNs, their simple attachment mechanisms cannot replicate the topology of real-world SCNs, as their capabilities are restricted to synthesizing networks that reproduce a few characteristics like power law degree distributions. Further, only a few of these models focus on creating resilient SCN topologies, without providing any insights into supply chain design principles. Thus, there is still a significant gap in developing a generalizable network growth model that can generate topologies mimicking real-world SCNs (Perera et al. 2017, 2017a).
Main contributions
In this paper, we focus on modeling of supply chain networks by utilizing the action-based framework (Arora and Ventresca 2017) for learning a compact probabilistic model for a given material flow SCN. The proposed framework can learn a compact model using a single observation of a real-world supply network and the obtained parameters can be used to synthesize, with high probability, statistically similar networks to a given supply network. (Arora and Ventresca 2018) modified the action-based approach for the supply chain context by considering directed networks and incorporating domain specific constraints. Additionally, (Arora and Ventresca 2018) used the role of a firm (manufacturer, supplier, distributor etc.) to infer constraints and growth mechanisms for SCNs. Here instead we utilize tier information to impose linking constraints among firms, while preserving the tiered structure of the target SCN. The modified network generator that captures critical real-world constraints concerning rules by which firms exchange goods is described in “Action-based networks” section. The novel framework is then used for modeling and synthesizing 10 realistic supply networks in “Results” section. The applicability of the framework for modeling real-world supply networks is tested, and the resilience of the synthesized networks is analyzed by subjecting them to random and targeted node disruptions. The probabilistic model can also be used to infer growth mechanisms of real-world SCNs by examining the optimized parameters. Finally, “Conclusions and future work” section concludes the paper with some conclusions and directions for future research.
Action-based networks
The underlying goal of this research is to define an adequately robust procedure that can synthesize networks exhibiting structural properties observed in real-world SCNs. A network generator is considered to be synthesizing realistic networks if a topological comparison between the synthesized and real networks is, with high likelihood, statistically similar across a subset of user-desired topological characteristics. In this way, the objective isn’t to exactly replicate the topology of a given real-world network because there is no utility in synthesizing isomorphic networks as it provides no additional insights. Further, given the input is a single SCN observation, strong assumptions about the dynamical growth of the network need to be made, and the network generator needs to be robust to any such assumptions. Finally, the parameters of the optimized network generator should ideally provide additional insights into the local decisions of the firms that might have lead to creation of the observed network topology.
The problem of discovering a network generator can be posed as a non-linear inverse problem having the form \(S(\mathcal {T}) \vdash F(\mathbf {M}, \xi)\) (i.e. F(M,ξ) can be inferred from \(S(\mathcal {T})\)). The target network \(\mathcal {T}\) and set of p user-desired network structural properties \(S(\mathcal {T}) = \{s_{1}(\mathcal {T}), \dots, s_{p}(\mathcal {T})\}\) of interest are given as input to the system. Therefore, the goal is to infer M under the assumption that network formation is performed by the forward operator F. Here, F is an algorithm capable of synthesizing networks based on a random process ξ∈Ξ that can be used to obtain a finite set of networks by repeated simulation of F(M,ξ).
Alderson (2009) considered network generation as an optimization-based reverse-engineering problem and concluded that a “good” forward model should consider both the structure and function of the network (although a procedure to accomplish the task was not given). An action-based network generator (ABNG) is proposed as the forward operator F, which assumes that complex networks emerge through local interaction among nodes that make linking decisions while completely ignoring the global network topology. This assumption is particularly appropriate for modeling supply chain networks because its overall structure can be understood as a self-organizing system that consists of various entities engaging in localized decision making (Perera et al. 2017). Given a network observation, it might not be possible to uncover the exact reason(s) behind the existence of a particular link/interaction among firms, but one could potentially list a finite number of decision processes that might have lead to creation of a particular link. A probability distribution on these decision processes can then be defined that can potentially model the existence of that link with a high likelihood. For example, the exact reason for interaction between two specific firms may not be known, but potential reasons for the interaction can be enumerated and assigned a corresponding probability.
The inverse problem of identifying the probabilities when ABNG is used as the forward operator can be formulated in an optimization-based framework, where the goal is to minimize a cost function D that can serve as a metric to evaluate the difference between the networks synthesized using ABNG and the given target network. Given an appropriate probabilistic model with a viable set of decision processes, it seems logical that a variety of network topologies can be synthesized. So, the fundamental idea behind action-based networks is to define a unifying network generative process, which follows from observations by (Zheng et al. 2014) who note that there must exist an assembling algorithm to combine local mechanisms for emergence of different complex network structures. Identifying such an assembling algorithm can help us distinguish between local decision processes that are responsible for network growth from those that emerge as byproducts of the network generation process.
Action set for SCNs
While empirical studies have highlighted that it is highly unlikely that a real-world SCN might have evolved through a single linking mechanism, it is possible to conceive growth and design principles from the global properties of existing SCNs (Perera et al. 2017). The action-based framework provides a platform for probabilistically aggregating various local linking mechanisms using a generative algorithm. Each action in ABNG serves as a single linking mechanism, which when combined with an appropriate synthesis algorithm F(·) can synthesize networks exhibiting varying topological characteristics. In the context of SCNs, an action is a decision process that a firm uses to select firms that it should supply its materials to. The supply chain literature provides a rich source for potential decision processes (Pathak et al. 2009; Xuan et al. 2011; Kim et al. 2011; Bellamy and Basole 2013; Hearnshaw and Wilson 2013; Wang et al. 2015), while providing insights regarding how to choose a set of actions that may lead to construction of topologically resilient SCNs. The idea is to carefully choose actions for network synthesis at the micro level such that the resilience of the whole supply network gets mirrored at the macro level. The reason behind this choice is that creation of resilient structures is an expected outcome of the local linking between nodes rather than a goal of the participating firms (a firm is more likely to focus on its operational efficiency).
Recent research (Kim et al. 2015; Hearnshaw and Wilson 2013) has suggested that existence of power law degree distributions in supply chain networks has a positive affect on its resilience. Preferential attachment mechanisms have been shown to synthesize networks that perform well under random failures and are among the most prominent rules for making linking decisions, hence making them a perfect candidate for actions for SCN modeling (Thadakamalla et al. 2004; Zhao et al. 2011b; Xuan et al. 2011; Mari et al. 2015). Preferential attachment also leads to creation of networks exhibiting power law degree distributions. A variety of preferential attachment mechanisms based on network centrality metrics can potentially lead to creation of a few different hubs, hence dispersing the influential nodes across the overall supply chain. Further, networks with power law degree distributions that are formed by fractal mechanisms show greater resilience against cascading failures as compared to those obtained from the simple preferential attachment mechanisms.
Consequently, the action set A will include preferentially selecting a node based on its out-degree, in-degree, vertex betweenness and closeness. These centrality metrics can induce the creation of a diverse range of hub nodes leading to creation of an overall resilient network structure. The use of network properties like betweenness and closeness for preferential linking can be seen as a proxy for more practical information such as price, performance, and quality that are more relevant in the context of supply chains (Jain et al. 2009; Li et al. 2013). A fractal mechanism based on difference in total degree (resulting in repulsion between hub nodes) has also been shown to produce resilient structures (Hearnshaw and Wilson 2013; Song et al. 2006), and is included as an action. It is possible that a firm does not prefer one particular firm over another based on the actions described above, leading to an action corresponding to random selection among the firms satisfying the tier constraints. An action is also based on connecting with closer nodes^{1}with higher probability (Zhao et al. 2011b). Finally a firm might choose to not add an edge, which is the final action in A. It should be noted that in the presence of no edges in the network all actions become equivalent to a random action, i.e. randomly selecting a firm satisfying the tier constraints. This is further explained along with the synthesis algorithm in “Network synthesis” section.
Network synthesis
A forward operator F in case of ABNG is a generative algorithm F(M,n,m,ξ) that can be used to synthesize networks containing n nodes and m edges using an action-based model M. The generative algorithm synthesizes networks by first creating the set of desired nodes, and then probabilistically assigning a node type t to each node according to \(\mathbb {P}(T = t)\). Monte Carlo simulation is then performed using the probabilities of node actions from \(\mathbb {P}(A = a_{l}|t)\). For example, a model of a simple preferential attachment network will contain a single node type that has a sufficiently high probability for the action of creating connections to nodes based on degree. Repeated sampling from \(\mathbb {P}(A = a_{l})\) will yield a preferential attachment network, as desired. Increasingly complicated topological properties will emerge with increased number of node types and variety of actions.
Importantly, the synthesis algorithm allows the network modeler to easily integrate domain specific rules or constraints by implementing a problem specific set of node actions (e.g., ways firms could interact with each other). Moreover, the modeler may wish to ensure a specific network backbone, which can be easily accommodated by defining the initial topology before executing the Monte Carlo simulation. Termination conditions for the synthesis algorithm are user defined, e.g., certain number of edges created or topological characteristics have satisfactorily emerged.
Incorporating tier constraints
Supply chain networks are formed from heterogeneous types of nodes, where each node has a specialized task. Hence, extra care must be taken to appropriately capture critical real-world constraints concerning the rules firms use to exchange goods. Some are trivial, while others are context-dependent. Failure to reasonably accommodate these constraints in the generative process will severely limit its utility to providing only very general insights into SCN design principles. Previous research has suggested that SCNs should be modeled as tiered networks, where each tier contains nodes performing different functional tasks and the constraints of edge formation apply to the entire set of nodes in a particular tier (Bell et al. 2017, Hearnshaw and Wilson 2013, Pathak et al. 2007, 2009, Wang et al. 2015). As described in “Introduction” section, each firm in a supply chain belongs to a unique tier, which corresponds to the number of hops from the consumer in the final supply chain. For a network \(\mathcal {G}=(V,E)\), the set of nodes can be partitioned into l tiers V=T_{0}∪⋯∪T_{l−1}, such that for α≠β, T_{α}∩T_{β}=∅,∀α,β∈{0,…,l−1}. Similarly, tiers also introduce constraints on the possible set of edges, such that a node v_{i}∈T_{α} (α≥1) can only supply materials to a node v_{j}∈T_{α−1}, i.e. supply-demand relations exist only between firms in adjacent tiers. Algorithm 1 shows how ABNG is used to synthesize tiered supply networks for a given action matrix M by restricting actions to select nodes that satisfy tier constraints.
Optimization and determining generator suitability
As seen in Eq. (1), the problem of finding an action matrix M is framed as a multiobjective problem. The decision to frame this within a multiobjective context is based on numerous observations in network science literature arguing that it is a robust approach to determining generator suitability (Pržulj 2007; Harrison et al. 2016; Fay et al. 2014; Yaveroǧlu et al. 2015). To solve this multi-objective search problem, we implement Pareto Simulated Annealing (PSA) (Czyzak and Jaszkiewicz 1998), as it is known to be a useful metaheuristic capable of global optimization in a large search space in a fixed amount of time. Additionally, only one evaluation of the objective function is required at each iteration when compared with population-based algorithms, which require an evaluation for each member of the population.
Choice of Objectives: An objective of the current research is to learn the action-based model for a given SCN, while preserving its resilience properties. Network resilience has emerged as a critical topic in supply chain research, and a summary of several metrics that may help understand supply network resilience can be seen in (Kim et al. 2015). Recent research (Zhao et al. 2011b; Thadakamalla et al. 2004) has uncovered the importance of network topology in determining resilience of SCNs under random and targeted disruptions, hence highlighting the importance of considering it as an essential component of SCN modeling. To preserve the structural and resilience properties of the real-world SCN, the action-based framework uses the 2-sample Kolmogorov-Smirnov statistic to quantify difference in distribution of node level properties between the synthesized and target networks. In the current experiments, node betweenness, in-degree and out-degree are utilized as the global network characteristics \(S(\mathcal {T})\), but the approach is indifferent to the choice of objectives, and other properties with alternative approaches like KL-divergence or entropy-related measures can be used to quantify the difference in distributions of network properties. The choice of objectives is based on the efficacy of these measures to capture the essential structural features of a network, especially in the the context of our action-based approach (Arora and Ventresca 2017). (Kim et al. 2015) uses these network properties to understand supply network resilience in different network structures.
Results
List of real-world SCNs used for modeling along with relevant network properties of the both the target \(\mathcal {T}\) and synthesized \(\mathcal {G}\) networks: total number of vertices n; total number of edges m; mean degree \(\bar {k}\); average path length (apl); network connectivity (NC); network heterogeneity (NH); fitted power law coefficients for in (α-in) and out (α-out) degree distributions
Ref # | SIC Description | n | m | \(\bar {k}\) | apl \(\mathcal {T}\) | apl \(\mathcal {G}\) | NC \(\mathcal {T}\) | NC \(\mathcal {G}\) | NH \(\mathcal {T}\) | NH \(\mathcal {G}\) | α−in \(\mathcal {T}\) | α−in \(\mathcal {G}\) | α-out \(\mathcal {T}\) | α-out \(\mathcal {G}\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
13 | Semiconductors and related devices | 108 | 452 | 8.37 | 1 | 1 | 0.74 | 0.59 | 1.84 | 1.52 | 2.43 | 2.34 | 11.61 | 7.64 |
18 | Computer peripheral equipment | 154 | 224 | 2.91 | 2.62 | 2.32 | 0.067 | 0.074 | 1.02 | 0.79 | 3.02 | 4.41 | 3.68 | 5.96 |
21 | Perfumes, cosmetics, and other toilet preparations | 186 | 359 | 3.86 | 2.82 | 3.03 | 0.082 | 0.087 | 1.06 | 0.91 | 5.44 | 3.28 | 3.18 | 3.46 |
24 | Power-driven handtools | 334 | 1245 | 7.45 | 2.70 | 2.70 | 0.18 | 0.43 | 1.83 | 2.05 | 2.07 | 1.95 | 2.15 | 5.19 |
27 | Electromedical and Electrotherapeutic Apparatus | 482 | 941 | 3.90 | 1.96 | 2.32 | 0.18 | 0.42 | 2.68 | 3.07 | 2.66 | 2.09 | 3.08 | 3.36 |
28 | Computer storage devices | 577 | 2262 | 7.84 | 2.56 | 2.48 | 0.34 | 0.14 | 2.47 | 1.50 | 2.11 | 2.40 | 3.14 | 10.88 |
32 | Perfumes, cosmetics, and other toilet preparations | 844 | 1685 | 3.99 | 1.96 | 2.38 | 0.074 | 0.027 | 1.56 | 1.10 | 2.42 | 6.99 | 2.59 | 4.36 |
34 | Telephone and telegraph apparatus | 1206 | 4063 | 6.74 | 1.07 | 1.29 | 0.12 | 0.33 | 2.75 | 3.94 | 2.88 | 3.17 | 2.32 | 7.43 |
36 | Farm machinery and equipment | 1451 | 4812 | 6.63 | 1.66 | 1.77 | 0.40 | 0.19 | 2.68 | 2.38 | 10.47 | 2.29 | 2.06 | 5.37 |
38 | Aircraft engines and engine parts | 2025 | 16225 | 16.02 | 2.38 | 2.47 | 0.11 | 0.10 | 2.45 | 2.18 | 2.86 | 21.21 | 1.9 | 16.76 |
Dataset
A key limitation of the SCN dataset is the absence of data on geographical locations of individual firms. This information was not provided in the original dataset due to confidentiality reasons. As discussed earlier, geographical location might play a significant role in linking decisions of firms and its unavailability might significantly limit our understanding of various structural features. Furthermore, this empirical study does not explore the dynamic nature of the SCNs since the dataset does not provide any information pertaining to temporal changes in the SCN topology. Lastly, the dataset does not provide information regarding amount of material flow between connected firms. Although specific production capabilities of firms within each tier are known, no information is available in relation to how much each upstream firm supplies to the downstream firms. Nevertheless, the size of the dataset, both in terms of the number of networks available and in terms of number of nodes in each network, make this a very attractive dataset to study.
Modeling SCNs
As seen in Fig. 2, the target networks might impose strict constraints on how nodes in two tiers are connected, for example the green and blue nodes in the supply chain of Computer Peripheral Equipment have a one-to-one mapping. The constraints imposed by such specialized sub-structures might lead to synthesis of disconnected networks using ABNG. Synthesis of SCNs that are not fully connected is not a desirable outcome. To deal with this issue, a clean-up phase was devised to ensure every node participating in the supply chain is connected to the synthesized SCN. If the algorithmic procedure described in Algorithm 1 synthesizes a disconnected network, the clean-up phase is initiated to create a connected supply chain by randomly connecting a disconnected node to a node that is already a part of the overall supply chain, while adhering to tier constraints described in “Incorporating tier constraints” section. The networks obtained after the clean-up phase are then subjected to further analysis.
The table shows optimized action matrix for a few SCNs
Network ↓| Action → | PAOD | PAID | PADD | PAB | PAC | Rand | InvSD | NA | \(\mathbb {P}(T=t)\) |
---|---|---|---|---|---|---|---|---|---|
Perfumes, cosmetics, and | 0.000 | 0.174 | 0.015 | 0.108 | 0.037 | 0.076 | 0.158 | 0.432 | 0.188 |
Other toilet preparations | 0.007 | 0.249 | 0.179 | 0.074 | 0.000 | 0.008 | 0.000 | 0.483 | 0.812 |
0.077 | 0.032 | 0.009 | 0.373 | 0.026 | 0.000 | 0.000 | 0.483 | 0.508 | |
Power-driven handtools | 0.053 | 0.193 | 0.236 | 0.223 | 0.096 | 0.021 | 0.178 | 0.000 | 0.091 |
0.018 | 0.000 | 0.000 | 0.094 | 0.023 | 0.010 | 0.000 | 0.855 | 0.401 | |
0.266 | 0.000 | 0.388 | 0.024 | 0.082 | 0.089 | 0.000 | 0.151 | 0.203 | |
Computer storage devices | 0.226 | 0.017 | 0.143 | 0.116 | 0.167 | 0.017 | 0.314 | 0.000 | 0.186 |
0.205 | 0.000 | 0.208 | 0.169 | 0.229 | 0.123 | 0.066 | 0.000 | 0.611 | |
Artificial SCN | 0.020 | 0.001 | 0.000 | 0.183 | 0.000 | 0.000 | 0.000 | 0.796 | 0.851 |
0.132 | 0.156 | 0.251 | 0.091 | 0.132 | 0.071 | 0.108 | 0.059 | 0.149 |
Resilience analysis
The supply chain literature emphasizes that specific measures are required for evaluating topological resilience of SCNs by incorporating the role of various nodes in the network. Analytical measures of resilience commonly used in the network science literature (Rubinov and Sporns 2010; Costa et al. 2005) are unable to account for node heterogeneity, which is a critical aspect in SCN modeling. For example, (Zhao et al. 2011b, 2011a) point out that in the context of SCNs, the distance between two supply nodes or two demand nodes are not as important as that between a supply and a demand node. To tackle this issue, researchers rely on simulation based metrics to analyze topological resilience through customized metrics. The usual approach consists of simulating random or targeted disruptions by removing nodes from the network. (Perera et al. 2017) provides an outline of the methodological framework that is typically used for analysis of topological resilience of SCNs. This procedure consists of sequentially repeating the following steps:(i) simulate node removal, and (ii) measure the relevant resilience metrics. This can provide general insights into the topological aspects of SCN resilience.
Once a set of measures for evaluating topological resilience of a network have been decided, the sequential procedure described earlier can be used to perform analysis on a network. In this research, we simulate random disruptions by randomly removing a supply node from the network, and targeted disruptions remove a supply node with the highest total degree (sum of in and out degree). Though we perform degree-based targeted disruptions, variations that use different centrality measures can also be used. Another useful technique to study the impact of removing nodes from a network is to devise a classification scheme for nodes in a SCN with reference to resilience. This can be achieved by altering the procedure outlined in (Savvopoulos and Moschoyiannis 2017) to incorporate SCN resilience, but is out of scope for this study.
Overall, the proposed model is capable of synthesizing networks that are structurally similar to real-world SCNs only by utilizing a few global network properties in form of objective functions \(S(\mathcal {T})\), and also incorporating context-dependent constraints on link formation between firms in different tiers. The ability of the synthesized networks to retain functionality under disruption demonstrates that the micro level linking decisions (actions) of individual firms can be used in a probabilistic manner to synthesize topologically resilient network structures. Using the information from node level actions and corresponding probabilities can provide network designers with a better understanding of supply chain dynamics, and hence make informed decisions regarding designing systems that can retain functionality under disruptions.
Conclusions and future work
The objective of this research was to investigate the possibility of using a network model to synthesize resilient supply networks capable of structurally replicating a given real-world supply chain. The framework incorporates essential features of SCNs like node heterogeneity by using tier information and allowing different mechanisms to connect with firms. The results indicate that decisions by firms at the micro level can lead to creation of networks that exhibit topological resilience, hence providing insights into network design principles. The framework can be extended to capture dynamics of such networks by adding features such as arrival of new nodes and rewiring of existing edges. Information regarding node demands and incorporating tighter constraints on demand fulfillment can make the model more representative of real-world SCNs, but the unavailability of material flow data might hinder the progress in this direction. Availability of demand data will also lead to synthesis of connected networks by ensuring that individual demands are satisfied. Firm fitness (generally evaluated using profit or loss) is seen as an important driving mechanism for supply chain evolution (Li et al. 2009, 2010) and can be included as an additional action in future research, and also used as a metric for addition and removal of firms/nodes in the network. This can effectively capture the dynamics of supply chains and how the evolution of the network effects its resilience.
This action is currently based on shortest distances in the network. If available, node information about location of firms can also be used.
Declarations
Acknowledgements
We would like to thank two anonymous referees for their comments and suggestions.
Funding
This material is based upon work supported by the National Science Foundation under Grant No. 1549608.
Availability of data and materials
The datasets used in this article are all publicly available and cited in the references.
Authors’ contributions
VA and MV contributed equally to this work. Both authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- Alcantara, P, Riglietti G, Aguada L (2017) BCI Supply Chain Resilience Report. Tech Rep.1–52.Google Scholar
- Alderson, DL (2009) Catching the ’Network Science’ Bug: Insight and Opportunities for the Operations Researchers. Oper Res 56(5):1047–1065.MathSciNetView ArticleMATHGoogle Scholar
- Anderson, CJ, Wasserman S, Crouch B (1999) A p* primer: Logit models for social networks. Soc Networks 21(1):37–66.View ArticleGoogle Scholar
- Arora, V, Ventresca M (2017) Action-based Modeling of Complex Networks. Sci Rep 7(1):6673.ADSView ArticleGoogle Scholar
- Arora, V, Ventresca M (2018) Action-Based Model for Topologically Resilient Supply Networks In: Studies in Computational Intelligence, vol. 689, 658–669.. Springer International Publishing, Cham.Google Scholar
- Barabási, AL, Albert R (1999) Emergence of scaling in random networks. Science 286(October):509–512.ADSMathSciNetMATHGoogle Scholar
- Barroso, AP, Machado VH, Carvalho H, Cruz Machado V (2015) Quantifying the Supply Chain Resilience In: Applications of Contemporary Management Approaches in Supply Chains, 13–32.. InTech, Rijeka.Google Scholar
- Barthélemy, M (2011) Spatial networks. Phys Rep 499(1-3):1–101.ADSMathSciNetView ArticleGoogle Scholar
- Bell, M, Perera S, Piraveenan M, Bliemer M, Latty T, Reid C (2017) Network growth models: A behavioural basis for attachment proportional to fitness. Sci Rep 7(October 2016):42431.ADSView ArticleGoogle Scholar
- Bellamy, MA, Basole RC (2013) Network analysis of supply chain systems: A systematic review and future research. Syst Eng 16(2):235–249.View ArticleGoogle Scholar
- Borgatti, SP, Li X (2009) On Social Network Analysis In A Supply Chain Context. J Supply Chain Manag 45(2):5–22.View ArticleGoogle Scholar
- Brintrup, A, Ledwoch A, Barros J (2016) Topological robustness of the global automotive industry. Logist Res 9(1):1.View ArticleGoogle Scholar
- Brintrup, A, Wang Y, Tiwari A (2015) Supply Networks as Complex Systems: A Network-Science-Based Characterization. IEEE Syst J PP(99):1–12.Google Scholar
- Choi, TY, Dooley KJ, Rungtusanatham M (2001) Supply networks and complex adaptive systems: control versus emergence. J Oper Manag 19(3):351–366.View ArticleGoogle Scholar
- Costa, LF, Rodrigues FA, Travieso G, Boas PRV (2005) Characterization of complex networks: A survey of measurements. Adv Phys 56(1):167–242.ADSView ArticleGoogle Scholar
- Czyzak, P, Jaszkiewicz A (1998) Pareto Simulated Annealing–A Metaheuristic Technique for Multiple-Objective Combinatorial Optimization. J Multi-Criteria Decis Anal 7(1):34–47.View ArticleMATHGoogle Scholar
- Erdös, P, Rényi A (1959) On random graphs. Publ Math Debr 6:290–297.MATHGoogle Scholar
- Fay, D, Moore AW, Brown K, Filosi M, Jurman G (2014) Graph metrics as summary statistics for Approximate Bayesian Computation with application to network model parameter estimation. J Complex Netw 3:009.MathSciNetGoogle Scholar
- Fienberg, SE (2012) A Brief History of Statistical Models for Network Analysis and Open Challenges. J Comput Graph Stat 21(4):825–839.MathSciNetView ArticleGoogle Scholar
- Goldenberg, A, Zheng AX, Fienberg SE, Airoldi EM (2010) A Survey of Statistical Network Models. Found Trends Mach Learn 2(2):129–233.View ArticleMATHGoogle Scholar
- Gao, J, Barzel B, Barabási AL (2016) Universal resilience patterns in complex networks. Nature 530(7590):307–312.ADSView ArticleGoogle Scholar
- Harrison, KR, Ventresca M, Ombuki-Berman BM (2016) A meta-analysis of centrality measures for comparing and generating complex network models. J Comput Sci 17:205–215.View ArticleGoogle Scholar
- Hearnshaw, EJS, Wilson MMJ (2013) A complex network approach to supply chain network theory. Int J Oper Prod Manag 33(4):442–469.View ArticleGoogle Scholar
- Jain, V, Wadhwa S, Deshmukh SG (2009) Select supplier-related issues in modelling a dynamic supply chain: Potential, challenges and direction for future research. Int J Prod Res 47(11):3013–3039.View ArticleMATHGoogle Scholar
- Keqiang, WKW, Zhaofeng ZZZ, Dongchuan SDS (2008) Structure Analysis of Supply Chain Networks Based on Complex Network Theory. 2008 Fourth International Conference on Semantics, Knowledge and Grid:493–494.Google Scholar
- Kim, Y, Chen YS, Linderman K (2015) Supply network disruption and resilience: A network structural perspective. J Oper Manag 33-34:43–59.View ArticleGoogle Scholar
- Kim, Y, Choi TY, Yan T, Dooley K (2011) Structural investigation of supply networks: A social network analysis approach. J Oper Manag 29(3):194–211.View ArticleGoogle Scholar
- Klibi, W, Martel A, Guitouni A (2010) The design of robust value-creating supply chain networks: A critical review. Eur J Oper Res 203(2):283–293.View ArticleMATHGoogle Scholar
- Li, G, Gu YG, Song ZH (2013) Evolution of cooperation on heterogeneous supply networks. Int J Prod Res 51(13):3894–3902.View ArticleGoogle Scholar
- Li, G, Ji P, Sun LY, Lee WB (2009) Modeling and simulation of supply network evolution based on complex adaptive system and fitness landscape. Comput Ind Eng 56(3):839–853.View ArticleGoogle Scholar
- Li, G, Yang H, Sun L, Ji P, Feng L (2010) The evolutionary complexity of complex adaptive supply networks: A simulation and case study. Int J Prod Econ 124(2):310–330.View ArticleGoogle Scholar
- Lomi, A, Pattison P (2006) Manufacturing Relations: An Empirical Study of the Organization of Production Across Multiple Networks. Organ Sci 17(3):313–332.View ArticleGoogle Scholar
- Mari, SI, Lee YH, Memon MS, Soo Park Y, Kim M (2015) Adaptivity of Complex Network Topologies for Designing Resilient Supply Chain Networks. Int J Ind Eng Theory, Appl Pract 22:102–116.Google Scholar
- Nair, A, Vidal JM (2011) Supply network topology and robustness against disruptions - an investigation using multi-agent model. Int J Prod Res 49(5):1391–1404.View ArticleGoogle Scholar
- Newman, MEJ (2003) The Structure and Function of Complex Networks. SIAM Rev 45(2):167–256.ADSMathSciNetView ArticleMATHGoogle Scholar
- Pathak, SD, Dilts DM, Biswas G (2007) On the evolutionary dynamics of supply network topologies. IEEE Trans Eng Manag 54(4):662–672.View ArticleGoogle Scholar
- Pathak, SD, Dilts DM, Mahadevan S (2009) Investigating population and topological evolution in a complex adaptive supply network. J Supply Chain Manag 45(3):54–67.View ArticleGoogle Scholar
- Perera, SS, Bell MGH, Bliemer MCJ (2015) Modelling Supply Chains as Complex Networks for Investigating Resilience : An Improved Methodological Framework In: Australasian Transport Research Forum (ATRF), 1–16.Google Scholar
- Perera, S, Bell MGH, Bliemer MCJ (2017) Network science approach to modelling the topology and robustness of supply chain networks: a review and perspective. Appl Netw Sci 2(1):33.View ArticleGoogle Scholar
- Perera, S, Perera HN, Kasthurirathna D (2017) Structural characteristics of complex supply chain networks In: 2017 Moratuwa Engineering Research Conference (MERCon), 135–140.. IEEE, Piscataway.View ArticleGoogle Scholar
- Perera, S, Perera HN, Kasthurirathna D (2017) Value chain approach for modelling resilience of tiered supply chain networks In: Engineering Research Conference (MERCon), 159–164.. IEEE, Moratuwa.Google Scholar
- Pržulj, N (2007) Biological network comparison using graphlet degree distribution. Bioinformatics 23(2):177–183.View ArticleGoogle Scholar
- Robins, G, Pattison P, Kalish Y, Lusher D (2007) An introduction to exponential random graph (p*) models for social networks. Soc Networks 29(2):173–191.View ArticleGoogle Scholar
- Rubinov, M, Sporns O (2010) Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52(3):1059–1069.View ArticleGoogle Scholar
- Savvopoulos, S, Moschoyiannis S (2017) Impact of removing nodes on the controllability of complex networks In: COMPLEX NETWORKS 2017: The 6th International Conference on Complex Networks & Their Applications, 361–363.Google Scholar
- Song, C, Havlin S, Makse Ha (2006) Origins of fractality in the growth of complex networks_nature. Nat Phys 2(April):275–281.View ArticleGoogle Scholar
- Strauss, D (1986) On a General Class of Models for Interaction. SIAM Rev 28(4):513–527.MathSciNetView ArticleMATHGoogle Scholar
- Surana, A, Kumara S, Greaves M, Raghavan UN (2005) Supply-chain networks: a complex adaptive systems perspective. Int J Prod Res 43(20):4235–4265.View ArticleGoogle Scholar
- Thadakamalla, HP, Raghavan UN, Kumara S, Albert A (2004) Survivability of Multiagent-Based Supply Networks: A Topological Perspective. IEEE Intell Syst 19(5):24–31.View ArticleGoogle Scholar
- Wang, W, Street WN, et al (2015) Topological resilience analysis of supply networks under random disruptions and targeted attacks In: Advances in Social Networks Analysis and Mining (ASONAM), 2015 IEEE/ACM International Conference on, 250–257.. IEEE.Google Scholar
- Wasserman, S, Pattison P (1996) Logit models and logistic regressions for social networks. Psychometrika 60:401–425.View ArticleMATHGoogle Scholar
- Watts, DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks,. Nature 393(6684):440–2.ADSView ArticleMATHGoogle Scholar
- Wen, L, Guo M, Wang L (2012) Statistic Characteristics Analysis of Directed Supply Chain Complex Network. Int J Advancements Comput Technol 4(21):84–91.View ArticleGoogle Scholar
- Willems, SP (2008) Data Set —Real-World Multiechelon Supply Chains Used for Inventory Optimization. Manuf Serv Oper Manag 10(1):19–23.View ArticleGoogle Scholar
- Xuan, Q, Du F, Li Y, Wu T-j (2011) A Framework to Model the Topological Structure of Supply Networks. IEEE Trans Autom Sci Eng 8(2):442–446.View ArticleGoogle Scholar
- Yaveroǧlu, ÖN, Malod-Dognin N, Davis D, Levnajic Z, Janjic V, Karapandza R, Stojmirovic A, Pržulj N (2015) Revealing the Hidden Language of Complex Networks. Sci Rep 4(1):4547.View ArticleGoogle Scholar
- Zhao, K, Kumar A, Yen J (2011a) Achieving High Robustness in Supply Distribution Networks by Rewiring. IEEE Trans Eng Manag 58(2):347–362.View ArticleGoogle Scholar
- Zhao, K, Kumar A, Harrison TP, Yen J (2011b) Analyzing the Resilience of Complex Supply Network Topologies Against Random and Targeted Disruptions. IEEE Syst J 5(1):28–39.ADSView ArticleGoogle Scholar
- Zheng, B, Wu H, Kuang L, Qin J, Du W, Wang J, Li D (2014) A simple model clarifies the complicated relationships of complex networks. Sci Rep 4:6197.ADSView ArticleGoogle Scholar