Development of Metrics and a Complexity Scale for the Topology of Assembly Supply Chains

Abstract

Abstract:In this paper, we present a methodological framework for conceptual modeling of assembly supply chain (ASC) networks. Models of such ASC networks are divided into classes on the basis of the numbers of initial suppliers. We provide a brief overview of select literature on the topic of structural complexity in assembly systems. Subsequently, the so called Vertex degree index for measuring a structural complexity of ASC networks is applied. This measure, which is based on the Shannon entropy, is well suited for the given purpose. Finally, we outline a generic model of quantitative complexity scale for ASC Networks.

Toward a Theory of Industrial Supply Networks: A Multi-Level Perspective via Network Analysis

“…The different interactions of networks has been investigated by Demetrius and Manke [36], who demonstrated four classic structures: regular, random, scale-free, and star networks with the same number of nodes n and links e. The average shortest path length L of different networks were shown as L regular > L random > L scale− f ree > L star , while the network entropy were reversely shown as H star > H scale− f ree > H random > H regular . Therefore shortening L in SN is considered as a way to increase SN efficiency [10,12,13,36,41]. Furthermore, we found that an SN with high network entropy represented the high complexity of SN interdependence, which led to SN efficiency.…”

“…It is well known that a higher complex network makes it more difficult to understand relational interactions and topological characteristics, so only a small change can cause a massive reaction [41]. On the other hand, as network is a nonlinear system, even given the same number of nodes and edges, networks can represent completely different structures such as regular, random, scale-free network and star networks [36].…”

“…According to the additivity of entropy [41], Equation (13) can also measure the information I t of node t. Figure 11b shows the variation of loss entropy ∆H 2 when the supply networks face degree-prior failure. Here, the results showed that ∆H 2 of each supply network (C 1 , C 2 , C 3 , C 4 , and C 5 ) self-organized into a scale-free power law distribution [24], and the slopes (solid lines) were k 1 = 3.83, k 2 = 4.00, k 3 = 4.16, k 4 = 3.41, and k 5 = 3.07.…”

“…Equation (11) is based on the Shannon entropy, which is well suitable for measuring the structural and topological complexity of networks [41]. It easily distinguished that regular networks represented a low complexity (entropy), whereas random networks represented a high complexity (entropy) [36].…”

“…Finally, we evaluated the SN resilience of distinctive communities from a vertex-level perspective. This paper employed the entropy [33][34][35][36][37][38][39][40], which is generated by node degree [41]. Several elimination scenarios of random failures and targeted attacks (i.e., degree-prior and P-prior) were simulated to investigate the complexity and robustness of the SN by sequentially removing the firms [10,18,42,43].…”