# Robustness of Cyber-Physical Supply Networks in Cascading Failures
## 2 Literature Review  
In this section, the relevant literature is discussed and classified. This review is intended to offer an overview of recent studies surrounding failure, cascading failure, cyber supply networks, physical supply networks, and robustness metrics. The review of the related works is summarized in Table 1.  
In a supply network, a firm's operation is usually influenced by its upstream and downstream firms, and the failure of any firm (node) could cause the whole network to fail [14]. Such failure may delay the flow of goods, information, and funds in supply networks and affect the normal operations of many other firms due to cascading failure [20]. The indirect effects of production failures due to propagation are substantially larger than their direct effects [21]. Adding only single links may undermine normal supply network operation and stimulate disturbances remotely from the location of the structural change, and even cause global cascades of failures [22]. The phenomena of cascading failures often occur in complex networks, where the node failures can trigger overloading and underloading. Overloading may cause further failures of neighbor nodes and, finally, cascading failures of the global network. In [18], an extended cascading failure process triggered by resource/load fluctuations was proposed, considering the overload of the supply nodes and resource deficiency of the demand nodes. The load is preferentially redistributed along those higher-capacity nodes attached to the failed node [20]. Unlike overload failures, firms' subsequent failures in supply networksresult from underloading [14]. For the underload cascading failure model without a recovery process, a discontinuous phase transition was found [13]. The size of cascades of underload failures is related to the lower limit of node capacity [19]. A supply network is a distinct interdependent network composed of a cyber supply network and a physical supply network [15]; additionally, [23] proposed that supply chain models integrate physical and cyber networks. In supply chain systems, the communication comprises the entity's supplier, manufacturers, and distribution centers, which can acquire the data of demand, stock, and production [2]. Intertwining the virtual supply chain with the physical supply chain and their operations makes the additive manufacturing process a cyber-physical system [24]. The author of [25] introduced the structure dynamics control concept and a dynamic model to orchestrate operations in cyber-physical supply chains in smart manufacturing. A cyber-physical e-commerce logistics system has been applied in Hong Kong. In the physical world, industrial wearable technology transforms assets into cloud assets. In the cyber world, synchronization mechanisms enhance the utilization ratio of resources and spaces while decreasing waiting and wastage [26]. Several robustness metrics have been developed to compute the damage caused by cascading failures. The author of [3] defined the giant mutually connected component as the mutually connected cluster spanning the entire network. The author of [15] used a comprehensive effectiveness index to represent the average robustness of an interdependent supply network. The robustness is also quantified as the surviving fraction of nodes at the end of cascading failures [17]. The concept of network efficiency can quantify the consequence of cascading failures in the supply network [14]. The literature survey observed that most related works have not specifically investigated the robustness of cyber-physical supply networks in overload and underload cascading failures. The existing model mainly considers the impact of overload on the cascading process of supply networks but ignores the impact of underload. The fact that supply networks consist of the cyber supply network and physical supply network is often unconsidered.