Consistency matters: Revisiting the structural complexity for supply chain networks

Modern supply chains are becoming increasingly complex. It is commonly believed that complexity is an impediment to performance, and proactively managing complexity can lead to better supply chain efficiency. However, complexity management has not been well-established and widely implemented in the industry, partly because little effort has been made to develop tools for quantifying the complexity. In this paper, we investigate the structural complexity of supply chain networks and aim to provide a supplement to the complexity measures in the literature. For supply chain networks, it is argued that a proper complexity measure should guarantee the consistency requirement, i.e., the complexity of a network should be higher than the complexity of its subnetwork. This is because the network has more members and interactions and normally incurs higher maintenance cost and imposes higher difficulties of management. With this argument, the contributions are three-fold. Firstly, by visualizing supply chain networks as directed graphs, this paper examines the consistency of six existing complexity measures with rigorous proofs. Unfortunately, only two of them are consistent. We point out that although the consistency check is only valid for unweighted graphs, it still has practical implications because it is prevailing in the literature to represent a large-scale supply chain network as an unweighted graph. Secondly, this paper shows those consistent measures are not suitable in multiple scenarios of supply chain networks because they may generate misleading results. Thirdly, to overcome their limitations, a consistent measure that leads to reasonable conclusions is proposed. Extensive numerical experiments are conducted to verify the usefulness of the proposed measure.