Smart supply chain management in Industry 4.0

The emerging information and communication technologies (ICT) related to Industry 4.0 play a critical role to enhance supply chain performance. Employing the smart technologies has led to so-called smart supply chains. Understanding how Industry 4.0 and related ICT affect smart supply chains and how smart supply chains evolve with the support of the advanced technologies are vital to practical and academic communities. Existing review works on smart supply chains with ICT mainly rely on the academic literature alone. This paper presents an integrated approach to explore the effects of Industry 4.0 and related ICT on smart supply chains, by combining introduction of the current national strategies in North America, the research status analysis on ICT assisted supply chains from the major North American national research councils, and a systematic literature review of the subject. Besides, we introduce a smart supply chain hierarchical framework with multi-level intelligence. Furthermore, the challenges faced by supply chains under Industry 4.0 and future research directions are discussed as well

An upper bound for the crossing number of augmented cubes

A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing. The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a good drawing of $G$ in the plane. The {\it $n$-dimensional augmented cube} $AQ_n$, proposed by S.A. Choudum and V. Sunitha, is an important interconnection network with good topological properties and applications. In this paper, we obtain an upper bound on the crossing number of $AQ_n$ less than $26/324^{n}-(2n^2+7/2n-6)2^{n-2}$.Comment: 39 page