Structural and State Controllability Study of the Supply Chain Network Based on the Complex Network Theory

Abstract

Based on the complex network theory, the state and structural controllability conditions of complex supply chain network (SCN) are analyzed in detail. The criterion for the state controllability of SCN is introduced, and the method for estimating the minimum number of control inputs for achieving the complete state/ global structural controllability is proposed. The proposed criterion can effectively assess the global controllability of SCN, while the introduced method can effectively determine the minimum number of control inputs for the global controllability of SCN. The respective theorem and its proof presented in this study yields a quite unexpected corollary: it is not necessary to control the inputs of core enterprises in SCN, to achieve the complete state controllability on the global scale. Alternatively, this goal can be accomplished by a reasonable choice of state nodes of suppliers in the uppermost stream and those of the distributors in the downstream. Strengthening of ties between suppliers can reduce the minimum number of control inputs required for the global structural controllability of SCN.