The impact of cooperation mechanism on the chaotic behaviours in nonlinear supply chains

Abstract

The chaotic behaviours of nonlinear inventory systems are investigated via control theory, nonlinear system theory, and chaos theory. Two well-established production and distribution scheduling algorithms, automatic pipeline, variable inventory and order-based production control system (APVIOBPCS) with demand information sharing (DIS) and vendor managed inventory (VMI) supply chains are adopted and analysed by bifurcation diagram and Lyapunov exponent spectrum. Simulation results show that with the target inventory parameter ([2) changes, behaviours of the DIS and VMI systems are different from that of traditional inventory system. The Lyapunov exponent confirms that behaviours of DIS supply chain members shift between chaotic and periodic movement with [2 increases. The system shows periodic movement when [2 is set between 1 and 1.5. For VMI system, the system is not sensitive to [2 and keeps periodic movement. Therefore, the DIS and VMI supply chain members can effectively reduce inventory, and keep periodic movement simultaneously. [Received 13 July 2013; Revised 13 January 2014; Revised 10 June 2014; Accepted 14 June 2014]