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Modelling Nonlinear Supply Chains Using Methods of System Dynamics

This paper treats a three level nonlinear supply chain, which consists from a manufacturer, a distributor and a retailer as a dynamical system. The dynamic behavior of supply chain is modelled by using the continuous Lorenz-like model with disturbances. The Lorenz model is known from physics in the study of dissipative hydrodynamical systems with excitation and represents a paradigmatic example of the deterministic system, which is able to exhibit chaotic motions. Very complex supply chain relationships are modelled due to the information flow distortion at the distributor, caused by disturbances, which appear at the retailer. By using the proposed nonlinear supply chain model, the steady state, the saturation and the chaotic state of the supply chain are analyzed,  respectively. The range of parameter values, which are characteristic for the appearance of such states are determined. In the paper, the meaning of the regular state in which the supply chain cannot keep due to the disturbances and the risk of the saturation state are explained. In the analysis of such states, the multistage homotopic perturbation method is used.  The gained results are checked analyticaly or by the help of standard numerical integration, such as the Runge-Kutta method.