Nonlinear dynamical systems and inventory management

Abstract

Surprisingly, deterministic time series can generate highly irregular, random-appearing trajectories. These deterministic time series result from nonlinear dynamical systems of differential or difference equations. The random appearance displayed by these systems is called nonlinear dynamical complexity. Properties of nonlinear complex systems include aperiodic random appearance, sensitive dependence on initial conditions and model parameters, and nonstationarity. Experiments involving the operation of simulated business environments and theoretical nonlinear dynamical models for inventory are reviewed to explore motivating factors that can give rise to demand with nonlinear complexities. The experimental and theoretical evidence reviewed indicates that nonlinear complexities in demand have significant implications for inventory management. Thus, researchers and practitioners in inventory management need to consider these properties when choosing inventory management methods. Characteristics of nonlinear dynamical systems and their implications for inventory management are presented in this paper. The use of the Brock, Dechert, and Scheinkman (1987) (BDS) test for nonlinear dependence is demonstrated on actual demand data.