Observations of Chaotic Behaviour in Nonlinear Inventory Models

This article describes the use of simulation to investigate incipient chaotic behaviour in inventory models. Model structures investigated were either capacity limited or of variable delay time, implemented in discrete and continuous transform algebras. Results indicate the absence of chaos for a continuous time model but gave limited evidence for chaos in both unrestricted discrete models and those with a positive orders only limit. The responses where interaction with the capacity limit occurred did not confirm chaotic behaviour at odds with published results. Using the Liapunov exponent as a measure of chaotic behaviour, the results indicated, where the delay varies in proportion to order rate, a larger fixed delay reduced the Liapunov exponent as did increasing the dependence of delay on order rate. The effect of the model structures showed that the IOBPCS model, produced the largest Liapunov exponent. Reducing the discrete model update time reduced the Liapunov exponent.