Investigating sustained oscillations in nonlinear production and inventory control models

Abstract

Even in a deterministic setting, nonlinearities can yield unexpected dynamic behaviours in a production and inventory control system, such as sustained oscillations or limit cycles. Describing function in combination with simulation is used to analyse the effect of discontinuous nonlinearities on the system responses. Utilising a nonlinear production and inventory control model, we investigate the occurrence of limit cycles and propose a technique to predict their amplitude, frequency and stability and to control such oscillations. Findings suggest that, even for an autonomous production and inventory control system, limit cycles do occur and this periodic behaviour occurs due to non-negativity constraint in the ordering rule. Moreover, we demonstrate the potential of the describing function method to provide insight into the impact of system constraints and therefore facilitate a more effective system design. This paper fills a gap in the literature on nonlinear supply chain dynamics by expanding and complementing the sparse recent research in this area. Most previous studies have either focused on linear mathematical models or relied on simulation, which greatly limit the relevancy and/or rigour of the published results.