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 e↵ect 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 e↵ective 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.

Identifying dynamical instabilities in supply networks using generalized modeling

“…These studies use variations of the inventory‐ and order‐based production control system (IOBPCS) (Towill, ), which are based on linear fractional control rules and constitute generalizations of the standard “inventory order up to level” models (Dejonckheere et al, ). Although the models in the literature are predominantly linear, some studies have sought to consider nonlinearities due to the nonnegativity of flows (Laugesen & Mosekilde, ; Wang, Disney & Wang, ; Warburton, ) and the strain on the system due to limited capacity and/or product availability (Spiegler & Naim, ; Spiegler, Naim, Towill, & Wikner, ; Venkateswaran & Son, ). These studies show that nonlinearities greatly influence the stability and the dynamics, leading for instance to chaotic behavior (Laugesen & Mosekilde, ).…”

The Impact of Lead Time Uncertainty on Supply Chain Performance Considering Carbon Cost

“…Through empirical and sensitivity analysis, they determined that the weight-distribution values of the shelf life of perishable drugs and the service level are reasonable. Spiegler et al [33] discussed the influence of lead time uncertainty on order quantity, inventory level, and work-in-process quantity. Assuming demand is stable, they followed the small disturbance principle to probe lead time disturbance related to system output, and they found that the order quantity, inventory level, and work-in-process quantity increase with the lead time.…”

Dynamic analysis and design of a semiconductor supply chain: a control engineering approach

“…There are several other future research opportunities based on this study. First, the application of nonlinear control engineering approaches should be considered by researchers, in particular for the context of the semiconductor supply chains to guide practitioners design and improve their systems, although common nonlinearities presented in the IOBPCS ordering family already be analytically traced by utilizing such methods Spiegler, Potter, et al 2016;Spiegler and Naim 2017). In addition, this study is limited to the analysis of the hybrid MTS-MTO system only and ignores cases in which the whole supply chain automatically switches to the pure MTS system if there is no feasible FGI/AWIP in the semiconductor production context.…”