Why do nonlinearities matter? The repercussions of linear assumptions on the dynamic behaviour of assemble-to-order systems

The hybrid assembly-to-order (ATO) supply chain, combining make-to-stock and make-to-order (MTS-MTO) production, separated by a customer order decoupling point (CODP), is well recognised in many sectors. Based on the well-established Inventory and Order Based Production Control Systems (the IOBPCS family), we develop a hybrid ATO system dynamics model and analytically study the impact of nonlinearities on its dynamic performance. Nonlinearities play an important, sometimes even a dominant, role in influencing the dynamic performance of supply chain systems. However, most IOBPCS based analytical studies assume supply chain systems are completely linear and thereby greatly limit the applicability of published results, making it difficult to fully explain and describe oscillations caused by internal factors. We address this gap by analytically exploring the non-negative order and capacity constraint nonlinearities present in an ATO system. By adopting nonlinear control engineering and simulation approaches, we reveal that, depending on the mean and amplitude of the demand, the non-negative order and capacity constraints in the ATO system may occur and their significant impact on system dynamics performance should be carefully considered. Failing to monitor non-negative order constraints may underestimate the mean level of inventory and overestimate the inventory recovery speed. Sub-assemblers may suffer increased inventory cost (i.e. the consequence of varying inventory levels and recovery speed) if capacity and non-negative order constraints are not considered at their production site. Future research should consider the optimal trade-off design between CODP inventory and capacity and the exploration of delivery lead-time dynamics.