On the stability and bullwhip effect of a production and inventory control system

This paper focuses on the discrete-time automatic pipeline, inventory and order-based production control system (APIOBPCS), a well-established production and inventory control model. The feedback mechanism within the replenishment rule enables the model to mitigate the bullwhip effect, but introduces a stability problem. In this research, a comprehensive stability analysis is conducted for arbitrary lead times using difference equation theory. On the basis of stability, a state space approach is advocated to analyse the impact of replenishment parameters, demand processes, and lead times on the robustness of the bullwhip effect. The stability results demonstrate that the production control system can easily be destabilised without incorporating the work-in-progress (WIP) feedback loop. Furthermore, it reveals that the stability problem for long lead times can be simplified with the stability condition independent of the lead time. The results obtained in this study provide useful guidelines for the selection of replenishment parameters to guarantee stability and mitigate the bullwhip effect.