On the dynamics of order pipeline inventory in a nonlinear order-up-to system

Junyi Lin, Hongfu Huang, Shanshan Li*, Mohamed M. Naim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Managing order pipeline inventory is important for controlling unwanted system dynamics, especially the bullwhip effect. We analytically explore the impact of desired target order pipeline inventory, advocated as a key decision in managing pipeline inventory, on system dynamics performance. Using control theory and system dynamics simulation, we evaluate two control mechanisms, termed as Reactive Pipeline Control (RPC) and Proactive Pipeline Control (PPC) approaches, in a nonlinear forbidden returns supply chain. We derive the analytical expressions of bullwhip under shock and seasonal demands and propose bullwhip avoidance strategies. The results indicate that an RPC based system always shows slower inventory convergence speed than that in the PPC based system, although the system with PPC policy may produce more unwanted oscillatory behaviour. Also, PPC always generates more bullwhip than that in an RPC-controlled system regardless of physical delays and system control parameters e.g. forecasting and inventory adjustment. Furthermore, compared with the linear system, the nonlinear forbidden returns system always generates less bullwhip and less oscillation at the expense of slow inventory recovery speed regardless of order pipeline control policies. Managers may consider different order pipeline control policies by jointly assessing their inherent system structure, control policies and customer demand characteristics, such as frequency and variance.

Original languageEnglish
Article number109061
JournalInternational Journal of Production Economics
Publication statusPublished - Dec 2023


  • Bullwhip effect
  • Forbidden returns
  • Nonlinear dynamics
  • Order pipeline inventory
  • Order-up-to policy
  • System dynamics


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