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

Manging 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 discrete system dynamics simulation, we evaluate two control mechanisms, termed as Reactive Pipeline Control (RPC) and Proactive Pipeline Control (PPC) approaches, in a nonlinear forbidden return based supply chain. We derive the analytical expression of bullwhip under shock and seasonal demands and propose the corresponding 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 unwanted oscillatory behaviour subject to inventory proportional adjustment speed. Also, PPC always generates more bullwhip than that in an RPC-controlled system regardless of physical delays and demand characteristics. The bullwhip generated by the PPC system can be significantly higher than that in the RPC system with an increase in system physical lead times. The simulation verifies our analytical results. Furthermore, compared with the linear system, the nonlinear forbidden returns system always generates less bullwhip at the expense of slow convergence speed and more oscillation regardless of order pipeline control policies. Managers may consider different order pipeline control policies by jointly assessing their inherent system structure and control, as well as customer demand characteristics.