A discrete transfer function model to determine the dynamic stability of a vendor managed inventory supply chain

This paper considers a well-established production and distribution scheduling algorithm, called the Automatic Pipeline, Inventory and Order Based Production Control System (APIOBPCS) within a Vendor Managed Inventory (VMI) supply chain. It develops a transfer function model of the system using causal loop diagrams, block diagrams, difference equations and z-transforms. Important insights into the VMI supply chain are derived from the mathematical model pertaining to the stability and robustness of the VMI system. Analysis confirmed by dynamic simulation clearly demonstrates instability arising from poor design. We also demonstrate its avoidance via our recommended parameter settings for tuning the two feedback loops within the supply chain for a specific production delay. The procedure is readily extended for other production delays and distributions.