Accepted for publication in the International Journal of Production Research, Page 1, Last Saved 06/08/01, discrete1.doc A Discrete Transfer Function Model to Determine the Dynamic Stability of a Vendor Managed Inventory Supply Chain By S.M. Disney # and D.R. Towill ~ ~# Logistics Systems Dynamics Group, Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff, CF10 3EU, UK. # DisneySM@cardiff.ac.uk , ~# Tel +44(0)29 2087 6083, ~# Fax +44(0)29 2087 4301 Word count 8408 in total, 6210 main body 0. Abstract This paper considers a well-established production and distribution scheduling algorithm termed 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. 0.1 Key Words Stability, Robustness, z-transforms, Supply Chains, VMI, Production and Inventory Control Disney, S.M. and Towill, D.R., (2002), "A discrete transfer function model to determine the dynamic stability of a Vendor Managed Inventory supply chain", International Journal of Production Research, Vol. 40, No. 1, pp179-204. DOI: 10.1080/00207540110072975.