On the Stability of Supply Chains

This paper examines the stability of autonomous supply chains. In an autonomous supply chain, suppliers only communicate with their downstream neighbor; i.e., their immediate customer. The inventory management policies used by the suppliers characterize a chain. An important property of a policy is its “gain”, which relates marginal changes in the average steady state inventory to small changes in the steady state demand rate. It is shown that all autonomous policies with positive gains are unstable when applied to a homogeneous supply chain if they do not use future order commitments. This generates the so-called “bullwhip” effect. Stability conditions for policies of all types are given. The paper also discusses a family of stable, autonomous policies that can dynamically maintain any desired inventory level for any demand rate. The family includes just-in-time strategies as a special case. If the target inventories are admissible, i.e. they are large enough to prevent stock-outs in the steady state (with some margin of safety) then the proposed policies avoid stock-outs in the dynamic case. Simulations are used as an illustration.