Some Properties of Decentralized Supply Chains

This paper analyzes the bullwhip effect in decentralized, linear and time-invariant (LTI) supply chains. It generalizes existing results by broadening the class of policies and customer demand processes under consideration. The supply chain is modeled as a single-input, singleoutput control system driven by arbitrary demands. The paper discusses the appropriateness of various metrics for the bullwhip effect, and derives analytical conditions to predict its presence independently of the demand process. The paper also gives a formula for the variance of the order stream at any stage when the demand process is known and ergodic. Advance demand information (ADI) is shown to mitigate the bullwhip effect for general ordering policies.