Robust Stability Analysis of Decentralized Supply Chains

This chapter summarizes recent findings on the bullwhip effect in decentralized multi-echelon supply chains based on a system-control approach. The influence of the supply chain operation (e.g., ordering policy and lead time) is separated from that of the customer demand. Robust results that hold for any customer demand are derived for both deterministically and stochastically operated chains. We demonstrate the importance of robust analysis. It is shown that instability is an inherent property of the system, e.g., of the ordering policies used by the suppliers, but it is independent of customer demand. We first present analytical stability conditions for deterministically operated chains. The demand can be arbitrary and random. These chains are modeled and their stability is evaluated in the frequency domain. We unify some techniques used in the literature, and present analytical results with or without the knowledge of customer demand. We also allow additional randomness to arise from unpredictably varying factors in the operating environment, such as supplier behavior and transportation lead times. We then develop linear matrix inequality stability conditions to predict the bullwhip effect and bound its magnitude. Examples are shown for both types of chains. We also show the effect of advance demand information on the bullwhip effect.