The Bullwhip Effect in Supply Chains with Stochastic Dynamics

This paper analyzes the bullwhip effect in single-echelon supply chains operated nondeterministically. The supply chain is modeled as a Markovian jump linear system driven by arbitrary customer demands. The paper presents robust analytical conditions to diagnose the bullwhip effect, and bound its magnitude. The tests are independent of the customer demand. Examples are given. Policies that pass these tests, and thus avoid the bullwhip effect in random environments for arbitrary customer demands, are shown to exist. The paper also presents extended tests for multi-echelon chains.