This paper analyzes the propagation and amplification of order fluctuations (i.e., the bullwhip effect) in supply chain networks operated with linear and time-invariant inventory management policies. The supply chain network is allowed to include multiple customers (e.g., markets), any network structure, with or without sharing information. The paper characterizes the stream of orders placed by any supplier for any stationary customer demand processes, and gives exact formulas for the variance of the orders placed and the amplification of order fluctuations. The paper also derives robust analytical conditions, based only on inventory management policies, to predict the presence of the bullwhip effect for any network structure, any inventory replenishment policies, and arbitrary customer demand processes. Numerical examples show that the analytical results accurately quantify the bullwhip effect; managerial insights are drawn from the analysis. The methodology presented in this paper generalizes those in previous studies for serial supply chains.

Original languageEnglish (US)
Pages (from-to)799-810
Number of pages12
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Mar 16 2010


  • Frequency domain analysis
  • Network
  • Supply chain management
  • The bullwhip effect

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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