Robust Stability Analysis of Decentralized Supply Chains

  • Yanfeng OuyangEmail author
  • Carlos Daganzo
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 151)


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.


Supply Chain Root Mean Square Error Linear Matrix Inequality Customer Demand Bullwhip Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Aviv Y (2003) A time-series framework for supply chain inventory management. Oper Res 51(2):210–227CrossRefGoogle Scholar
  2. Baganha MP, Cohen MA (1998) The stabilizing effect of inventory in supply chains. Oper Res 46(3):572–583CrossRefGoogle Scholar
  3. Blinder AS (1986) Can the production smoothing model of inventory behavior be saved? Q J Econ 101:431–454CrossRefGoogle Scholar
  4. Chen F, Drezner Z, Ryan J, Simchi-Levi D (2000a) Quantifying the bullwhip effect in a simple supply chain: The impact of forecasting, lead times, and information. Manage Sci 46(3): 436–443CrossRefGoogle Scholar
  5. Chen F, Ryan J, Simchi-Levi D (2000b) The impact of exponential smoothing forecasts on the bullwhip effect. Nav Res Logistics 47(4):271–286CrossRefGoogle Scholar
  6. Cooke JA (1993) The $30 Billion Promise. Traffic Manag 32:57–59Google Scholar
  7. Cachon G (2007) In search of the bullwhip effect. Manuf Serv Oper Manage 9(4):457–479CrossRefGoogle Scholar
  8. Daganzo CF (2001) A theory of supply chains. Institute of Transportation Studies Research Report, UCB-ITS-RR-2001-7. University of California, Berkeley, CA, USAGoogle Scholar
  9. Daganzo CF (2003) A Theory of Supply Chains. Springer, Heidelberg, GermanyGoogle Scholar
  10. Daganzo CF (2004) On the stability of supply chains. Oper Res 52(6):909–921CrossRefGoogle Scholar
  11. Dejonckheere J, Disney SM, Lambrecht MR, Towill DR (2003) Measuring and avoiding the bullwhip effect: A control theoretic approach. Eur J Oper Res 147:567–590CrossRefGoogle Scholar
  12. Forrester J (1958) Industrial dynamics, a major breakthrough for decision makers. Harv Bus Rev 36:37–66Google Scholar
  13. Forrester J (1961) Industrial Dynamics. MIT Press, Cambridge, MAGoogle Scholar
  14. Gaur V, Giloni A, Seshadri S (2005) Information sharing in a supply chain under ARMA demand. Manage Sci 51(6):961–969CrossRefGoogle Scholar
  15. Gavirneni S, Kapuscinski R, Tayur S (1999) Value of information in capacitated supply chains. Manage Sci 45(1):16–24CrossRefGoogle Scholar
  16. Gilbert K (2005) An ARIMA supply chain model. Manage Sci 51(2):305–310CrossRefGoogle Scholar
  17. Goodwin J, Franklin S (1994) The beer distribution game: using simulation to teach systems thinking. J Manage Dev 13(8):7–15CrossRefGoogle Scholar
  18. Graves S (1999) A single item inventory model for a nonstationary demand process. Manuf Serv Oper Manage 1:50–61CrossRefGoogle Scholar
  19. Holt CC, Modigliani F, Muth J, Simon HA (1960) Planning Production, Inventories and Work Force. Prentice Hall, Englewood Cliffs, NYGoogle Scholar
  20. Kahn J (1987) Inventories and the volatility of production. Am Econ Rev 77:667–679Google Scholar
  21. Kaminsky P, Simchi-Levi D (1998) The Computerized Beer Game: Teaching the Value of Integrated Supply Chain Management. In: Hau Lee, Shu Ming Ng (eds) Supply Chain and Technology Management, The Production and Operations Management Society.Google Scholar
  22. Lee HL, Padmanabhan V, Whang S (1997a) The Bullwhip effect in supply chains. Sloan Manage Rev 38(3):93–102Google Scholar
  23. Lee HL, Padmanabhan V, Whang S (1997b) Information Distortion in a Supply Chain: The Bullwhip Effect. Manage Sci 43(4):546–558CrossRefGoogle Scholar
  24. Lee HL, So KC, Tang CS (2000) The value of information sharing in a two level supply chain. Manage Sci 46(5):628–643CrossRefGoogle Scholar
  25. Magee JF (1956) Guides to inventory control (Part II). Harv Bus Rev 1956:106–116Google Scholar
  26. Magee JF, Boodman D (1967) Production Planning and Inventory Control, 2nd edn. McGraw-Hill, NYGoogle Scholar
  27. Mariton M (1990) Jump Linear Systems in Automatic Control. Marcel Dekker Inc., New York, USAGoogle Scholar
  28. Naish HF (1994) Production smoothing in the linear quadratic inventory model. Econ J 104(425): 864–875CrossRefGoogle Scholar
  29. Ouyang Y (2005) System-level Stability and Optimality of Decentralized Supply Chains. Ph.D. Dissertation, University of California, BerkeleyGoogle Scholar
  30. Ouyang Y (2007) The effect of information sharing on supply chain stability and the bullwhip effect. Eur J Oper Res 182(3):1107–1121CrossRefGoogle Scholar
  31. Ouyang Y, Daganzo CF (2006) Characterization of the bullwhip effect in linear, time-invariant supply chains: some formulae and tests. Manage Sci 52(10):1544–1556CrossRefGoogle Scholar
  32. Ouyang Y, Daganzo CF (2006) Counteracting the bullwhip effect with decentralized negotiations and advance demand information. Physica A 363(1):14–23CrossRefGoogle Scholar
  33. Ouyang Y, Daganzo CF (2006) Robust tests for the bullwhip effect in supply chains with stochastic dynamics. Eur J Oper Res 185(1):340–353CrossRefGoogle Scholar
  34. Ouyang Y, Li X (2010) The bullwhip effect in supply chain networks. Eur J Oper Res 201:799–810CrossRefGoogle Scholar
  35. Ramey VA (1991) Nonconvex costs and the behavior of inventories J Polit Econ 99:306–334Google Scholar
  36. Ridder A, van der Laan E, Salomon M (1998) How Larger Demand Variability May Lead to Lower Costs in the Newsvendor Problem. Oper Res 46(6):934–946CrossRefGoogle Scholar
  37. Seiler PJ (2001) Coordinated Control of Unmanned Aerial Vehicles. Ph.D. Dissertation, University of California, BerkeleyGoogle Scholar
  38. So KC, Zheng X (2003) Impact of supplier’s lead time and forecast demand updating on retailer’s order quantity variability in a two-level supply chain. Int J Prod Econ 86:169–179CrossRefGoogle Scholar
  39. Sterman J (1989) Modelling managerial behaviour: Misperceptions of feedback in a dynamic decision making experiment. Manage Sci 35(3):321–339CrossRefGoogle Scholar
  40. Swaroop D, Hedrick JK (1996) String stability of interconnected systems. IEEE Trans Automat Contr 41(3):349–357CrossRefGoogle Scholar
  41. Zhang X (2004) Evolution of ARMA demand in supply chains. Manuf Serv Oper Manage 6: 195–198CrossRefGoogle Scholar
  42. Zipkin PH (2000) Foundations of Inventory Management McGraw-Hill/Irwin, New York, USAGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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