Skip to main content
SpringerLink
Log in

Robust Stability Analysis of Decentralized Supply Chains

  • Chapter
  • First Online:
Planning Production and Inventories in the Extended Enterprise

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 151))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This linear policy utilizes current inventory position, current in-stock inventory, and past orders received. It is similar to the generalized kanban policy in Zipkin [2000]. For more details see Dejonckheere et al. [2003], pages 582–584.

  2. 2.

    This constant lead time assumption is also used in the literature, e.g., Chen et al. [2000a,b], Gavirneni et al. [1999], Lee et al. [2000]. It is relaxed in Sect.18.3.

  3. 3.

    This is unrelated to the “gain” or “inventory gain” defined earlier.

  4. 4.

    This is largely a matter of taste. The same results are obtained with both approaches. See Appendix A in Daganzo [2003] for more details.

  5. 5.

    Subscripts are added to capture inhomogeneity.

  6. 6.

    Just-in-time chains can operate in this mode.

References

  • Aviv Y (2003) A time-series framework for supply chain inventory management. Oper Res 51(2):210–227

    Google Scholar 

  • Baganha MP, Cohen MA (1998) The stabilizing effect of inventory in supply chains. Oper Res 46(3):572–583

    Google Scholar 

  • Blinder AS (1986) Can the production smoothing model of inventory behavior be saved? Q J Econ 101:431–454

    Google Scholar 

  • 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): 436–443

    Google Scholar 

  • Chen F, Ryan J, Simchi-Levi D (2000b) The impact of exponential smoothing forecasts on the bullwhip effect. Nav Res Logistics 47(4):271–286

    Google Scholar 

  • Cooke JA (1993) The $30 Billion Promise. Traffic Manag 32:57–59

    Google Scholar 

  • Cachon G (2007) In search of the bullwhip effect. Manuf Serv Oper Manage 9(4):457–479

    Google Scholar 

  • Daganzo CF (2001) A theory of supply chains. Institute of Transportation Studies Research Report, UCB-ITS-RR-2001-7. University of California, Berkeley, CA, USA

    Google Scholar 

  • Daganzo CF (2003) A Theory of Supply Chains. Springer, Heidelberg, Germany

    Google Scholar 

  • Daganzo CF (2004) On the stability of supply chains. Oper Res 52(6):909–921

    Google Scholar 

  • Dejonckheere J, Disney SM, Lambrecht MR, Towill DR (2003) Measuring and avoiding the bullwhip effect: A control theoretic approach. Eur J Oper Res 147:567–590

    Google Scholar 

  • Forrester J (1958) Industrial dynamics, a major breakthrough for decision makers. Harv Bus Rev 36:37–66

    Google Scholar 

  • Forrester J (1961) Industrial Dynamics. MIT Press, Cambridge, MA

    Google Scholar 

  • Gaur V, Giloni A, Seshadri S (2005) Information sharing in a supply chain under ARMA demand. Manage Sci 51(6):961–969

    Google Scholar 

  • Gavirneni S, Kapuscinski R, Tayur S (1999) Value of information in capacitated supply chains. Manage Sci 45(1):16–24

    Google Scholar 

  • Gilbert K (2005) An ARIMA supply chain model. Manage Sci 51(2):305–310

    Google Scholar 

  • Goodwin J, Franklin S (1994) The beer distribution game: using simulation to teach systems thinking. J Manage Dev 13(8):7–15

    Google Scholar 

  • Graves S (1999) A single item inventory model for a nonstationary demand process. Manuf Serv Oper Manage 1:50–61

    Google Scholar 

  • Holt CC, Modigliani F, Muth J, Simon HA (1960) Planning Production, Inventories and Work Force. Prentice Hall, Englewood Cliffs, NY

    Google Scholar 

  • Kahn J (1987) Inventories and the volatility of production. Am Econ Rev 77:667–679

    Google Scholar 

  • 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 

  • Lee HL, Padmanabhan V, Whang S (1997a) The Bullwhip effect in supply chains. Sloan Manage Rev 38(3):93–102

    Google Scholar 

  • Lee HL, Padmanabhan V, Whang S (1997b) Information Distortion in a Supply Chain: The Bullwhip Effect. Manage Sci 43(4):546–558

    Google Scholar 

  • Lee HL, So KC, Tang CS (2000) The value of information sharing in a two level supply chain. Manage Sci 46(5):628–643

    Google Scholar 

  • Magee JF (1956) Guides to inventory control (Part II). Harv Bus Rev 1956:106–116

    Google Scholar 

  • Magee JF, Boodman D (1967) Production Planning and Inventory Control, 2nd edn. McGraw-Hill, NY

    Google Scholar 

  • Mariton M (1990) Jump Linear Systems in Automatic Control. Marcel Dekker Inc., New York, USA

    Google Scholar 

  • Naish HF (1994) Production smoothing in the linear quadratic inventory model. Econ J 104(425): 864–875

    Google Scholar 

  • Ouyang Y (2005) System-level Stability and Optimality of Decentralized Supply Chains. Ph.D. Dissertation, University of California, Berkeley

    Google Scholar 

  • Ouyang Y (2007) The effect of information sharing on supply chain stability and the bullwhip effect. Eur J Oper Res 182(3):1107–1121

    Google Scholar 

  • Ouyang Y, Daganzo CF (2006) Characterization of the bullwhip effect in linear, time-invariant supply chains: some formulae and tests. Manage Sci 52(10):1544–1556

    Google Scholar 

  • Ouyang Y, Daganzo CF (2006) Counteracting the bullwhip effect with decentralized negotiations and advance demand information. Physica A 363(1):14–23

    Google Scholar 

  • Ouyang Y, Daganzo CF (2006) Robust tests for the bullwhip effect in supply chains with stochastic dynamics. Eur J Oper Res 185(1):340–353

    Google Scholar 

  • Ouyang Y, Li X (2010) The bullwhip effect in supply chain networks. Eur J Oper Res 201:799–810

    Google Scholar 

  • Ramey VA (1991) Nonconvex costs and the behavior of inventories J Polit Econ 99:306–334

    Google Scholar 

  • 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):934–946

    Google Scholar 

  • Seiler PJ (2001) Coordinated Control of Unmanned Aerial Vehicles. Ph.D. Dissertation, University of California, Berkeley

    Google Scholar 

  • 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 86:169–179

    Google Scholar 

  • Sterman J (1989) Modelling managerial behaviour: Misperceptions of feedback in a dynamic decision making experiment. Manage Sci 35(3):321–339

    Google Scholar 

  • Swaroop D, Hedrick JK (1996) String stability of interconnected systems. IEEE Trans Automat Contr 41(3):349–357

    Google Scholar 

  • Zhang X (2004) Evolution of ARMA demand in supply chains. Manuf Serv Oper Manage 6: 195–198

    Google Scholar 

  • Zipkin PH (2000) Foundations of Inventory Management McGraw-Hill/Irwin, New York, USA

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Yanfeng Ouyang

Authors
  1. Yanfeng Ouyang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos Daganzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanfeng Ouyang .

Editor information

Editors and Affiliations

  1. Decision Technologies, Intel Corporation, W. Chandler Blvd. 5000, Chandler, 85226, Arizona, USA

    Karl G. Kempf

  2. School of Industrial &, Systems Engineering, Georgia Institute of Technology, Ferst Drive NW., 765, Atlanta, 30332-0205, Georgia, USA

    Pınar Keskinocak

  3. , Edward P. Fitts Department of Industrial, North Carolina State University, Daniels Hall 300, Raleigh, 27695, North Carolina, USA

    Reha Uzsoy

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Ouyang, Y., Daganzo, C. (2011). Robust Stability Analysis of Decentralized Supply Chains. In: Kempf, K., Keskinocak, P., Uzsoy, R. (eds) Planning Production and Inventories in the Extended Enterprise. International Series in Operations Research & Management Science, vol 151. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6485-4_18

Download citation

Publish with us

Policies and ethics

Search

Navigation