OR Spectrum

, Volume 28, Issue 1, pp 127–149 | Cite as

Bullwhip and inventory variance in a closed loop supply chain

  • Li ZhouEmail author
  • Stephen M. Disney
Regular Article


A simple dynamic model of a hybrid manufacturing/remanufacturing system is investigated. In particular we study an infinite horizon, continuous time, APIOBPCS (Automatic Pipeline Inventory and Order Based Production Control System) model. We use Åström’s method to quantify variance ratios in the closed loop supply chain. Specifically we highlight the effect of a combined “in-use” and remanufacturing lead-time and the return rate on the inventory variance and bullwhip produced by the ordering policy. Our results clearly show that a larger return rate leads to less bullwhip and less inventory variance in the plant producing new components. Thus returns can be used to absorb demand fluctuations to some extent. Longer remanufacturing and “in-use” lead-times have less impact at reducing inventory variance and bullwhip than shorter lead-times. We find that, within our specified system, that inventory variance and bullwhip is always less in supply chains with returns than supply chains without returns. We conclude by separating out the remanufacturing lead-time from the “in-use” lead-time and investigating its impact on our findings. We find that short remanufacturing lead-times do not qualitatively change our results.


Manufacturing Remanufacturing Inventory variance Bullwhip Return rate Lead-time 


  1. Åström KJ (1970) Introduction to stochastic control theory. Richard Bellman, University of Southern CaliforniaGoogle Scholar
  2. Barron Y, Frostig E, Levikson B (2004) Analysis of R out of N systems with several repairmen, exponential life times and phase type repair times: an algorithmic approach. Eur J Oper Res (forthcoming); available online at
  3. Chen YF, Drezner Z, Ryan JK, Simchi-Levi D (2000) Quantifying the Bullwhip effect in a simple supply chain: the impact of forecasting, lead-times and information. Manage Sci 46:436–443CrossRefGoogle Scholar
  4. Dejonckheere J, Disney SM, Farasyn I, Janssen F, Lambrecht M, Towill DR, Van de Velde W (2002) Production and inventory control: the variability trade-off. Proceedings of the 9th EUROMA, June 2–4 2002, Copenhagen, Denmark, ISBN 1 85790 088xGoogle Scholar
  5. Dejonckheere J, Disney SM, Lambrecht MR, Towill DR (2003) Measuring and avoiding the bullwhip effect: a control theoretic approach. Eur J Oper Res 47(3):567–590CrossRefGoogle Scholar
  6. Disney SM, Grubbström RW (2003) The economic consequences of a production and inventory control policy, 17th International Conference on Production Research, Virginia, USA, 3–7 AugustGoogle Scholar
  7. Disney SM, Towill DR (2003) On the bullwhip and inventory variance produced by an ordering policy. OMEGA: Int J Manag Sci 31(3):157–167CrossRefGoogle Scholar
  8. Disney SM, Towill DR, Van de Velde W (2004) Variance amplification and the golden ratio in production and inventory control. Int J Prod Econ 90(3):295–309CrossRefGoogle Scholar
  9. Fleischmann M, Kuik R (2003) On optimal inventory control with independent stochastic item returns. Eur J Oper Res 151:25–37CrossRefGoogle Scholar
  10. Fleischmann M, Bolemhof-Ruwaard J, Dekker R, van der Laan E, van Nunen J, Van Wassenhove L (1997) Quantitative models for reverse logistics: a review. Eur J Oper Res 103:1–17CrossRefGoogle Scholar
  11. Guide VDR Jr (2000) Production planning and control for remanufacturing: industry practice and research needs. J Oper Manag 18:467–483CrossRefGoogle Scholar
  12. Inderfurth K, van der Laan E (2001) Lead-time effects and policy improvement for stochastic inventory control with remanufacturing. Int J Prod Econ 71:381–390CrossRefGoogle Scholar
  13. John S, Naim MM, Towill DR (1994) Dynamic analysis of a WIP compensated decision support system. Int J Manuf Syst Des 1(4):283–297Google Scholar
  14. Kiesmüller GP (2003) A new approach for controlling a hybrid stochastic manufacturing/remanufacturing system with inventories and different lead-times. Eur J Oper Res 147:62–71CrossRefGoogle Scholar
  15. Kiesmüller GP, van der Laan EA (2001) An inventory model with dependent product demands and returns. Int J Prod Econ 72:73–87CrossRefGoogle Scholar
  16. Kleber R, Minner S, Kiesmüller G (2002) A continuous time inventory model for a product recovery system with multiple options. Int J Prod Econ 79:121–141CrossRefGoogle Scholar
  17. Kondo Y, Deguchi K, Hayashi Y (2003) Reversibility and disassembly time of part connection. Resour Conserv Recycl 38:175–184CrossRefGoogle Scholar
  18. Lee HL, Padmanabhan V, Whang S (1997) The bullwhip effect in supply chains. Sloan Management Review, Spring, pp 93–102Google Scholar
  19. Lin GC, Kroll DE, Lin CJ (2005) Determining a common production cycle time for an economic lot scheduling problem with deteriorating items. Eur J Oper Res (forthcoming); available online at
  20. Magee JF (1958) Production planning and inventory control. McGraw-Hill, New York, pp 80–83Google Scholar
  21. Mahadevan B, Pyke DF, Fleischmann M (2003) Periodic review, push inventory policies for remanufacturing. Eur J Oper Res 151(3):536–551CrossRefGoogle Scholar
  22. Muckstadt J, Isaac MH (1981) An analysis of single item inventory systems with returns. Nav Res Logist Q 28:237–254CrossRefGoogle Scholar
  23. Newton GC, Gould LA, Kaiser JF (1957) Analytical design of linear feedback controls. Wiley, New York, pp 39–51Google Scholar
  24. Nise NS (1994) Control systems engineering. California, Benjamin/CummingsGoogle Scholar
  25. Seitz MA, Disney SM, Naim MM (2003) Managing product recovery operations: the case of automotive engine remanufacturing. EUROMA POMS Conference, Como Lake, Italy, 16–18 June, Vol 2, pp 1045–1053Google Scholar
  26. Simon HA (1952) On the application of servomechanism theory to the study of production control. Econometrica 20:247–268CrossRefGoogle Scholar
  27. Sterman J (1989) Modelling managerial behaviour: misperceptions of feedback in a dynamic decision making experiment. Manage Sci 35(3):321–339CrossRefGoogle Scholar
  28. Tang O, Naim MM (2004) The impact of information transparency on the dynamic behaviour of a hybrid manufacturing/remanufacturing system. Int J Prod Res 42(19):4135–4152CrossRefGoogle Scholar
  29. Teunter RH, Vlachos D (2002) On the necessity of a disposal option for returned items that can be remanufactured. Int J Prod Econ 75:257–266CrossRefGoogle Scholar
  30. Thierry M, Salomon M, van Nunen J, van Wassenhove L (1995) Strategic issues in product recovery management. Calif Manage Rev 37(2):114–135Google Scholar
  31. Towill DR (1970) Transfer function techniques for control engineers. Lliffe Books, LondonGoogle Scholar
  32. Towill DR (1982a) Optimisation of an inventory and order based production control system. Proceedings of the 2nd International Symposium on Inventories, Budapest, HungaryGoogle Scholar
  33. Towill DR (1982b) Dynamic analysis of an inventory and order based production control system. Int J Prod Res 20:369–383CrossRefGoogle Scholar
  34. Towill DR, Lambrecht MR, Disney SM, Dejonckheere J (2001) Explicit filters and supply chain design. Proceedings of the EUROMA conference, Salzburg, Austria, pp 401–411Google Scholar
  35. van der Laan E (2003) An NPV and AC analysis of a stochastic inventory system with joint manufacturing and remanufacturing. Int J Prod Econ 81–82:317–331CrossRefGoogle Scholar
  36. van der Laan E, Salomon M, Dekker R (1999a) An investigation of lead-time effects in manufacturing/remanufacturing systems under simple PUSH and PULL control strategies. Eur J Oper Res 115:195–214CrossRefGoogle Scholar
  37. van der Laan E, Salomon M, Dekker R, van Wassenhove L (1999b) Inventory control in hybrid systems with remanufacturing. Manage Sci 45(5):733–747Google Scholar
  38. Wang JH (2002) Adaptation of the beer game to reverse logistics. MSc Thesis, Cardiff Business School, Wales, UKGoogle Scholar
  39. Wang CH (2004) The impact of a free-repair warranty policy on EMQ model for imperfect production systems. Comput Oper Res 31:2021–2035CrossRefGoogle Scholar
  40. Warburton RDH, Disney SM (2005) Variance amplification: the equivalence of discrete and continuous time analyses, 18th International Conference on Production Research, Salerno, Italy, 1–4 AugustGoogle Scholar
  41. Wikner J, Towill DR, Naim MM (1991) Smoothing supply chain dynamics. Int J Prod Econ 22:231–248CrossRefGoogle Scholar
  42. Zhou L, Disney SM, Lalwani CS, Wu HL (2004) Reverse logistics: a study of bullwhip in continuous time. Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, China, June 14–18, 2004, Vol 6(4), pp 3539–3542Google Scholar
  43. Zhou L, Naim MM, Tang O, Towill DR (2005) Dynamic performance of a hybrid inventory system with a Kanban policy in remanufacturing process. OMEGA: Int J Manag Sci (forthcoming); available online on 5 March 2005Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Logistics System Dynamics Group, Cardiff Business SchoolCardiff UniversityCardiffUK

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