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Exploring the oscillatory dynamics of a forbidden returns inventory system

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  • Wang, Xun
  • Disney, Stephen M.
  • Wang, Jing

Abstract

We present an analytical investigation of the intrinsic oscillations in a nonlinear inventory system where excessive inventory cannot be returned to the supplier. Mathematically this is captured by a non-negative constraint on the replenishment order. By studying the eigenvalues of the characteristic matrices of the system, the criteria for different types of dynamic behaviour (including convergence, periodicity, quasi-periodicity, chaos, and divergence) are derived. The upper and lower bounds of the order and inventory oscillations are found via a time-domain analysis. Our results are verified by bifurcation diagrams. We find that the closer the replenishment rule feedback parameters are to the convergence area, the milder the intrinsic oscillation of the system.

Suggested Citation

  • Wang, Xun & Disney, Stephen M. & Wang, Jing, 2014. "Exploring the oscillatory dynamics of a forbidden returns inventory system," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 3-12.
    • Handle: RePEc:eee:proeco:v:147:y:2014:i:pa:p:3-12
    DOI: 10.1016/j.ijpe.2012.08.013
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    1. Hau L. Lee & Kut C. So & Christopher S. Tang, 2000. "The Value of Information Sharing in a Two-Level Supply Chain," Management Science, INFORMS, vol. 46(5), pages 626-643, May.
    2. Yossi Aviv, 2003. "A Time-Series Framework for Supply-Chain Inventory Management," Operations Research, INFORMS, vol. 51(2), pages 210-227, April.
    3. Hosoda, Takamichi & Disney, Stephen M., 2009. "Impact of market demand mis-specification on a two-level supply chain," International Journal of Production Economics, Elsevier, vol. 121(2), pages 739-751, October.
    4. Nagatani, Takashi & Helbing, Dirk, 2004. "Stability analysis and stabilization strategies for linear supply chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 644-660.
    5. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    6. Hwarng, H. Brian & Xie, Na, 2008. "Understanding supply chain dynamics: A chaos perspective," European Journal of Operational Research, Elsevier, vol. 184(3), pages 1163-1178, February.
    7. Hosoda, Takamichi & Disney, Stephen M., 2012. "A delayed demand supply chain: Incentives for upstream players," Omega, Elsevier, vol. 40(4), pages 478-487.
    8. Dejonckheere, J. & Disney, S. M. & Lambrecht, M. R. & Towill, D. R., 2004. "The impact of information enrichment on the Bullwhip effect in supply chains: A control engineering perspective," European Journal of Operational Research, Elsevier, vol. 153(3), pages 727-750, March.
    9. Sterman, John D., 1989. "Misperceptions of feedback in dynamic decision making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 43(3), pages 301-335, June.
    10. Geary, S. & Disney, S.M. & Towill, D.R., 2006. "On bullwhip in supply chains--historical review, present practice and expected future impact," International Journal of Production Economics, Elsevier, vol. 101(1), pages 2-18, May.
    11. Disney, S. M. & Towill, D. R., 2003. "On the bullwhip and inventory variance produced by an ordering policy," Omega, Elsevier, vol. 31(3), pages 157-167, June.
    12. John D. Sterman, 1989. "Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment," Management Science, INFORMS, vol. 35(3), pages 321-339, March.
    13. Wang, Kung-Jeng & Wee, Hui-Ming & Gao, Shin-Feng & Chung, Shen-Lian, 2005. "Production and inventory control with chaotic demands," Omega, Elsevier, vol. 33(2), pages 97-106, April.
    14. Disney, S. M. & Towill, D. R., 2003. "The effect of vendor managed inventory (VMI) dynamics on the Bullwhip Effect in supply chains," International Journal of Production Economics, Elsevier, vol. 85(2), pages 199-215, August.
    15. Dejonckheere, J. & Disney, S. M. & Lambrecht, M. R. & Towill, D. R., 2003. "Measuring and avoiding the bullwhip effect: A control theoretic approach," European Journal of Operational Research, Elsevier, vol. 147(3), pages 567-590, June.
    16. Wu, Y. & Zhang, D.Z., 2007. "Demand fluctuation and chaotic behaviour by interaction between customers and suppliers," International Journal of Production Economics, Elsevier, vol. 107(1), pages 250-259, May.
    17. Frank Chen & Zvi Drezner & Jennifer K. Ryan & David Simchi-Levi, 2000. "Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information," Management Science, INFORMS, vol. 46(3), pages 436-443, March.
    18. Vedran Kordic (ed.), 2008. "Supply Chain," Books, IntechOpen, number 26, January-J.
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    8. Spiegler, Virginia L.M. & Naim, Mohamed M., 2017. "Investigating sustained oscillations in nonlinear production and inventory control models," European Journal of Operational Research, Elsevier, vol. 261(2), pages 572-583.
    9. Wang, Xun & Disney, Stephen M., 2016. "The bullwhip effect: Progress, trends and directions," European Journal of Operational Research, Elsevier, vol. 250(3), pages 691-701.
    10. A. V. Thomas & Biswajit Mahanty, 2021. "Dynamic assessment of control system designs of information shared supply chain network experiencing supplier disruption," Operational Research, Springer, vol. 21(1), pages 425-451, March.
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