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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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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Spiegler, Virginia L.M. & Naim, Mohamed M. & Towill, Denis R. & Wikner, Joakim, 2016. "A technique to develop simplified and linearised models of complex dynamic supply chain systems," European Journal of Operational Research, Elsevier, vol. 251(3), pages 888-903.
    2. Phillips, Christina Jane & Nikolopoulos, Konstantinos, 2019. "Forecast quality improvement with Action Research: A success story at PharmaCo," International Journal of Forecasting, Elsevier, vol. 35(1), pages 129-143.
    3. Li, Qinyun & Disney, Stephen M. & Gaalman, Gerard, 2014. "Avoiding the bullwhip effect using Damped Trend forecasting and the Order-Up-To replenishment policy," International Journal of Production Economics, Elsevier, vol. 149(C), pages 3-16.
    4. Ponte, Borja & Puche, Julio & Rosillo, Rafael & de la Fuente, David, 2020. "The effects of quantity discounts on supply chain performance: Looking through the Bullwhip lens," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    5. 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.
    6. 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.
    7. V.L.M. Spiegler & A.T. Potter & M.M. Naim & D.R. Towill, 2016. "The value of nonlinear control theory in investigating the underlying dynamics and resilience of a grocery supply chain," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 265-286, January.
    8. Lin, Junyi & Naim, Mohamed M. & Spiegler, Virginia L.M., 2020. "Delivery time dynamics in an assemble-to-order inventory and order based production control system," International Journal of Production Economics, Elsevier, vol. 223(C).

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