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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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    8. Ponte, Borja & Dominguez, Roberto & Cannella, Salvatore & Framinan, Jose M., 2022. "The implications of batching in the bullwhip effect and customer service of closed-loop supply chains," International Journal of Production Economics, Elsevier, vol. 244(C).
    9. 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.
    10. Chong, You Quan & Wang, Bin & Yue Tan, Gladys Li & Cheong, Siew Ann, 2014. "Diversified firms on dynamical supply chain cope with financial crisis better," International Journal of Production Economics, Elsevier, vol. 150(C), pages 239-245.
    11. 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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