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Stability analysis and stabilization strategies for linear supply chains

Author

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  • Nagatani, Takashi
  • Helbing, Dirk

Abstract

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:335:y:2004:i:3:p:644-660
    DOI: 10.1016/j.physa.2003.12.020
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    Citations

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    Cited by:

    1. Lin, Junyi & Huang, Hongfu & Li, Shanshan & Naim, Mohamed M., 2023. "On the dynamics of order pipeline inventory in a nonlinear order-up-to system," International Journal of Production Economics, Elsevier, vol. 266(C).
    2. 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).
    3. Mizgier, Kamil J. & Wagner, Stephan M. & Holyst, Janusz A., 2012. "Modeling defaults of companies in multi-stage supply chain networks," International Journal of Production Economics, Elsevier, vol. 135(1), pages 14-23.
    4. Konishi, Keiji, 2010. "A tuning strategy to avoid blocking and starving in a buffered production line," European Journal of Operational Research, Elsevier, vol. 200(2), pages 616-620, January.
    5. 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.
    6. Li, Gang & Yang, Hongjiao & Sun, Linyan & Ji, Ping & Feng, Lei, 2010. "The evolutionary complexity of complex adaptive supply networks: A simulation and case study," International Journal of Production Economics, Elsevier, vol. 124(2), pages 310-330, April.
    7. Scholz-Reiter, Bernd & Tervo, Jan Topi & Freitag, Michael, 2006. "Phase-synchronisation in continuous flow models of production networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 32-38.
    8. Kastsian, Darya & Mönnigmann, Martin, 2011. "Optimization of a vendor managed inventory supply chain with guaranteed stability and robustness," International Journal of Production Economics, Elsevier, vol. 131(2), pages 727-735, June.
    9. Helbing, Dirk & Treiber, Martin & Kesting, Arne, 2006. "Understanding interarrival and interdeparture time statistics from interactions in queuing systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 62-72.
    10. Wang, Xun & Disney, Stephen M. & Wang, Jing, 2012. "Stability analysis of constrained inventory systems with transportation delay," European Journal of Operational Research, Elsevier, vol. 223(1), pages 86-95.

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