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Stability analysis of constrained inventory systems with transportation delay

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

    Stability is a fundamental design property of inventory systems. However, the often exploited linearity assumptions in the current literature create a major gap between theory and practice. In this paper the stability of a constrained production and inventory system with a Forbidden Returns constraint (that is, a non-negative order rate) is studied via a piecewise linear model, an eigenvalue analysis and a simulation investigation. The APVIOBPCS (Automatic Pipeline, Variable Inventory and Order Based Production Control System) and EPVIOBPCS (Estimated Pipeline, Variable Inventory and Order Based Production Control System) replenishment policies are adopted. Surprisingly, all kinds of non-linear dynamical behaviours of systems can be observed in these simple models. Exact expressions of the asymptotic stability boundaries and Lyapunovian stability boundaries are derived when actual and perceived transportation lead-time is 1 and 2 periods long respectively. Asymptotically stable regions in the non-linear Forbidden Return systems are identical to the stable regions in its unconstrained counterpart. However, regions of bounded fluctuations that continue forever, including both periodicity and chaos, exist in the parametrical plane outside the asymptotically stable region. Simulation shows a complex and delicate structure in these regions. The results suggest that accurate lead-time information is essential to eliminate inventory drift and instability and that ordering policies have to be designed properly in accordance with the actual lead-time to avoid these fluctuations and divergence.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 1 ()
    Pages: 86-95

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:86-95

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Inventory; Logistics; System dynamics; Complexity theory;

    References

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    1. 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.
    2. 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.
    3. Kim, Jeon G. & Chatfield, Dean & Harrison, Terry P. & Hayya, Jack C., 2006. "Quantifying the bullwhip effect in a supply chain with stochastic lead time," European Journal of Operational Research, Elsevier, vol. 173(2), pages 617-636, September.
    4. 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.
    5. 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.
    6. 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.
    7. Larsen, Erik R. & Morecroft, John D. W. & Thomsen, Jesper S., 1999. "Complex behaviour in a production-distribution model," European Journal of Operational Research, Elsevier, vol. 119(1), pages 61-74, November.
    8. 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.
    9. Rossi, Roberto & Tarim, S. Armagan & Hnich, Brahim & Prestwich, Steven, 2010. "Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times," International Journal of Production Economics, Elsevier, vol. 127(1), pages 180-189, September.
    10. Disney, S.M. & Towill, D.R., 2005. "Eliminating drift in inventory and order based production control systems," International Journal of Production Economics, Elsevier, vol. 93(1), pages 331-344, January.
    11. 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.
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