Stability analysis of constrained inventory systems with transportation delay
AbstractStability 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 223 (2012)
Issue (Month): 1 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/eor
Inventory; Logistics; System dynamics; Complexity theory;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.