Skip Navigation



IMA Journal of Management Mathematics Advance Access published online on December 13, 2007
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpm033
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
19/2/101    most recent
dpm033v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Disney, S. M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Supply chain aperiodicity, bullwhip and stability analysis with Jury's inners

Stephen M. Disney{dagger}

Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff CF10 3EU, UK

{dagger} Email: disney{at}cardiff.ac.uk.

Received on 18 October 2006. Accepted on 3 October 2007.

Jury (1974, Inners and the Stability of Dynamic Systems. New York: John Wiley) presents a novel method for the analysis of dynamical systems based on matrices of the coefficients of the systems transfer function and its ‘inners’. Here, we exploit his procedure for an analysis of a supply chain replenishment or ordering decision known as the order-up-to policy. We study the discrete-time case and generalize the classical order-up-to policy by the addition of two independent proportional controllers in the policy's feedback loops. The addition of the proportional controllers is well known to allow the order-up-to policy to eliminate the bullwhip problem and we quantify this herein using Jury's inners approach. However, care has to be taken with the use of independent controllers as they can introduce stability problems. This is because the roots of the characteristic equation become complex, and they may even move out of the unit circle in the z-plane. We identify the conditions of stability using Jury's inners approach. We also investigate further the root distribution in the characteristic equation to identify the conditions under which the order-up-to policy is aperiodic. An aperiodic system has only a limited number of maxima and minima in its dynamic response. Thus, aperiodicity is an important characteristic of a supply chain replenishment policy as it will not induce rogue seasonality.

Keywords: supply chains; aperiodicity; bullwhip; stability; z-transforms; order-up-to policy


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.