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Stability analysis of constrained inventory systems with transportation delay

Wang, Xun, Disney, Stephen Michael and Wang, Jing 2012. Stability analysis of constrained inventory systems with transportation delay. European Journal of Operational Research 223 (1) , pp. 86-95. 10.1016/j.ejor.2012.06.014

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Centre for Advanced Manufacturing Systems At Cardiff (CAMSAC)
Subjects: H Social Sciences > HE Transportation and Communications
Uncontrolled Keywords: Inventory; Logistics; System dynamics; Complexity theory
Additional Information: PDF uploaded in accordance with publisher's policy at
Publisher: Elsevier
ISSN: 0377-2217
Date of First Compliant Deposit: 30 March 2016
Last Modified: 03 Mar 2020 02:29

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