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Stability analysis of a constrained inventory system

Wang, Xun and Disney, Stephen Michael 2011. Stability analysis of a constrained inventory system. Presented at: 21st International Conference on Production Research : Innovation in Product and Production, Stuttgart, Germany, 31 July - 4 August 2011. Published in: Spath, Dieter and Ilg, Rolf eds. 21st International Conference on Production Research (ICPR 21) Conference Proceedings. Fraunhofer Verlag,

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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: Conference or Workshop Item (Paper)
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: logistics; operations management
Publisher: Fraunhofer Verlag
ISBN: 3839602939
Related URLs:
Date of First Compliant Deposit: 25 August 2017
Last Modified: 03 Mar 2020 02:27

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