Modeling and Its Stability Analysis of Supply Chain with Grey and Time Delay Properties

Abstract

Abstract: In supply chain management, it is important to operate a supply chain smoothly. However, with grey and time delay properties, it is very challenging to model and control a supply chain. By using interval gray characteristics matrix and time delay system method, a multilayer model with grey and time delay properties is developed for such a supply chain. Then, a Lyapunov function is presented to analyze the stability of the system. Thus, an effective and practical criterion of stability is obtained. A supply chain system with 2layer interval grey and time delay is used to test the performance of the proposed method. By using Matlab 70, numerical results show that the supply chain system is randomly stable. The results obtained are useful and can be used as guide in practical application.

Key words: grey system, supply chain modeling, stability analysis, Lyapunov function

Zhang Xuelong1,2,Wang Daoping1, Zhao Xiangzhong2. Modeling and Its Stability Analysis of Supply Chain with Grey and Time Delay Properties[J]. Industrial Engineering Journal , 2012, 15(3): 20-23.

References

［1］黄小原,葛汝刚.动态供应链与控制问题研究进展［J］.控制与决策,2008,23(11):1201-1204. Huang X Y, Ge R G. Survey of dynamic supply chain and control［J］.Control and Decision,2008,23(11):1201-1204. ［2］Disney S M, Towill D R. A procedure for the optimization of the dynamic response of a vendor managed inventory system［J］. Computer and Industrial Engineering,2002,43(1):27-58. ［3］Geary S, Disney S M, Towill D R. On bullwhip in supply chain historical review: present practice and expected future impact［J］. Internationl Journal of Production Research,2006,101(1):2-18. ［4］Schwartz J D, Wang W, Rivera D E. Simulationbased optimization of process control policies for inventory management in supply chains［J］.Automatica,2006,42(8):1311-1320. ［5］黄小原,郭海峰,卢震.供应链时滞系统模型及其牛鞭效应的H∞控制［J］.系统工程学报,2005,20(6): 585-590. 〖DW〗Huang X Y, Guo H F, Lu Z. H∞ Control of supply chain time delay system model and its bullwhip effect［J］.Journal of Systems Engineering,2005,20(6):585590. ［6］Riddalls C E, Beneft S. Production inventory system controller design and supply chain dynamics［J］. International Journal of Systems Science,2002,33(3):181195. ［7］苏春华,刘思峰.灰色随机线性时滞系统的渐近稳定性［J］.控制与决策, 2008,23(5):571580. 〖DW〗Su C H, Liu S F. Asymptotic stability of grey stochastic linear delay systems［J］. Control and Decision, 2008, 23(5): 571580. 8］纪雪洪,陈荣秋,唐中君.供应链中延迟研究的发展与展望［J］.管理工程学报,2007,21(4):6266. 〖DW〗Ji X H, Chen R Q, Tang Z J. The development and prospect of postponement research［J］.Journal of Engineering Management,2007,21(4):6266. ［9］Dong Y, Jian A F, Sang C W. Delaydependent robust stability of stochastic uncertain systems with time delay and markovian jump parameters［J］. Circuits Systems Signal Processing,2003,22(4):351365.〖ZK)〗 ［10］〖ZK(#〗Yuan C G, Mao X. Robust stability and controllability of stochastic differential delay equations with markovian switching［J］. Automatica,2004,40(3):343354. ［11］〖WB〗张先明,吴敏,何勇.区间矩阵的稳定性［J］.中南工业大学学报,2003,34(5):590592. 〖DW〗Zhang X M, Wu M, He Y. The stability of interval matrices［J］.Journal of Central South University of Technology,2003,34(5):590592. ［12］Mao X. A note on the lasalletype theorems for stochastic differential delay equations［J］.Journal of Mathematical Analysis and Applications,2002,268(1):125142. ［13］Mao X, Koroleva N, Rodkina A. Robust stability of uncertain stochastic differential delay equations［J］.Systems & Control Letters,1998,35(5):325-336. ［14］Riddalls C E, Beneft S. Production inventory system controller design and supply chain dynamics［J］.International Journal of Systems Science,2002,33(3):181-195. ［15］Daganzo C F. On the stability of supply chains［J］.Operations Research,2004,52(6):909-921.

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