基于LMI的灰色非线性精敏供应链稳定性判定方法

摘要/Abstract

摘要： 平稳运行是精敏供应链管理的重要基础，针对具有区间灰色非线性特征的精敏供应链系统波动性的难题，以非线性时滞精敏供应链系统为研究基础，建立了灰色非线性精敏供应链系统，采用线性矩阵不等式算法分析其稳定性问题，并获取了一种灰色非线性精敏供应链系统的稳定性判定方法。为验证该方法的有效性和可行性，以医药行业YL集团核心产品的供应链系统为案例分析对象，通过观测两个时点的运行数据，使用Matlab70计算工具，得出［0,20］和［20,40］2个时间段供应链系统的稳定性状态变化图。并假设当客户订货分离点(CODP)下移时，运用同样的观测数据，模拟系统稳定性状态的变化。对比案例分析的结果得出结论：随着CODP从精敏供应链的上游端在下移至下游端时，不仅仅体现的是供应链系统类型的改变，而且更重要的是揭示了精益供应链和敏捷供应链稳定性的影响因素不同，前者受订单量大小程度的影响，而后者由市场需求预测的准确性程度决定。

关键词: 精敏供应链, 灰色非线性, 稳定性, 线性矩阵不等式

Abstract: In leagile supply chain management, it is important to operate a supply chain smoothly. However, with grey and non-linearity, it is very challenging to model and control such a supply chain. On the basis of non-linear and time delay leagile supply chain systems, a grey and non-linear model is developed for a leagile supply chain. Then, a linear matrix inequality method is used to analyze its stability and an effective stability criterion is obtained. In order to verify the feasibility and effectiveness of the proposed method, a core product supply chain systems of YL Group in the medicine industry is used as a case study. By using Matlab 7.0, the stability of the system state diagram is drawn before and after customer order decoupling point(CODP). Results show that when CODP moves down, not only the supply chain type is changed but also different influence factor of stability between lean supply chain and agile supply chain is uncovered. The former is affected by order size, and the latter is affected by the accuracy of market demand forecast.

Key words: leagile supply chain, grey and nonlinearity, stability, linear matrix inequality (LMI)

张学龙1，2, 王云峰1. 基于LMI的灰色非线性精敏供应链稳定性判定方法[J]. 工业工程, 2014, 17(2): 64-69.

Zhang Xue-long1,2 , Wang Yun-feng1. LMI-based Research on Stability of Leagile Supply Chain with Grey Non-linear Characteristics[J]. Industrial Engineering Journal , 2014, 17(2): 64-69.

参考文献

［1］马士华,林勇,陈志祥.供应链管理［M］.北京:机械工业出版社,2000. ［2］Womack J P, Jones D T, Roos D. The machine that changed the world［M］.New York: Simon & Schuster Inc,1990. ［3］何勇,赵林度,何炬,等.供应链协同创新管理模式研究［J］.管理科学,2007,20(5):9-13. He Yong, Zhao Lin-du, He Ju, et al. Study on supply chain coordination in innovation［J］.Journal of Management Science,2007,20(5): 9-13. ［4］Power D J, Sohal A S, Rahman S. Critical success factors in agile supply chain management: an empirical study［J］. International Journal of Physical Distribution and Logistics,2001,31(4):247-265. ［5］Christopher M. The agile supply chain, competing in volatile markets［J］.Industrial Marketing Management,2000，29（1):37-44. ［6］Naylor J B, Naim M M, Berry D. Leagility: interfacing the lean and agile manufacturing paradigm in the total supply chain［J］. International Journal of Production Economies,1999，62（1-2):107-118. ［7］Lee H L, Padmanabhan V, Whang S. The bullwhip effect in supply chains［J］.Sloan Management Review,1997, 38(3):93-102. ［8］Lee H L, Padmanabhan V, Whang S. Information distortion in a supply chain: the bullwhip effect［J］.Management Science, 1997,43(4):546-558. ［9］Chen F, Drezner Z, Ryan J K, et al. Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead times, and information［J］.Management Science,2000,46(3):436-443. ［10］Gaur V, Giloni A, Seshadri S. Information sharing in a supply chain under ARMA demand［J］.Management Science,2005,51(6):961-969. ［11］Gilbert K. An ARIMA supply chain model［J］.Management Science,2005,51(2):305-310. ［12］Ouyang Y, Daganzo C. Characterization of the bullwhip effect in linear, timeinvariant supply chains: Some formulae and tests［J］.Management Science,2006,52(10):15441556. ［14］刘开军,张子刚.需求未知情况下供应链中的信息汇聚效应［J］.管理科学学报,2009,12(4):103-144. 〖DW〗Liu Kai-jun, Zhang Zhi-gang. Pooled information effect in supply chains with unknown demand［J］.Journal of Management Science in China,2009,12(4):103-144. ［15］Dejonckheere J, Disney S M, Lambrecht M R, et al. The impact of information enrichment on the bullwhip effect in supply chains: a control engineering perspective［J］.European Journal of Operational Research,2004,153(3):727750. ［16］Ouyang Y, Daganzo C. Robust tests for the bullwhip effect in supply chains with stochastic dynamics［J］.European Journal of Operational Research,2008,185(1):340-353. ［17］汪传旭.基于ARMA(1,1)需求的供应链历史订单量信息价值的分析［J］.管理工程学报,2006,20(4):25-30. Wang Chuan-xu. Value of history order quantity information in a supply chain with ARMA(1,1) demand［J］.Journal of Industrial Engineering/Engineering Management,2006,20(4):25-30. ［18］韩文民,袁丽丽,叶涛锋.基于随机Petri网的生产提前期牛鞭效应测度研究［J］.中国管理科学,2011,19(2):116-124. Han Wenmin, Yuan Li-li, Ye Tao-feng. Research on the lead time bullwhip effect measure based on stochastic Petri nets［J］.Chinese Journal of Management Science,2011,19(2):116-124. ［19］胡丹丹,杨超.α鲁棒随机截流选址问题的模型和算法［J］.中国管理科学,2008,16(6):87-94. Hu Dandan, Yang Chao. The model and algorithms of stochastic αrobust interception flow location problem［J］.Chinese Journal of Management Science,2008,16(6):8794. ［20］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. Su Chun-hua, Liu Shi-feng. Asymptotic stability of grey stochastic linear delay systems［J］.Control and Decision,2008,23(5):571-580. ［21］王道平,张学龙,赵相忠.具有灰色随机动态特征的供应链牛鞭效应的鲁棒性分析［J］.中国管理科学,2013,21(1):57-62. Wang Dao-ping, Zhang Xue-long, Zhao Xiang-zhong. Robustness analysis of the bullwhip effect in supply chain with grey stochastic dynamics［J］. Chinese Journal of Management Science,2013,21(1):57-62. ［22］张学龙,王道平,赵相忠.区间灰色时滞特征的供应链建模及稳定性分析［J］.工业工程,2012,15(3):20-23. Zhang Xue-long, Wang Dao-ping, Zhao Xiang-zhong. Modeling and its stability analysis of supply chain with grey and time delay properties［J］. Industrial Engineering Journal,2012,15(3):20-23. ［23］Liao X, Chen G, Sanchez E N. LMIbased approach for asymptotically stability analysis of delayed neural networks［J］.IEEE Transaction Circuits and Systems I, Fundamental Theory and Applicaions,2002,49(7):1033-1039.

[1]	唐军, 周冰, 文里梁, 陈爱明, 何邦华, 唐丽, 曾仲大. 工业生产过程数据稳定性评价方法的适应性研究[J]. 工业工程, 2020, 23(6): 131-137.
[2]	胡卉, 马海, 李博, 赵姣. 基于捕食者—猎物模型的突发事件下供应链稳定性研究[J]. 工业工程, 2017, 20(6): 39-46.
[3]	肖旦1，刘芳1，陆达林1，史欣向1，周永务2 . 变质性产品零售商联合采购与运输联盟的稳定性分析[J]. 工业工程, 2016, 19(3): 18-23.
[4]	李随科, 白思俊, 郭云涛, 王续伯. 基于Logistic模型的型号研制异地协同模式[J]. 工业工程, 2014, 17(1): 50-54.
[5]	肖旦，周永务，汤勤深. 考虑次品率的零售商库存联盟订货量与稳定性分析[J]. 工业工程, 2013, 16(3): 32-37.
[6]	张学龙12，王道平1，赵相忠2. 区间灰色时滞特征的供应链建模及稳定性分析[J]. 工业工程, 2012, 15(3): 20-23.
[7]	胡卉，胡大伟，陈栋. 面向供应链协同的实体关联稳定性[J]. 工业工程, 2011, 14(5): 31-35.