导　　师： 于景元

学科专业： H1103

授予学位： 博士

作　　者： ;

机构地区： 中国航天科工集团公司第二研究院

摘　　要： 随着全球经济一体化、市场国际化，供应链作为一种“扩展”的企业，结构非常复杂，每一个环节都存在着潜在的风险，任何一个环节出了问题，都会给整条供应链造成严重的影响．供应链协调运行是建立在各个环节可靠基础之上的，因此有效的供应链管理离不开对供应链的可靠性的评价和保障．因此，在全球化趋势下，对于供应链这个日益复杂的系统，如何分析、评价、控制和提高其可靠性变得日益迫切，并受到越来越多的关注．但在理论上，还存在着一些不完善的地方，而这些问题的解决将会对进一步分析系统的动态可靠度、稳态可用度、鲁棒稳定性、寻求系统的最优调整时间等方面产生深刻的影响． 本文的目的就是借助可靠性工程研究的方法对供应链的可靠性及其系统稳定性做深入的分析，进而为研究供应链的优化策略提供理论基础。 本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C0-半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助MATLAB工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C0-半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础，由于文章选取的状态空间为L1空间，因此，对系统解规范化后即可直接得到系统稳态可用度的解析表达式，并且该表达式中包含了系统优化调整时间(变量T)，这就为寻求系统最优调整时间提供了可能．最后，文章以分析的形式给出了系统最优调整时间，为企业乃至整个供应链正确地选择适宜的管理策略提供了理论指导。 本文的主要创新之处在于： 1)以补充变量的方法作基础，引进偏微分方程组分别对供应链系统及供应链优化调整进行了描述，给出供应链系统模型和供应链优化模型，丰富了供应链的理论； 2)采用离散化的数值计算方法借助MATLAB工具直接模拟供应链系统模型系统解的性态，给出动态解的仿真图； 3)运用泛函分析中的C0-半群理论，从理论上严格证明了供应链系统模型和供应链优化模型系统解的存在唯一性、非负性及渐近稳定性，其中供应链系统模型的解证到指数阶渐近稳定； 4)对系统模型进行了动态分析，利用系统的稳态解给出了系统稳态可用度的解析表达式，为进一步确定和求解系统的动态可靠度、可用度以及进一步分析和为寻求系统的最优调整时间提供方法。 Supply chain, as an extended enterprise, is a complex and dynamic system. It’s complexity and dynamism are further intensified by the global economic integration and market internationalization. The performance of a supply chain is a result of the coordinated operations between companies in the supply chain. Any breakdown on the coordinated operations in the supply chain /(i.e. the reliability of the coordinated operations/) will largely affect the performance of a supply chain. Hence, effective supply chain management relies on the appraisal and maintenance of the reliability of a supply chain. How to analyze, evaluate, monitor, control and improve the supply chain reliability is gaining more and more attention recently, however, there are still some knowledge gaps. Those knowledge gaps include the study of dynamic margin of safety and the stable state availability, the research of optimal adjustment time of the system. The purpose of this dissertation is to apply reliability engineering methodology to analyze the reliability and robustness of supply chain, and provide theory foundation for research on optimization strategy. Firstly, this dissertation briefly describes the supply chain theory, analyzes the existing risk in supply chain, states the research status on reliability of supply chain and the prospect of managing reliability of supply chain. Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system. Since the state space selected in this study is the L1 space, it directly obtains the system stable state availability analytic expression after standardizing the system solution. In the expression, it has identified the optimization adjustment time of system /(Variable T/), which makes the optimization adjustment time of system possible. Therefore, it analyzes and states the optimization adjustment time of system, providing the theory instruction for the enterprises and even the entire supply chain to choose the suitable reliability management strategy. The major contributions and innovations of this paper includes: 1/) Supplementary variable technique is successfully introduced into the research for the reliability of supply chain. By applying this method, this paper formulates the mathematic model of the system and optimal model for supply chain; 2/) With the help of Matlab, discretization of the numerical method is adopted to directly simulate the solution of the reliability model for supply chain, and presented the simulation figure; 3/) Using the theory of semigroup, a strictly mathematical proof is provided for the existence, uniqueness , non-negativity and asymptotic properties of the reliability model and the optimal model for the supply chain. The exponential stability of the solution of the reliability model for supply chain is proved; C0 ? 4/) By dynamically analyzing the optimal model for the supply chain system, a mathematical expression of availability of the system is obtained corresponding to steady solution of the system. This provides a new approach to solve dynamical stability and dynamical availability of the system and to research the optimal schedule to performing adjustment.

关 键 词： 供应链管理 鲁棒性 半群 可靠性 广义马尔可夫过程

分 类 号： [F274 O213.2]

领　　域： [经济管理] [经济管理] [理学] [理学]