随着全球经济格局的快速变化和市场竞争压力的日益增长，供应链逐渐发展成为一个复杂的动态网络系统。由于在供应链网络中产品的库存状态不断变化，为了减少成本生产商需要根据不同的库存状态及时地调整生产策略。因此，针对库存变化的最优生产调度一直是供应链管理中的热点问题。本文的主要内容和创新点包括如下几点： 首先，研究减少库存成本的供应链最优生产调度问题，构建线性切换系统的最优调度模型，并设计线性分支定界求解算法。由于在供应链中库存成本是关于库存状态的线性结构，本文通过矩阵变换和矩阵的迹运算构建目标泛函的一个动态下界系统。在各个生产阶段，利用下界与当前最优值进行比较，基于深度优先搜索策略设计分支定界算法，数值实验验证了算法能够在线性调度系统中以很高的效率搜索到全局最优解。 其次，研究安全库存下的最优生产调度问题，构建线性二次型切换系统的最优调度模型，并设计线性二次型分支定界求解算法。为了应对市场波动而产生的供给风险，寻找一个最优的生产调度方案，使得库存状态在多阶段生产过程中尽量维持在安全水平附近，本文将目标泛函表达成关于库存状态的二次型结构，然后利用矩阵论和半定规划等技巧，构建一个适用于二次型目标泛函的新的动态下界系统。基于这种新的下界，线性二次型分支定界法被设计，数值实验验证了算法在线性二次型最优生产调度问题中搜索全局最优解的有效性。 再次，研究抑制切换频率的最优生产调度问题，构建混杂切换系统的最优调度模型，并设计精确分支定界求解算法。由于在生产周期内生产调度过于频繁不利于人员的操作且严重影响设备的使用寿命，为了在多种可行的方案中选择比较平稳的调度方式，本文引入调度序列的全变函数度量它的变化频率和幅度。针对这种混杂的最优调度问题，本文为目标泛函构建一个精确的动态下界系统，该下界使得分支定界法在任意的正则化参数下都能够精确地搜索到所有的全局最优解，数值实验验证了算法在混杂调度系统中搜索全局最优解的效率和全变函数对调度序列变化的抑制作用。 最后，研究交易存在延迟的最优生产调度问题，构建时滞切换系统的最优调度模型，并设计时滞分支定界求解算法。由于在多阶段上下游成员的交易过程中往往存在延迟的现象，供应链中的目标泛函受到当前状态、时滞状态和生产调度序列的共同影响，本文利用矩阵维数扩张技巧将相互耦合的状态和调度信号进行分离，然后将目标泛函等价地转化为只涉及初始状态的标准二次型结构，并构造目标泛函的一个精确动态下界系统，接着深度优先搜索策略的时滞分支定界法被设计和执行，数值实验进一步验证算法能在各种时滞调度系统中搜索到全局最优的生产调度方案。 关键词：供应链；库存管理；切换系统；最优生产调度；分支定界法

 With the rapid change of global economic pattern and the increasing pressure of market competition, supply chain has gradually developed into a complex dynamic network system. Because the inventory state of products in the supply chain network changes constantly, in order to reduce the cost, the manufacturer needs to adjust the production strategy according to the inventory state. Therefore, the optimal production scheduling for inventory changes has been a hot issue in supply chain management. The main content and innovation points of the thesis include the following: Firstly, the optimal production scheduling problem of supply chain to reduce inventory cost is studied, the optimal scheduling model of linear switching system is constructed, and the linear branch and bound method is designed. Since the inventory cost is a linear structure with respect to the inventory state in supply chain, the thesis constructs a dynamic lower bound system of the linear cost functional by matrix transformation and matrix trace operation. In each production stage, the lower bound is compared with the current optimal value, and the branch and bound algorithm is designed based on the depth-first search strategy. Numerical experiments verify that the algorithm can search for the global optimal solution in the linear scheduling system with high efficiency. Secondly, the optimal production scheduling problem under safety inventory is studied, the optimal scheduling model of the linear-quadratic switched system is constructed, and the linear-quadratic branch and bound method is designed. In response to the supply risk of market fluctuations, search for an optimal production scheduling sequence, make the inventory state as far as possible to maintain near the safety level with multiple stages, the thesis expresses the cost functional into a quadratic structure with respect to the inventory state, and then using the matrix theory and semi-definite programming techniques to build a new dynamic lower bound system of the quadratic cost functional. Based on the new lower bound, the linear-quadratic branch and bound method is designed, and numerical experiments verify the effectiveness of the algorithm in searching all global optimal solutions for linear-quadratic optimal production scheduling problems. Thirdly, the optimal production scheduling problem that restrains the switching frequency is studied, the optimal scheduling model of hybrid switched system is constructed, and the exact branch and bound method is designed. Because the frequent production scheduling is not conducive to the operation in the production cycle and seriously affects the service life of equipment, in order to choose a more stable scheduling sequence, the thesis introduces the total variable function with respect to the scheduling sequence to measure its changing frequency and amplitude. For this kind of hybrid optimal scheduling problem, the thesis constructs an exact dynamic lower bound system for the cost functional, which enables the branch and bound method to exactly search for all the global optimal solutions under any regularization parameter. Numerical experiments verify the efficiency of the algorithm in searching the global optimal solution in hybrid scheduling systems and the inhibitory effect of the total variable function with respect to the scheduling sequence. Finally, the optimal production scheduling problem with transaction delay is studied, the optimal scheduling model of time-delay switched system is constructed, and the time-delay branch and bound method is designed. Because the transaction process between upstream and downstream members often has delay phenomenon in multiple stages, the cost functional in the supply chain is influenced by the current state, the time-delay state and the production scheduling sequence, the thesis uses the dimension expansion technique of matrix to decouple the state and the scheduling signal. Then the cost functional is converted to the standard quadratic form with respect to the initial state equivalently, and an exact dynamic lower bound system is constructed. Thus the time-delay branch and bound method is designed based on the depth-first search strategy. Numerical experiments further verify that the algorithm can search for the global optimal production scheduling sequence in the time-delay scheduling system. Keywords: Supply chain; inventory management; switched system; optimal production scheduling; branch and bound method