按单装配系统中组件生产和库存分配控制策略研究

针对由两种组件、三类顾客需求组成的按单装配系统, 本文研究了其中的组件生产控制与库存分配问题. 在各类顾客需 求是泊松到达过程, 各种组件加工时间服从指数分布的假设下, 我们运用马尔科夫决策理论建立了无限期折扣总成本模型, 根据Lippman转换得到了相应归一化后的离散最优方程, 在此基础之上分析了生产和库存分配联合最优控制策略的结构性质. 本文证明了最优策略是依赖于系统状态的动态策略. 组件的最优生产策略是动态基库存策略, 其中基库存水平是关于系统中其他组件库存水平的非减函数. 而最优的分配策略是动态的阈值策略, 对于只需一种组件构成的顾客需求, 组件的分配阈值是系统中另一组件库存水平的增函数; 而对于同时需要两种组件组成的顾客需求, 其各组件的分配阈值是另一组件库存水平的减函数. 最后通过数值试验给出了各个参数对联合最优控制策略的影响, 并得到了相应的管理启示.     

柔性制造系统（FMS）的一种建模方法及最优控制策略

本文针对ＦＭＳ的调度问题，考虑到多台机器、机器不可靠及缓冲库容量有限等特点，在满负载平衡的条件下，建立了一种近似的布朗网络模型，然后基于求解这个模型的最优控制问题而得到的最优队长和最优空闲时间，提出了一种最优控制策略，包括排序策略和输入控制策略。因为不涉及随机变量的分布类型，所以本文的方法适用于一般的ＦＭＳ。     

随机需求不可靠制造系统的最优服务率分配策略

本文讨论了一类随机需求不可靠制造系统的最优服务率控制问题。所研究的系统能同时生产多类产品，但生产能力受常数限制。目标是通过最小化库顾和欠缺的期望折扣费用，寻找最优服务率分配策略，本文证明了最优策略具有开关结构，并针对生产单类和两类产品的系统详细研究了最优控制策略的结构性质，最后以数值例子验证了本文的结论。     

离散非线性零和博弈的事件驱动最优控制方案

在求解离散非线性零和博弈问题时,为了在有效降低网络通讯和控制器执行次数的同时保证良好的控制效果,本文提出了一种基于事件驱动机制的最优控制方案.首先,设计了一个采用新型事件驱动阈值的事件驱动条件,并根据贝尔曼最优性原理获得了最优控制对的表达式.为了求解该表达式中的最优值函数,提出了一种单网络值迭代算法.利用一个神经网络构建评价网.设计了新的评价网权值更新规则.通过在评价网、控制策略及扰动策略之间不断迭代,最终获得零和博弈问题的最优值函数和最优控制对.然后,利用Lyapunov稳定性理论证明了闭环系统的稳定性.最后,将该事件驱动最优控制方案应用到了两个仿真例子中,验证了所提方法的有效性.     

两能级封闭量子系统任意量子态的最优制备

在分析单量子位的Bloch球面表示的基础上，结合量子门实现量子态幺正演化的量子态调控机制，提出一种针对两能级封闭量子系统任意量子态的最优制备策略．该策略首先建立两能级量子系统及其控制场的模型；然后借助李群李代数．由经典最优控制的思想和约化动力学来获得最优控制，从而达到两能级封闭量子系统任意量子态的最优制备．理论分析与仿真实验表明了该策略的优越性．     

多移动机器人实时最优运动规划

研究多移动机器人的实时运动规划问题，提出了运动规划问题的体系结构，并将最优控制与智能决策相结合，建立实时专家系统，在其支持下，使机器人在时间—能量最优情况下完成规划策略。仿真结果表明该方法具有很强的实时性。     

一类部分信息下带有劳动力收入的最优投资消费问题

最优投资消费问题属于一类典型的随机最优控制问题. 劳动力收入可通过影响期望效用从而影响投资消 费策略的制定. 本文首次在股票收益率和劳动力收入均为不可观测过程情形下, 研究了一类部分信息下的最优投资 消费问题. 首先综合运用Kalman滤波和非线性滤波, 得到了Zakai方程的显式解, 将部分信息下的随机最优控制问题 转化为完备信息下的随机最优控制问题. 其次通过求解HJB方程以及证明验证定理, 得到了该类最优投资消费问题 的最优策略以及值函数的显式表达. 最后采用真实市场数据进行仿真, 对比经典完备信息模型与本文部分信息模型 所得最优策略的差异, 验证了本文所得最优策略在有效利用市场信息方面的优越性.     

开放式基金流动性风险的最优控制

在证券价格服从离散时间算术布朗运动的假设下，得到资产流动性风险最优控制策略，并对该策略进行有关参数的敏感性分析。研究结果表明，流动性系数较大时，最优控制策略接近于线性策略；流动性系数较小时，资产管理者会迅速将资产头寸降至理想水平，并在大部分时间内保持这种状态，直到变现期末达到资产目标头寸。最优策略对管理者的风险厌恶程度、资产波动率和流动性系数较为敏感，而对证券超额收益率敏感程度较低。     

基于自适应动态规划的一类带有时滞的离散时间非线性系统的最优控制策略

针对一类状态和控制变量均带有时滞的非线性系统的带有二次性能指标函数最优控制问题, 本文提出了一种基于新的迭代自适应动态规划算法的最优控制方案. 通过引进时滞矩阵函数, 应用动态规划理论, 本文获得了最优控制的显式表达式, 然后通过自适应评判技术获得最优控制量. 本文给出了收敛性证明以保证性能指标函数收敛到最优. 为了实现所提出的算法, 本文采用神经网络近似性能指标函数、计算最优控制策略、求解时滞矩阵函数、以及给非线性系统建模. 最后本文给出了两个仿真例子说明所提出的最优策略的有效性.     

果树种群模型和最优控制

本文在生物种群增长模型基础上,建立了具有控制变量的果树种群状态方程,特别是具有植入和伐除的龄类果树动态系统。应用极大值原理推导了最优控制,并对国家苹果基地(瓦房店市)果树发展提出了最优策略。     

A simulation optimization based control policy for failure prone one-machine,two-product manufacturing systems

This paper presents the optimal flow control for a one-machine, two-product manufacturing system subject to random failures and repairs. The machine capacity process is assumed to be a finite state Markov chain. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that for constant demand rates and exponential failure and repair time distributions of the machine, the hedging point policy is optimal. Next, the hedging point policy is extended to non-exponential failure and repair time distributions models. The structure of the hedging point policy is parameterized by two factors representing the thresholds of involved products. With such a policy, simulation experiments are coupled with experimental design and response surface methodology to estimate the optimal control policy. Our results reveal that the hedging point policy is also applicable to a wide variety of complex problems (i.e. non-exponential failure and repair time distributions) where analytical solutions may not be easily obtained.     

A simulation optimization approach in production planning of failure prone manufacturing systems

In this paper, the implementation of a new method to control the production rate of manufacturing systems, based on the combination of stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology is outlined. The system under study consists of several parallel machines, multiple-product manufacturing system. Machines are subject to failures and repairs and their capacity process is assumed to be a finite state Markov chain throughout the analytical control model. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. The structure of the hedging point policy is then parameterized by factors representing the thresholds of involved products. With such a policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal control policy. We obtain that the hedging point policy is also applicable to a wide variety of complex problems including non-exponential failure and repair times distributions and random demand rates. Analytical solutions may not be easily obtained for such complex situations.     

制造系统的递阶滚动优化调度模型

研究的对象是只有一台不可靠（failure-prone)机器的非完全柔性制造系统，该系统能生产多种产品，但在同一时刻只能生产一种产品，并且当机器由生产一种产品向生产另一种产品切换时，需要考虑setup时间及其成本，待决策变量是setup序列及产品生产率，本文基于非完全柔性制造系统的特点，引入递阶层控的思想，采用新的递阶结构框架和阈值控制策略，对问题进行分解，建立了考虑setup时间及成本的递阶流率控制最优化调度模型，并给出了递阶的滚动优化算法，仿真结果表明，这种调度策略更易于工程实现。     

Scheduling and control of failure prone systems with demand uncertainty and job overlaps

Given that the overlapping of jobs is permitted, the paper studies the scheduling and control of failure prone production systems,i, e.so-called settings with demand uncertainty and job overlaps. Because a variable demand resource is revolved in the production and corrective maintenance control problems of the system, which switched randomly between zero and a maximum level, it is difficult to obtain the analytical solutions of the optimal single hedging point policy. An asymptotic optimal scheduling policy is presented and a double hedging point policy is offered to control simultaneously the production rate and the corrective maintenance rate of the system. The corresponding analytical solutions and approximate solutions are obtained. Considering the relationship of production, corrective maintenance and demand variable, an approximate optimal single hedging point control policy is proposed. Numerical results are presented.     

The queueing equivalence to a manufacturing system with failures

The authors consider optimal production rate control in a failure prone manufacturing system. It is well known that the hedging point policy is the optimum controller for such a system. They show that under the hedging point policy the system can be treated as an M/M/1 queue. Therefore, existing results in queuing theory can be readily applied to obtaining the steady-state probability density function of the production surplus, based on which the optimal hedging point policy can be computed. To a large extent, the approach is based on sample path analysis. It not only provides an alternative way to solve the problem but also reveals some interesting insights     

Single period stochastic inventory problems with ordering or returns policies

In recent years, there has been an increasing adoption of returns policies in the coordination of the supply chain, where market demand is always assumed to be satisfied by manufacturing or by ordering from suppliers. However, many industries face the important decision of how to balance their inventory level. This problem has long been studied in financial institutions such as banks. This study presents an optimal inventory policy under a given stochastic demand such as a uniformly distributed demand, single-item, and single period review inventory system. The optimal inventory control policy obtained in this study is called a four-point policy: that is, when the entity’s inventory level is below a reorder point, the entity must increase his stock level by ordering and order up-to a fixed level (second point); when the entity’s inventory level is over a return point (third point); the stock level must be decreased by returns and decreased to a fixed level (fourth point); otherwise, nothing should be done. We also analyze the (K, S)-convex properties of the inventory cost function.     

具有不确定需求的混杂系统的生产与维修控制

针对不可靠生产环境, 在需求不确定并且有可能存在需求大于生产的一般性情况下, 探讨了系统生产与维修的控制问题, 提出了一种考虑追加生产能力的具有较强即时动态特性的复合三阈值控制策略. 通过将有限时域上的问题分解到无限时域上的简化方法, 在给出了相应阈值求解方法的同时, 也建议了一种近似最优的复合单阈值控制策略. 仿真结果说明及验证了各控制策略及方法.     

Production rate control for failure-prone production systems withno backlog permitted

In this paper, we consider systems in which backlog is not allowed. We show that the hedging point policy is still optimal. For systems with backlog, it is usually quite straightforward to show that their optimal cost-to-go functions are convex-a key property that is needed for the hedging point policy to be optimal. With no backlog permitted, it becomes much more difficult to establish the convexity property, and the explicit formulas for the optimal hedging point and the optimal cost-to-go functions have to be obtained, based on which the convexity property can then be verified. The method we use in this paper to derive these explicit formulas is mainly based on an interesting relationship between the inventory process of the system under the hedging point policy and some stochastic processes which are well studied in queueing theory     

Optimal hedging point control for a failure-prone manufacturing system

This paper considers a manufacturing system with multiple operational modes producing one part type. The part processing time at each operational mode is exponentially distributed and its rate is controllable. The demand arrival is random and described by a Poisson process. By minimizing an infinite-horizon discounted expected cost function, the optimal service rate control is derived. It is proved that the optimal policy is of a hedging point structure by examining the properties of the optimal cost function such as convexity, monotonicity and asymptotic behaviours. The hedging points at different operational modes can be ordered according to their production capacities. The relationships of the hedging points with some system parameters are presented. These structural properties of the optimal control policy are helpful in finding simple and realistic suboptimal policies for practical manufacturing systems. A numerical example is given to demonstrate our results.