随机生产系统安全库存的ЛТ控制策略

本文研究了随机工件加工时间的生产系统在ЛТ（Ｊｕｓｔ－Ｉｎ一Ｔｉｍｅ）控制策略下的运行机制．基于文［１］所提出的看板控制生产系统的生产率与其马尔柯夫模型的状态空间相对应的理论．本文探讨了在ЛТ控制策略下生产系统的看板在安全库存受限的条件下的最优配置问题，并给出了工作站数目小于５的生产系统看板最优配置公式．     

多目标决策非凸锥Λ－有效点的存在性与控制性质

本文提出了多目标决策偏好及最优解的一般概念和集诱导偏好的概念．给出了判断ρ－完备集的一系列条件，从而指出了ρ－完备集是十分广泛的集类．得到了集合的Λ－有效点的存在性定理和ρ－下闭集与截面的Λ－有效点的性质．通过引入函数Λ－下半连续的概念，得到了多目标决策一般集诱导偏好最优解的存在性定理．在这些结果的基础上，最后得到了集合Ｙ关于Λ和多目标决策问题的控制性质．     

多目标规划αk-较多有效解类的若干性质

在［１］中,作者提出多目标规划的较多有效解和较多最优解概念,并研究了它们的基本性质．文［３］则讨论了ｋ－较多最优解的若干性质．文［４］利用较多序类进一步引进多目标规划问题的αｋ－较多有效解,并证明了这类解的最优性必要条件．本文再给出多目标规划问题的αｋ－较多最优解的概念,并讨论了多目标规划αｋ－较多有效解和αｋ－较多最优解的若干重要性质．     

非牛顿流体中对称扩散的稳态解

本文研究来源于非牛顿流体等许多物理现象中产生的一类扩散方程的稳态解．这类方程一般具有退化性和奇异性．利用摄动技巧证明了具对称性的古典解的存在性，并在某种一般的条件下讨论了解的唯一性     

一类不可微规划的多项式型算法

本文考虑了由教育最优投资问题导出的一类不可微规划，讨论了可行解是最优解的充要条件，在对乘子作某些假设下，利用Kuhu－Tucker定理给出了求解的一种多项式算法．     

三维与二维晶体生长控制方程的精确解

本文通过将未知函数展开成复数形式的Fourier级数,求出了一类二阶偏微分方程的三角级数形式的解析解,并严格证明了其收敛性．三维稳态与二维稳态和二维非稳态晶体生长控制方程都是这类二阶偏微分方程特例．利用这一特点,本文求出了三维稳态与二维稳态和二维非稳态晶体生长控制方程的解析解．理论结果有助于揭示稳态晶体生长的本质特性．本文还给出了三维非稳态晶体生长控制方程的解析解．     

加工时间依赖于机器的自由作业排序问题

1992年M．Dror提出工件的加工时间依赖于机器的排序问题（schedulingwithmachinedependentprocessingtimes），并研究以最大完工时间（makespan）和以总的完工时间为优化目标的两种这类排序问题．然而，M．Dror对以总的完工时间为优化目标提出的“最优算法”是错误的．本文用算例表明他提出的算法不是最优的，并在机器连续加工的条件下，把这个排序问题转化成指派问题（assignmentproblem），从而可以用匈牙利算法得到最优解．最后，我们提出几个尚未解决的问题，以期引起国内外同行进一步研究．     

极大熵方法与非单调曲线搜索可行方向法

1．引言逼近方法是解决复杂的最优问题的有效方法之一．目前，已有许多研究工作【‘一句．己有的工作主要是从理论上讨论逼近问题和原问题的最优解之间的关系．另一方面，寻求具体而有效的逼近方法不仅具有理论意义，而且更具有实用价值．近年来出现的求解非线性规划（minimaxfbi题）的极大滴方法I‘－‘］就是一种具体而有效的逼近方法．［1－3］中的有关结果可以用于这种方法．［7］则从另一途径给出了强凸规划的极大嫡方法的收敛性质．已有的极大滴方法的收敛性结果均是在最优解意义下得到的．由于一般情况下只能求得优化问题的Kuhn－T…     

多目标规划ak—较多有效解类的若干性质

在（１）中,作者提出多目标规划的较多有效解和较多最优解概念,并研究了它们的基本性质,文（３）则讨论ｋ－较多最优解的若干性质。文（４）利用较多序类进一步引进多目标规划问题的ａｋ－较多有效解,并证明了这类解的最优性必要条件。本文再给出多目标规划问题的ａｋ－较多最优解的概念,并讨论了多目标规划ａｋ－较多有效解和ａｋ－较多最优解的若干重要性质。     

随机生产系统安全库存的JIT控制策略

本文研究了随机工件加工时间的生产系统在JIT（Just-In-Time）控制策略下的运行机制。基于文[1]所提出的看板控制生产系统的生产率与其马尔柯夫模型的状态空间相对应的理论，本文探讨了在JIT控制策略下生产系统的看板在安全库存受限的条件下的最优配置问题，并给出了工作站数目小于5的生产系统看板最优配置公式。     

Q-learning and policy iteration algorithms for stochastic shortest path problems

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in Bertsekas and Yu (Math. Oper. Res. 37(1):66-94, 2012). The main difference from the standard policy iteration approach is in the policy evaluation phase: instead of solving a linear system of equations, our algorithm solves an optimal stopping problem inexactly with a finite number of value iterations. The main advantage over the standard Q-learning approach is lower overhead: most iterations do not require a minimization over all controls, in the spirit of modified policy iteration. We prove the convergence of asynchronous deterministic and stochastic lookup table implementations of our method for undiscounted, total cost stochastic shortest path problems. These implementations overcome some of the traditional convergence difficulties of asynchronous modified policy iteration, and provide policy iteration-like alternative Q-learning schemes with as reliable convergence as classical Q-learning. We also discuss methods that use basis function approximations of Q-factors and we give an associated error bound.     

Multi-location transshipment problem with capacitated transportation

We consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, transfer of a product among locations at the same echelon level. We incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location’s transshipment policy. We model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, we show the impact of transshipment capacity between stocking locations on system behavior. We observe that transportation capacity constraints not only increase total cost, they also modify the inventory distribution throughout the network.     

极大极小随机规划逼近问题最优解集和最优值的稳定性

研究了特殊的二层极大极小随机规划逼近收敛问题. 首先将下层初始随机规划最优解集拓展到非单点集情形, 且可行集正则的条件下, 讨论了下层随机规划逼近问题最优解集关于上层决策变量参数的上半收敛性和最优值函数的连续性. 然后把下层随机规划的epsilon-最优解向量函数反馈到上层随机规划的目标函数中, 得到了上层随机规划逼近问题的最优解集关于最小信息概率度量收敛的上半收敛性和最优值的连续性.     

Optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k + 1 states, including k failure states and one working state, is studied. The system after repair is not ‘as good as new’ and the deterioration of the system is stochastic. Under these assumptions, we study a replacement policy, called policy N, based on the failure number of the system. The objective is to maximize the long-run expected profit per unit time. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal solution may be determined analytically or numerically. Furthermore, we prove that the model for the multistate system in this paper forms a general monotone process model which includes the geometric process repair model as a special case. A numerical example is given to illustrate the theoretical results.     

Asymptotic properties of a stochastic predator–prey system with Holling II functional response

A stochastic predator–prey system with Holling II functional response is proposed and investigated. We show that there is a unique positive solution to the model for any positive initial value. And we show that the positive solution to the stochastic system is stochastically bounded. Moreover, under some conditions, we conclude that the stochastic model is stochastically permanent and persistent in mean.     

Optimal premium policy of an insurance firm: Full and partial information

Herein, we study the optimization problem faced by an insurance firm who can control its cash-balance dynamics by adjusting the underlying premium rate. The firm’s objective is to minimize the total deviation of its cash-balance process to some pre-set target levels by selecting an appropriate premium policy. Our problem is totally new and has three distinguishable features: (1) both full and partial information cases are investigated here; (2) the state is subject to terminal constraint; (3) a forward-backward stochastic differential equation formulation is given which is more systematic and mathematically advanced. This formulation also enables us to continue further research in a generalized stochastic recursive control framework (see Duffie and Epstein (1992), El Karoui et al. (2001), etc.). The optimal premium policy with the associated optimal objective functional are completely and explicitly derived. In addition, a backward separation technique adaptive to forward-backward stochastic systems with the state constraint is presented as an efficient and convenient alternative to the traditional Wonham’s (1968) separation principle in our partial information setup. Some concluding remarks are also given here.     

与年龄相关的随机分数阶种群系统温和解的存在性、唯一性

本文研究了一类与年龄相关的随机分数阶种群动态系统.利用不动点定理、随机分析和算子半群理论,讨论了与年龄相关的随机分数阶种群系统温和解的存在性、唯一性.本文是随机整数阶种群系统的推广.     

Stabilization of a class of nonlinear composite stochastic systems

This paper deals with the stability for a class of nonlinear composite stochastic systems by feedback laws.Firstly,we give sufficient conditions for the existence of feedback laws which render the equilibrium solution of the stochastic system globally asymptotically stable in probability.Secondly,for stochastic systems of the same type,we prove that there exists a linear feedback law which exponentially stabilizes in mean square the closed–loop stochastic system at its equilibrium.     

On a stochastic nonlinear equation in one-dimensional viscoelasticity

In this paper we discuss an initial-boundary value problem for a stochastic nonlinear equation arising in one-dimensional viscoelasticity. We propose to use a new direct method to obtain a solution. This method is expected to be applicable to a broad class of nonlinear stochastic partial differential equations.

     

具有标准发生率的随机SIR传染病模型的建立及平稳分布与疾病灭绝研究

研究了一类具有标准发生率以及考虑随机扰动与系统变量成正比的随机SIR传染病模型.首先,对于任意的正的初值,系统存在唯一的全局正解以及通过构造合适的随机李雅普诺夫函数,得到了模型遍历平稳分布存在的充分条件.其次,给出了疾病灭绝的充分条件,并与模型遍历平稳分布存在的充分条件作对比,得出了在特定条件下随机SIR模型的阈值.最后通过数值模拟验证了结果的正确性.