A characterization of optimal base‐stock levels for a multistage serial supply chain

In this article, we present a multistage model to optimize inventory control decisions under stochastic demand and continuous review. We first formulate the general problem for continuous stages and use a decomposition solution approach: since it is never optimal to let orders cross, the general problem can be broken into a set of single‐unit subproblems that can be solved in a sequential fashion. These subproblems are optimal control problems for which a differential equation must be solved. This can be done easily by recursively identifying coefficients and performing a line search. The methodology is then extended to a discrete number of stages and allows us to compute the optimal solution in an efficient manner, with a competitive complexity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 32–46, 2016     

The probability of the existence of a feasible flow in a stochastic transportation network

Stochastic transportation networks arise in various real world applications, for which the probability of the existence of a feasible flow is regarded as an important performance measure. Although the necessary and sufficient condition for the existence of a feasible flow represented by an exponential number of inequalities is a well‐known result in the literature, the computation of the probability of all such inequalities being satisfied jointly is a daunting challenge. The state‐of‐the‐art approach of Prékopa and Boros, Operat Res 39 (1991) 119–129 approximates this probability by giving its lower and upper bounds using a two‐part procedure. The first part eliminates all redundant inequalities and the second gives the lower and upper bounds of the probability by solving two well‐defined linear programs with the inputs obtained from the first part. Unfortunately, the first part may still leave many non‐redundant inequalities. In this case, it would be very time consuming to compute the inputs for the second part even for small‐sized networks. In this paper, we first present a model that can be used to eliminate all redundant inequalities and give the corresponding computational results for the same numerical examples used in Prékopa and Boros, Operat Res 39 (1991) 119–129. We also show how to improve the lower and upper bounds of the probability using the multitree and hypermultitree, respectively. Furthermore, we propose an exact solution approach based on the state space decomposition to compute the probability. We derive a feasible state from a state space and then decompose the space into several disjoint subspaces iteratively. The probability is equal to the sum of the probabilities in these subspaces. We use the 8‐node and 15‐node network examples in Prékopa and Boros, Operat Res 39 (1991) 119–129 and the Sioux‐Falls network with 24 nodes to show that the space decomposition algorithm can obtain the exact probability of these classical examples efficiently. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 479–491, 2016     

On the hierarchy of γ‐valid cuts in global optimization

Concavity Cuts play an important role in concave minimization. In Porembski, J Global Optim 15 ( 17 ), 371–404 we extended the concept underlying concavity cuts which led to the development of decomposition cuts. In numerical experiments with pure cutting plane algorithms for concave minimization, decomposition cuts have been shown to be superior to concavity cuts. However, three points remained open. First, how to derive decomposition cuts in the degenerate case. Second, how to ensure dominance of decomposition cuts over concavity cuts. Third, how to ensure the finite convergence of a pure cutting plane algorithm solely by decomposition cuts. These points will be addressed in this paper. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

捷联惯导大失准角误差模型在快速传递对准中的应用

针对快速传递对准中主子惯导相对姿态存在大角度的情况,推导了捷联惯导大失准角误差模型.该模型采用欧拉角表示姿态误差,并用欧拉运动方程准确描述其传播规律.鉴于该模型中的姿态观测方程是复杂的非线性函数,采用无需求导的UKF算法,并采用奇异值分解(SVD)解决方差阵的病态问题.仿真结果表明,该算法在小角度误差条件下滤波精度优于线性模型,并且适用于大角度误差条件.     

四元数长方矩阵的同时复对角化

利用四元数矩阵的奇异值分解(SVD),对两个四元数长矩阵给出了其同时复对角化的充要条件,进一步对一个四元数长矩阵集合,针对其同时复对角化问题,给出了一系列充分必要条件.     

爆轰波斜冲击作用下破片飞散特性研究

为研究非对称结构战斗部的破片飞散特性,利用斜激波理论对爆轰波作用于壳体表面的过程进行研究,并利用自由面速度倍增定律对波在自由面反射后质点速度的计算进行简化,得到了破片飞散角的计算模型。利用D型战斗部试验数据对计算模型进行验证,结果表明,斜激波理论计算得到的破片飞散与试验结果吻合很好;当入射角较小时,壳体飞散角与入射角成线性关系。     

带运力限制及单边时变约束下多出发机场航空战略投送兵力分配模型研究

利用民航力量由多个机场向一个目标机场实施航空战略投送时,由于各民航机场都具有运力限制约束,不可能无限制地快速投送兵力,因此,考虑了在多个出发机场存在运力限制约束的情况下,构建了"投送时间最短,动员机场最少"多目标决策模型,并给出了优化算法和算例.     

球面高斯投影及其变形的闭合公式

将地球视为球体时,高斯投影与横墨卡托投影是同一种投影,因此高斯投影公式可表示为形式紧凑的闭合形式。根据相关定义,以高斯投影的闭合公式为基础,通过一系列数学变换,推导出高斯投影反解公式、经纬线投影方程、投影的长度比及子午线收敛角公式的严格解析式,并借助算例验证了推导结果的可靠性与正确性。与以往根据高斯投影的幂级数公式推得的结果进行了对比分析,结果表明:所推导出的公式逻辑上更严密、形式上更紧凑,既丰富了高斯投影理论,又完善了地图投影数学基础。     

基于投影分解与k最近邻距离的异常证据检测算法

为降低异常证据对合成结果的影响,提出了基于投影分解与k最近邻距离的异常证据检测算法。该算法在对证据集中所有证据进行焦元单一元素投影分解的基础上,重新构造证据的基本概率赋值,然后利用证据之间形成的欧式距离,采用k最近邻距离算法对异常证据进行检测。无线传感器网络应用实验分析表明:该算法可有效地对异常证据进行检测。对检测前后的证据利用证据合成规则进行融合对比结果发现,剔除了异常证据的合成结果并具有良好的峰值性和可分辨性,合成结果有利于融合决策。     

合成双射流冲击平板流场结构与模态分解分析

为揭示合成双射流冲击平板流场结构特征,通过大涡模拟方法对合成双射流冲击平板流动进行了仿真,采用有限时间Lyapunov指数方法对流场的拉格朗日涡结构进行了识别,并与欧拉框架下的速度矢量和涡量结果进行了对比分析。结果表明,在合成双射流两股射流交替作用下,射流核心区涡系结构较为复杂且涡量丰富,远离核心区存在一对稳定的涡结构,且拉格朗日涡结构与涡量对应较好,为合成双射流冲击冷却的布局设计提供了指导。另外,流场本征正交分解表明,第一阶模态关于激励器出口中心轴线大致对称,其能量占总体能量的35%,前6阶模态的能量占80%;根据前6阶模态所反映的流场特性,合成双射流冲击平板流场具有高度的对称性。