Exact algorithms for scheduling multiple families of jobs on parallel machines

In many practical manufacturing environments, jobs to be processed can be divided into different families such that a setup is required whenever there is a switch from processing a job of one family to another job of a different family. The time for setup could be sequence independent or sequence dependent. We consider two particular scheduling problems relevant to such situations. In both problems, we are given a set of jobs to be processed on a set of identical parallel machines. The objective of the first problem is to minimize total weighted completion time of jobs, and that of the second problem is to minimize weighted number of tardy jobs. We propose column generation based branch and bound exact solution algorithms for the problems. Computational experiments show that the algorithms are capable of solving both problems of medium size to optimality within reasonable computational time. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 823–840, 2003.     

Modified couple stress and thickness-stretching included formulation of a sandwich micro shell subjected to electro-magnetic load resting on elastic foundation

This paper studies electromagnetoelastic static investigation of a sandwich doubly curved microshell subjected to multi-field loading based on a new thickness stretching included refined higher order shear/normal deformable model. Modified-couple-stress-theory (MCST) is used for accounting small-scale-dependency. The numerical results are derived using an analytical method. The effect of small scale parameter in micro scale, initial electric and magnetic potentials and foundation parameters is studied on the electromagnetoelastic bending results. It is confirmed an enhancing in stiffness of small scale shell with an increase in micro length scale parameter.     

某自行战车火控系统动态航路制定及软件实现

根据某型自行战车对空中目标作战的精度需求,为突破火控系统自带动态航路的局限性,提出了动态航路制定模型.在基准战车时目标起始点坐标进行测量的基础上,由连战斗队形配置确定全连其余战车相对基准车档坐标值,通过坐标转换计算,得到其余战车动态航路参数.采用面向对象的可视化编程语言C#2.0编写程序,设计动态航路制定软件.通过举例分析,证明了该方法的可行性,为有效提高自行战车的射击精度提供了一种较为科学的方法.     

The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy

We consider a two‐level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order‐up‐to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot‐sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state‐of‐the art solver reveal that our formulations are very effective in solving large‐size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Formulations for dynamic lot sizing with service levels

In this article, we study deterministic dynamic lot‐sizing problems with a service‐level constraint on the total number of periods in which backlogs can occur over a finite planning horizon. We give a natural mixed integer programming formulation for the single item problem (LS‐SL‐I) and study the structure of its solution. We show that an optimal solution to this problem can be found in \begin{align*}\mathcal O(n^2\kappa)\end{align*} time, where n is the planning horizon and \begin{align*}\kappa=\mathcal O(n)\end{align*} is the maximum number of periods in which demand can be backlogged. Using the proposed shortest path algorithms, we develop alternative tight extended formulations for LS‐SL‐I and one of its relaxations, which we refer to as uncapacitated lot sizing with setups for stocks and backlogs. {We show that this relaxation also appears as a substructure in a lot‐sizing problem which limits the total amount of a period's demand met from a later period, across all periods.} We report computational results that compare the natural and extended formulations on multi‐item service‐level constrained instances. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

线-面传输线Taylor与Agrawal模型解的比较

基于Maxwell方程推导描述外电磁场对导线的耦合传输线模型有Taylor,Agrawal和Rachidi三种模型,每个耦合公式给出相同的传输线响应,但是它们之间又有细微的差别,Nucci和Rachidi通过数值方法验证在圆柱形雷电电磁场激励下这三种线-面传输线模型在负载终端具有相同的全电压解。本文采用解析的方法对线-面传输线Taylor模型和Agrawal模型进行研究,获得了这两个模型基于平面电磁波激励下的终端负载响应的解析解,证明了它们的解析解是相同的。也就是说,线-面传输线Taylor模型和Agrawal模型其实是对同一个解的不同描述。因此,在实际应用时,可以根据具体情况来选择不同的传输线模型进行求解。     

索的UL列式分析方法

通过求解索的微分方程边值问题 ,提出了分析索的收敛迭代公式。利用迭代解可顺利地确定索端位置坐标差、索力及索重之间的关系。算例表明 :本文计算索的方法 ,理论上可达到任意高的精度 ,可十分方便地用于含有索或索网混合复杂结构物的大变形分析 ,用这种方法能解决斜拉桥缆索应力松驰的计算问题。     

Robust shortest path planning and semicontractive dynamic programming

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019