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.     

基于蒙特卡罗方法的多散射修正模型

针对现有的基于蒙特卡罗方法的非视线传输模型的不足和局限性,提出了基于蒙特卡罗方法的多散射修正模型,给出了模型的数学描述。利用坐标系变换方法,得出了光子迁移的坐标递推公式。设计了接收判断机制,给出了到达时间的计算公式。通过跟踪大量光子的随机迁移,验证了光子传输的多散射现象。绘制了接收天线功率密度曲线,模拟了脉冲展宽效应。比较结果表明,在满足单散射近似的条件下,该模型与Luett-gen单散射模型吻合较好;在不满足单散射近似条件时,该模型得出的接收功率密度大于Luettgen单散射模型的接收功率密度,分析了结果的正确性,并指出了现有模型信道零延迟的错误。理论分析表明,模型能准确反映信道的时延特性。     

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising. Size dependency is included in governing equations based on the modified couple stress theory. Hamilton's principle is used to derive governing equations of the cylindrical micro/nano shell. Solution procedure is developed using Navier technique for simply-supported boundary conditions. The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters, material properties, applied voltages and temperature rising on the free vibration responses.     

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.     

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     

Influence of thickness and projectile shape on penetration resistance of the compliant composite

The present study deals with development of conceptual proof for jute rubber basedflexible composite block to completely arrest the projectile impacting the target at high velocity impact of 400 m/s through numerical simulation approach using finite element (FE) method. The proposed flexible composite blocks of repeating jute/rubber/jute (JRJ) units are modelled with varying thickness from 30 mm to 120 mm in increments of 30 mm and impacted by flat (F), ogival (O) and hemispherical (HS) shaped projectiles. All the considered projectiles are impacted with proposed flexible composite blocks of different thicknesses and the penetration behaviour of the projectile in each case is studied. The penetration depth of the projectile in case of partially penetrated cases are considered and the effect of thickness and projectile shape on percentage of penetration depth is statistically analyzed using Tagu-chi's design of experiments (DOE). Results reveal that the though proposedflexible composite block with thickness of 90 mm is just sufficient to arrest the complete penetration of the projectile, considering the safety issues, it is recommended to use theflexible composite with thickness of 120 mm. The nature of damage caused by the projectile in the flexible composite is also studied. Statistical studies show that thickness of the block plays a prominent role in determining the damage resistance of the flexible composite.     

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.     

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。     

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