Risk‐sensitive sizing of responsive facilities

We develop a risk‐sensitive strategic facility sizing model that makes use of readily obtainable data and addresses both capacity and responsiveness considerations. We focus on facilities whose original size cannot be adjusted over time and limits the total production equipment they can hold, which is added sequentially during a finite planning horizon. The model is parsimonious by design for compatibility with the nature of available data during early planning stages. We model demand via a univariate random variable with arbitrary forecast profiles for equipment expansion, and assume the supporting equipment additions are continuous and decided ex‐post. Under constant absolute risk aversion, operating profits are the closed‐form solution to a nontrivial linear program, thus characterizing the sizing decision via a single first‐order condition. This solution has several desired features, including the optimal facility size being eventually decreasing in forecast uncertainty and decreasing in risk aversion, as well as being generally robust to demand forecast uncertainty and cost errors. We provide structural results and show that ignoring risk considerations can lead to poor facility sizing decisions that deteriorate with increased forecast uncertainty. Existing models ignore risk considerations and assume the facility size can be adjusted over time, effectively shortening the planning horizon. Our main contribution is in addressing the problem that arises when that assumption is relaxed and, as a result, risk sensitivity and the challenges introduced by longer planning horizons and higher uncertainty must be considered. Finally, we derive accurate spreadsheet‐implementable approximations to the optimal solution, which make this model a practical capacity planning tool.© 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

巡航导弹航迹规划中雷达探测盲区的快速构造算法

现代防空系统对巡航导弹的低空飞行和突防造成极大的威胁,利用防空系统中预警雷达的探测盲区进行隐蔽飞行是提高巡航导弹生存能力的重要手段,在此雷达探测盲区的快速构造算法是关键。说明了什么是雷达探测盲区,分析了影响雷达探测盲区的三个主要因素,并就对巡航导弹影响最大的雷达地形遮蔽盲区构造了基于极坐标的快速算法,并用一个地形实例验证了该方法的有效性。     

Approximation algorithms for general one‐warehouse multi‐retailer systems

Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross‐docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ε‐optimality can be obtained by solving a related piece‐wise linear concave cost multi‐commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ε) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece‐wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece‐wise concavity feature of the cost functions. This gives rise to a unified and generic LP‐based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

A risk function for the stochastic modeling of electric capacity expansion

We present a stochastic optimization model for planning capacity expansion under capacity deterioration and demand uncertainty. The paper focuses on the electric sector, although the methodology can be used in other applications. The goals of the model are deciding which energy types must be installed, and when. Another goal is providing an initial generation plan for short periods of the planning horizon that might be adequately modified in real time assuming penalties in the operation cost. Uncertainty is modeled under the assumption that the demand is a random vector. The cost of the risk associated with decisions that may need some tuning in the future is included in the objective function. The proposed scheme to solve the nonlinear stochastic optimization model is Generalized Benders' decomposition. We also exploit the Benders' subproblem structure to solve it efficiently. Computational results for moderate‐size problems are presented along with comparison to a general‐purpose nonlinear optimization package. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:662–683, 2001     

基于A~*算法的虚拟士兵城市作战路径规划

针对虚拟士兵在城市作战仿真领域的需求,重点研究了虚拟士兵在城市环境中路径规划问题。通过对三维城市虚拟环境空间进行分层信息处理,生成虚拟士兵能够感知的虚拟信息层。用A*算法求出虚拟士兵从初始位置到达目标位置的最佳路径,并给出算法的具体设计与实现。     

Models for production planning under power interruptions

We present a robust optimization model for production planning under the assumption that electricity supply is subject to uncertain interruptions caused by participation in interruptible load contracts (ILCs). The objective is to minimize the cost of electricity used for production while providing a robust production plan which ensures demand satisfaction under all possible interruption scenarios. The combinatorial size of the set of interruption scenarios makes this a challenging problem. Furthermore, we assume that no probabilistic information is known about the supply uncertainty: we only use the information given in the ILC to identify an uncertainty set that captures the possible scenarios. We construct a general robust framework to handle this uncertainty and present a heuristic to compute a good feasible solution of the robust model. We provide computational experiments on a real‐world example and compare the performance of an exact solver applied to the robust model with that of the heuristic procedure. Finally, we include the operational impact of interruptions such as “recovery modes” in the definition of the uncertainty set. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Making long-range planning work: the case of the US Army's 30-year strategic modernization plan

The extensive timespan of evolving assumptions about future adversaries, US military engagements, and technology inherent in the US Army's 30-year modernization strategy can overwhelm the management capacity of planners, and misdirect acquisition investments. Some military scholars have argued that long-range planning is futile due to the complexities of the global security environment. So how can the US Army manage the evolving assumptions inherent in its 30-year modernization strategy to ensure it remains a superior global force? This study will answer the above question by arguing that the US Army's 30-year modernization strategy, while emulative of a similar modernization approach in the threat-based planning environment of the Cold War, is viable if supported by a method and a tool that manage investments and planning assumptions.     

Route optimization for multiple searchers

We consider a discrete time‐and‐space route‐optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. This article formulates a novel convex mixed‐integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target‐ and location‐dependent search effectiveness. We present two solution approaches, one based on the cutting‐plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting‐plane approach solves many realistically sized problem instances in a few minutes, while existing branch‐and‐bound algorithms fail. A specialized cut improves solution time by 50[percnt] in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting‐plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

多无人机梯次攻击航路规划

为了解决多无人机协同攻击航路规划问题,基于一种雷达威胁等效方法,以及无人机在不同姿态下雷达散射截面RCS(Radar Cross-Section)值随之改变的特性,结合多机作战战术思想,提出了一种多无人机梯次协同攻击同一目标的方法,并利用Dijkstra算法进行多无人机航路规划.仿真结果表明,该方法具有更高的应用价值.     

基于CPN的TDRS操作规划建模与仿真

以中继卫星(Racking and Data Relay Satellite,TDRS)为研究对象,以有色Petri网(Colored Petri Net,CPN)为数学工具,根据自顶向下的原则和层次化建模思想,提出一种基于CPN的TDRS操作规划模型,该模型分为顶层模型、控制模型、前向链路数据接收任务与发送任务的操作规划模型和返向链路数据接收任务与发送任务的操作规划模型,有效地描述了TDRS的动态行为特性。最后,通过仿真实验得到了TDRS操作规划方案,验证了所建模型的有效性。与PDDL模型比较分析表明:所建模型可以有效引入TDRS的领域知识,能够有效提高求解效率。所建模型可以为TDRS操作规划方案的制定提供理论参考。