火箭助飞鱼雷与空投鱼雷齐射攻潜射击方法

火箭助飞鱼雷与空投鱼雷齐射攻潜是水面舰艇中远距离攻潜的有效方法之一。由于火箭助飞鱼雷和空投鱼雷齐射的平台、弹道不同,为了有效的组织鱼雷的齐射,必须解决相关的问题。因此,从火箭助飞鱼雷与空投鱼雷的作战使用特点出发,首先探讨两雷齐射的定义及实施方法,其次通过计算机仿真研究了实施齐射时的直升机安全问题,并研究了两雷射击的间隔时间,拟合了计算公式。总之,此问题的研究对发挥水面舰艇中远距离反潜作战能力具有一定的意义。     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

Interception probability simulation and analysis of salvo of two electromagnetic coil launched anti-torpedo torpedoes

Electromagnetic coil launch is an important branch of electromagnetic launch (EML) technology, which is suitable for launching anti-torpedo torpedo (ATT). This paper focuses on the EML parameters and the interception probability of the EML two ATTs salvo. Based on the launching model of a multi-stage coil launcher, the trajectory model of the ATT and the attacking torpedo, a calculation method for the EML two ATTs salvo parameters is proposed, with the conditions of capture and interception given reasonably. An adaptive particle swarm optimization (APSO) algorithm is proposed to calculate the optimal launching parameters, by designing the adaptive inertia weight and time-varying study factors. According to the analysis of the simulation with Monte Carlo method, EML will improve the interception probability effectively, and the interception probability is affected by the launching range. The results demonstrate good performance of the proposed APSO in calculating EML parameters for the two ATTs salvo in certain combat situation. Implications of these results are particular regarding the command and decision in the anti-torpedo combat.     

火箭深弹人工散布射击方法

为提高火箭深弹对潜攻击作战效能,根据现在火箭深弹武器系统的特点,分析了影响火箭深弹射击效果的因素,提出了几种组织火箭深弹人工散布的射击方案,建立了火箭深弹齐射毁伤概率计算模型,进行了计算机仿真,对组织人工散布的火箭深弹齐射毁伤概率进行了分析计算,得出了使用火箭深弹组织人工散布的最优方案,进而给出了火箭深弹人工散布射击方法,采用该种射击方法,可有效提高火箭深弹毁伤目标概率.     

Effective attacks in the salvo combat model: Salvo sizes and quantities of targets

This article considers two related questions of tactics in the context of the salvo model for naval missile combat. For a given set of targets, how many missiles should be fired to produce an effective attack? For a given available salvo size, how many enemy targets should be fired at? In the deterministic version of the model I derive a simple optimality relationship between the number of missiles to fire and the number of targets to engage. In the stochastic model I employ the expected loss inflicted and the probability of enemy elimination as the main performance measures and use these to derive salvo sizes that are in some sense “optimal.” I find that the offensive firepower needed for an effective attack depends not only on a target's total strength but also on the relative balance between its active defensive power and passive staying power. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The salvo combat model with area fire

This article analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. Although these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Although the relative size of each force is important with aimed fire, with area fire, it is the absolute size that matters. Similarly, although aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area fire and the other uses aimed fire, the model displays a mix of square and linear law behavior. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 652–660, 2013     

声自导雷平行齐射发现概率解析计算模型

为了准确快速地评估声自导鱼雷平行齐射的作战效能（发现概率）,从鱼雷、目标的相对运动入手,将目标位置及运动随机误差转移到鱼雷航向上;如此建立了计算声自导鱼雷平行齐射发现概率的一重积分解析模型（不考虑鱼雷航行性能误差）和四重积分解析计算模型（考虑鱼雷航行性能误差）。最后以统计模型为标准来验证两个解析模型的正确性。仿真结果显示,对于90%左右的考察态势,解析模型与统计模型的结果差的绝对值在1%之内,另外10%左右的考察态势,也在1%-3%之间。从而验证了所建解析模型的正确性和可行性。     

Discounted production scheduling and employment smoothing

We consider the problem of minimizing the sum of production, employment smoothing, and inventory costs over a finite number of time periods where demands are known. The fundamental difference between our model and that treated in [1] is that here we permit the smoothing cost to be nonstationary, thereby admitting a model with discounting. We show that the values of the instrumental variables are nondecreasing in time when demands are nondecreasing. We also derive some asymptotic properties of optimal policies.     

When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Concavity and monotonicity properties in a groundwater management model

We consider a discrete‐time groundwater model in which the cost of pumping takes a slightly different form to that which has been traditional in the research literature to date. This enables us to prove that (a) the optimal pumping quantity is nondecreasing in the ground water stock, (b) the stock level remaining after each period's pumping is also nondecreasing in the groundwater stock, (c) the optimal decision is determined by maximizing a concave function, and finally (d) the optimal pumping quantity is nonincreasing in the number of periods to go. We show that (a)–(c), while intuitive, do not hold under traditional modeling assumptions. We also explain the connections between our results and similar ones for some classic problems of operations research. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2011     

弹着时间可控的机动目标多弹协同制导律*

针对机动目标的多导弹齐射攻击,运用最优控制和卡尔曼滤波理论探索机动目标下弹着时间可控制导律问题。设计了一种最优弹着时间可控的制导律,它由指定弹着时间和预计弹着时间的误差作为反馈信号与传统比例制导律结合推导得出,称之为弹着时间可控制导律（Impact-time-control Guidance Law,简称ITCG）,同时利用卡尔曼滤波估计了目标加速度。通过对作战模型情况的仿真,可以看出这种新型的制导律应用于引导多发导弹以指定时间同时攻击目标时的有效性和可行性。     

潜艇鱼雷武器多通道射击控制研究

在论述潜艇武器系统演变到武器通道的客观必然和技术特点的基础上,分析了反鱼雷技术在海上攻防对抗过程中给潜艇鱼雷攻击带来的困难。为了弥补鱼雷同一种自导方式齐射在对抗阶段存在的不足,提出了潜艇鱼雷武器多通道射击控制(或多自导方式鱼雷混合齐射)的概念。研究了实现鱼雷混合自导方式齐射所涉及的技术环节,给出了解决齐射各雷相互干扰、射击参数解算等问题的相应方法和模型。     

Three-machine flowshop stochastic scheduling to minimize distribution of schedule length

This article studies a special case of stochastic three-machine, permutation flowshop scheduling. It is proved that a sequence where processing times on the first and third machines are in a monotone nondecreasing and nonincreasing order of the likelihood ratio, respectively, and on the second machine are equally distributed, minimizes distribution of schedule length.     

Effects of lethality in naval combat models

In the context of both discrete time salvo models and continuous time Lanchester models we examine the effect on naval combat of lethality: that is, the relative balance between the offensive and defensive attributes of the units involved. We define three distinct levels of lethality and describe the distinguishing features of combat for each level. We discuss the implications of these characteristics for naval decision‐makers; in particular, we show that the usefulness of the intuitive concept “more is better” varies greatly depending on the lethality level. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

弹着时间可控的机动目标多弹协同制导律

针对机动目标的多导弹齐射攻击,运用最优控制和卡尔曼滤波理论探索机动目标下弹着时间可控制导律问题。设计了一种最优弹着时间可控的制导律,它由指定弹着时间和预计弹着时间的误差作为反馈信号与传统比例制导律结合推导得出,称之为弹着时间可控制导律（Impact-time-control Guidance Law,简称ITCG）,同时利用卡尔曼滤波估计了目标加速度。通过对作战模型情况的仿真,可以看出这种新型的制导律应用于引导多发导弹以指定时间同时攻击目标时的有效性和可行性。     

A planning horizon algorithm for deterministic inventory management with piecewise linear concave costs

We consider a single-product, discrete-time production/inventory-control problem with nonstationary concave nondecreasing costs. Given a forecast horizon K, the problem is to find a decision horizon. We specialize to piecewise linear costs a general approach whereby a problem with horizon K + 1 and arbitrary final demand is parametrically solved. The resulting algorithm is polynomial in the input size.     

Analysis of artillery shoot‐and‐scoot tactics

Firing multiple artillery rounds from the same location has two main benefits: a high rate of fire at the enemy and improved accuracy as the shooter's aim adjusts to previous rounds. However, firing repeatedly from the same location carries significant risk that the enemy will detect the artillery's location. Therefore, the shooter may periodically move locations to avoid counter‐battery fire. This maneuver is known as the shoot‐and‐scoot tactic. This article analyzes the shoot‐and‐scoot tactic for a time‐critical mission using Markov models. We compute optimal move policies and develop heuristics for more complex and realistic settings. Spending a reasonable amount of time firing multiple shots from the same location is often preferable to moving immediately after firing an initial salvo. Moving frequently reduces risk to the artillery, but also limits the artillery's ability to inflict damage on the enemy.     

An improved algorithm for the dynamic lot-sizing problem with learning effect in setups

The dynamic lot-sizing problem with learning in setups is a variation of the Wagner-Whitin lot-sizing problem where the setup costs are a concave, nondecreasing function of the cumulative number of setups. This problem has been a subject of some recent research. We extend the previously studied model to include nonstationary production costs and present an O(T²) algorithm to solve this problem. The worst-case complexity of our algorithm improves the worst-case behavior of the algorithms presently known in the literature. © 1993 John Wiley & Sons, Inc.     

A network flow approach for capacity expansion problems with two facility types

A deterministic capacity expansion model for two facility types with a finite number of discrete time periods is described. The model generalizes previous work by allowing for capacity disposals, in addition to capacity expansions and conversions from one facility type to the other. Furthermore, shortages of capacity are allowed and upper bounds on both shortages and idle capacities can be imposed. The demand increments for additional capacity of any type in any time period can be negative. All cost functions are assumed to be piecewise, concave and nondecreasing away from zero. The model is formulated as a shortest path problem for an acyclic network, and an efficient search procedure is developed to determine the costs associated with the links of this network.     

Bin‐packing problem with concave costs of bin utilization

We consider a generalized one‐dimensional bin‐packing model where the cost of a bin is a nondecreasing concave function of the utilization of the bin. Four popular heuristics from the literature of the classical bin‐packing problem are studied: First Fit (FF), Best Fit (BF), First Fit Decreasing (FFD), and Best Fit Decreasing (BFD). We analyze their worst‐case performances when they are applied to our model. The absolute worst‐case performance ratio of FF and BF is shown to be exactly 2, and that of FFD and BFD is shown to be exactly 1.5. Computational experiments are also conducted to test the performance of these heuristics. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006