Some simple victory-prediction conditions for lanchester-type combat between two homogeneous forces with supporting fires

This paper develops new “simple” victory-prediction conditions for a linear Lanchester-type model of combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. These simple victory-prediction conditions involve only the initial conditions of battle and certain assumptions about the nature of temporal variations in the attrition-rate coefficients. They are developed for a fixed-force-ratio-breakpoint battle by studying the force-ratio equation for the linear combat model. An important consideration is shown to be required for developing such simple victory-prediction conditions: victory is not guaranteed in a fixed-force-ratio-breakpoint battle even when the force ratio is always changing to the advantage of one of the combatants. One must specify additional conditions to hold for the cumulative fire effectivenesses of the primary weapon systems in order to develop correct victory-prediction conditions. The inadequacy of previous victory-prediction results is explained by examining (for the linear combat model without the supporting fires) new “exact” victory-prediction conditions, which show that even the range of possible battle outcomes may be significantly different for variable-coefficient and constant-coefficients models.     

An examination of the effects of the criterion functional on optimal fire-support policies

This paper examines the dependence of the structure of optimal time-sequential fire-support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantification of objectives (i.e. criterion functional). We consider the optimal time-sequential allocation of supporting fires during the “approach to contact” of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester-type equations of warfare, and the optimal fire-support policy for each one-sided combat optimization problem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular difficulty in one of them. For the same combat dynamics, the splitting of supporting fires between two enemy forces in any optimal policy (i.e. the optimality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an “overall” military advantage or a “local” one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fire-support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.     

Theoretical analysis of lanchester-type combat between two homogeneous forces with supporting fires

This paper studies combat between two homogeneous forces modelled with variable-coefficient Lanchester-type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential-equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable-coefficient Lanchester-type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.     

A Lanchester-type aggregated-force model of conventional ground combat

This article develops a Lanchester-type model of large-scale conventional ground combat between two opposing forces in a “sector”. It is shown that nonlinear Helmbold-type equations of warfare with operational losses may be used to represent the loss-rate curves that have been used in many aggregated-force models. These nonlinear differential equations are used to model the attrition of combat capability (as quantified by a so-called firepower index) in conjunction with a rate-of-advance equation that relates motion of the contact zone (or FEBA) between the opposing forces to the force ratio and tactical decisions of the combatants. This simplified auxiliary model is then used to develop some important insights into the dynamics of FEBA movement used in large-scale aggregated-force models. Different types of behavior for FEBA movement over time are shown to correspond to different ranges of values for the initial force ratio, for example, an attack will “stall out” for a range of initial force ratios above a specific threshold value, but it will “break out” for force ratios above a second specific threshold value. Such FEBA-movement predictions are essentially based on being able to forecast changes over time in the force ratio.     

Unpacking the various meanings of redundancy: from refining the concept to military planning

The authors engage in the debate over waste in military force structure planning by rigorously deconstructing the concept of “redundancy.” First, a typology of redundancy is constructed that provides a common framework for identifying variety among redundant structures. These are labeled “true redundancy,” “expanded capacity,” “portfolio diversification,” and “mission overlap.” Further, a number of mechanisms are identified that produce these types of structures, and show the conditions under which planners may utilize redundant structure in the search for optimization. In sum, the article provides refined concepts for analysts and planners to identify when redundancy is deleterious or beneficial.     

Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

谈大型石油化工企业火灾灭火指挥要则

大型石油化工企业在生产、储运过程中具有较大的火灾危险性 ,而且一旦发生火灾 ,火情复杂 ,燃烧与爆炸共存 ,易出现立体、大面积、多火点燃烧和复燃、复爆现象 ,灭火难度相当大。在灭火救援中 ,必须快速集中优势兵力和装备 ,实行“两级指挥”下的统一指挥 ,坚持计划指挥与临场指挥相结合 ,发挥固定灭火装置和工程技术人员的作用 ,打好攻防组合战。     

“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

Local perceptions of the EU’s role in peacebuilding: The case of security sector reform in Palestine

ABSTRACT

Perception research can make a valuable contribution to the study of the local dimension in EU peacebuilding. The conceptual framework developed in this article distinguishes between perceptions of the “legitimacy,” “effectiveness,” and “credibility” of EU peacebuilding practices, which are crucial factors for successful peacebuilding. Relying on the case of the EU’s support for security sector reform (SSR) in Palestine, this article shows that local stakeholders—which participate in various EU-sponsored training and capacity-building programs—display considerable support for liberal peacebuilding norms. Yet, perceived discrepancies between the EU’s peacebuilding rhetoric and its SSR activities have severely undermined the potential of the EU’s liberal peacebuilding model in the eyes of Palestinian stakeholders. Critical local perceptions are frequently articulated with reference to the EU’s own liberal peacebuilding discourse, pointing to a lack of inclusiveness of the SSR process and deficits in terms of democratic governance and the rule of law.     

Optimal scheduling of objects in circulating systems

A “circulating system” is a finite collection of objects, each of which is oscillaling between two states. The prototype system is that of ships on patrcl,each subject to a quasi-regular “duty-service” cycle. There are various restrictions on the time spent in either state by an object and on the number of objects in a state at any one time. Schedules are sought in which the total number in one state is as large and as constant as possible. The maximal average number in one state is calculated, and a necessary and sufficient condition is given for a schedule to achieve it. Procedures are developed for constructing a schedule which achieves the maximal average in the most constant manner.     

Optimal nonmyopic gambling strategy for the generalized Kelly criterion

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the optimal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997     

Systems defense games: Colonel blotto,command and control

The classical “Colonel Blotto” games of force allocation are generalized to include situations in which there are complementarities among the targets being defended. The complementarities are represented by means of a system “characteristic function,” and a valuation technique from the theory of cooperative games is seen to indicate the optimal allocations of defense and attack forces. Cost trade-offs between systems defense and alternative measures, such as the hardening of targets, are discussed, and a simple example is analyzed in order to indicate the potential of this approach.     

Changing the paradigm: Simulation,now a method of first resort

Decades ago, simulation was famously characterized as a “method of last resort,” to which analysts should turn only “when all else fails.” In those intervening decades, the technologies supporting simulation—computing hardware, simulation‐modeling paradigms, simulation software, design‐and‐analysis methods—have all advanced dramatically. We offer an updated view that simulation is now a very appealing option for modeling and analysis. When applied properly, simulation can provide fully as much insight, with as much precision as desired, as can exact analytical methods that are based on more restrictive assumptions. The fundamental advantage of simulation is that it can tolerate far less restrictive modeling assumptions, leading to an underlying model that is more reflective of reality and thus more valid, leading to better decisions. Published 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 293–303, 2015     

一类搜索型多对二随机格斗的获胜概率

研究搜索型多对二随机格斗战斗模型。假设格斗开始时A方有m件武器,B方有2件武器,B方处于隐蔽状态,格斗开始后B方可以直接对A方进行射击,A方需先搜索到B方后才能进行射击。双方各为同类武器,都是集火射击,所有开火都是独立的,每件武器开火射击直到毁伤对方才重新射击下一个目标。对搜索时间和毁伤间隔时间都服从一般分布的随机格斗模型,通过分析各状态的特征,利用状态概率分析方法和向后递归时间方法建立状态方程,求出了格斗处在各个状态的概率,并得到双方的获胜概率计算公式。     

Bringing Military Conduct out of the Shadow of Law: Towards a Holistic Understanding of Rules of Engagement

In this article, I outline a holistic approach to the military concept of “Rules of Engagement” (ROE), which complements the legal aspects of ROE with considerations of operational and political requirements for the use of military force. Drawing upon two illustrative cases from the US military experience with the use of ROE, I demonstrate that ROE for any particular military operation should be formulated to balance optimally, if not harmonize fully, the legal, operational and political concerns related to the use of force. In this task, political decision-makers and military practitioners alike are confronted with unavoidable and real-life dilemmas. How these dilemmas are handled has significant implications for how legal requirements concerning accountability and concerns for civilian lives in military combat can be preserved through ROE.     

“Effing” the military: a political misunderstanding of management

The use of commercial business management techniques is widespread in all government departments, including the Ministry of Defence. This article examines the use of popular management techniques in the Armed Forces and argues that their application is misplaced. It looks at what the “effs” – “efficiency” and “effectiveness” – mean in the business world and to the Armed Forces. It compares the definitions both in business and the Armed Forces and finds that there are few, if any, situations where the same measurements can be applied. Whilst many management techniques are suited for business, the function of the Armed Forces and its output cannot be measured in the same way, complicated by the different metrics of “efficiency” in peace and in war. This difference may not be clearly understood by some politicians, or indeed by some senior military personnel. Using examples from some of the most popular management techniques such as “Lean” and “Agile” it is possible to see that their use might actually diminish the capabilities of the Armed Forces when it comes to performing their principal role – the use of force to achieve political objectives.     

Walking the Line: Brokering Humanitarian Identities in Conflict Research

ABSTRACT

Increasingly, academic research in conflict-affected contexts relies on support from humanitarian organizations. Humanitarian organizations constitute sites of study in and of themselves; they partner with academics to roll out surveys or randomized program interventions; and they frequently facilitate security, logistics and transportation for independent researchers. We use a research partnership between IRC, the World Bank, and academic researchers in the UK, the US and eastern DR Congo, to explore the effects of humanitarian affiliation on conflict field research. In investigating when, how and under what conditions humanitarian identities are adopted by researchers (and how these affiliations shape research dynamics) we identify three paradoxes. First, “wearing humanitarian clothes” to facilitate research logistics can both facilitate and constrain access. Second, humanitarian affiliations invoked by researchers to ensure security and protection in volatile research sites can undermine the “insider” status of local staff. Finally, working through humanitarian organizations allows local and international researchers to benefit from the protections and privileges afforded to humanitarian employees without providing any of the services on which privileged access rests. In this article, we map out decisions faced by local and international researchers concerning when to adopt and discard humanitarian identities, and the fraught logistical, ethical and methodological consequences of these decisions.     

Strategic “defensivism” and post-reset blues: US–Russian nuclear arms reductions,missile defenses and minimum deterrence

US nuclear deterrence and arms control policy may be moving, by design and by inadvertence, toward a posture of strategic “defensivism”. Strategic “defensivism” emphasizes the overlapping and reinforcing impact of: (1) reductions in US, Russian and possibly other strategic nuclear forces, possibly down to the level of “minimum deterrence,” (2) deployment of improved strategic and/or theater antimissile defenses for the US, NATO allies and other partners; and (3) additional reliance on conventional military forces for some missions hitherto preferentially assigned to nuclear weapons. This article deals with the first two of these aspects only: the interaction between missile defenses and offensive force reductions in US–Russian strategy and policy. The findings are that stable deterrence as between the USA and Russia is possible at lower than New Strategic Arms Reduction Treaty levels, but reductions below 1000 deployed long-range weapons for each state, toward a true minimum deterrent posture, will require multilateral as opposed to bilateral coordination of arms limitations. Missile defenses might provide some denial capability against light attacks by states with small arsenals, but they still fall short of meaningful damage limitation as between powers capable of massive nuclear strikes.     

Quality control and the sales process

Product quality is emerging as a major strategic instrument for competition. The purpose of this article is to assess the effects of quality control on sales, and, vice versa, the effects of the sales process on quality control. A model relating quality control and the sales process (advertising, repeat purchase, and word-of-mouth effects) is developed to evaluate the above relationships. Two special cases, with degenerate and beta distribution for defect items in the production lot, are analyzed in detail. In the former case, analytical results for the optimal quality control schemes are obtained, whereas in the latter, efficient bounds are derived to search for the optimal scheme. It is shown, analytically and numerically, that the sales parameters have significant impact on whether more “stringent” or “tighter” quality control is warranted. Future research directions are also discussed.     

战争制胜机理何以发生变化

信息化战争已经登上了当今世界的舞台,这是军事领域发生的革命性变化。在信息化战争条件下,传统的战争制胜机理发生的新的变化。