An attacker with homogeneous weapons aims to destroy a target via sequential engagements over a finite planning horizon. Each weapon, with an associated cost, has a nonzero probability of destroying the target. At each decision epoch, the attacker can allocate a salvo of weapons to increase its chances, however this comes at the increasing linear cost of allocating additional weapons. We assume complete information in that the target status (dead or alive) is known. The attacker aims to maximize its chances of destroying the target while also minimizing the allocation cost. We show that the optimal salvo size, which is a function of time and inventory levels, is monotonic nondecreasing in both variables. In particular, we show that the salvo size either stays the same or decreases by one when the inventory level drops by one. The optimal allocation can be computed by solving a nonlinear stochastic dynamic program. Given the computational burden typically associated with solving Bellman recursions, we provide a scalable linear recursion to compute the optimal salvo size and numerical results to support the main ideas.

中文翻译：

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顺序攻击齐射的大小在时间和库存水平上都是单调不变的

拥有同质武器的攻击者旨在通过在有限的计划范围内进行连续交战来摧毁目标。每件具有相应成本的武器，其摧毁目标的机率均不为零。在每个决策时期，攻击者都可以分配大量武器来增加其机会，但这是以分配额外武器的线性成本不断增加为代价的。我们假定目标状态（死或活）的完整信息是已知的。攻击者旨在最大程度地破坏目标，同时还使分配成本最小化。我们表明，最优齐射大小是时间和库存水平的函数，在两个变量中都是单调不变的。特别是，我们显示，当库存水平下降1时，齐射尺寸保持不变或下降1。最优分配可以通过求解非线性随机动态程序来计算。给定通常与解决Bellman递归相关的计算负担，我们提供了可伸缩的线性递归，以计算最优的齐射大小和数值结果来支持主要思想。