Sequential attack salvo size is monotonic nondecreasing in both time and inventory level
研究攻击者在有限时间内使用同质武器进行顺序攻击时，最优齐射规模如何随时间和库存变化，发现其单调非减且库存减少时规模最多减一，并提出高效算法。
Abstract 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.