Sequential attack salvo size is monotonic nondecreasing in both time and inventory level

Kalyanam, K. and Clarkson, J. (2020) Sequential attack salvo size is monotonic nondecreasing in both time and inventory level. Naval Research Logistics. ISSN 0894-069X

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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.

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Journal Article
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Naval Research Logistics
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13 Jan 2021 15:20
Last Modified:
03 Mar 2021 12:02