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The Generalized Weapon Target Assignment Problem

Abstract : Dynamic command and control and battle management functions require fast and effective decision aids to provide optimal allocation of resources (object/sensor pairing, weapon/target assignment) for effective engagement and real-time battle damage assessment. The basic Weapon Target Assignment (WTA) problem considers the assignment of a set of platforms/weapons to a set of targets such that the overall expected effect is maximized. In the present study, we extend the basic WTA problem by allowing for multiple target assignments per platform, subject to the number of weapons available and their effectiveness. We formulate the problem as a linear integer programming problem and investigate two solution methods. The first method is a greedy approach based on the sequential application of the auction algorithm that was generalized for assigning n assets/resources to m targets. The second method is built on a branch-and-bound framework that enumerates feasible tours of assets/resources a process that can become computationally intensive with increasing number of sources and targets but will find an optimal solution. We provide results of Monte Carlo experiments and provide comparative evaluation of the two solution methods. Finally, we extend the brand-and bound technique to assigning multiple platforms per target and thereby demonstrate its utility for collaborative asset planning. While this study focuses on weapon target pairing for illustration purposes, the methods and results herein are readily applicable to sensor tasking and similar resource allocation problems.