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Weapon-target allocation and scheduling for air defense with time varying hit probabilities

Gülez, Taner
In this thesis, mathematical modeling and heuristic approaches are developed for surface-to-air weapon-target allocation problem with time varying single shot hit probabilities (SSHP) against linearly approaching threats. First, a nonlinear mathematical model for the problem is formulated to maximize sum of the weighted survival probabilities of assets to be defended. Next, nonlinear objective function and constraints are linearized. Time varying SSHP values are approximated with appropriate closed forms and adapted to the linear model obtained. This model is tested on different scenarios and results are compared with those of the original nonlinear model. It is observed that the linear model is solved much faster than the nonlinear model and produces reasonably good solutions. It is inferred from the solutions of both models that engagements should be made as late as possible, when the threats are closer to the weapons, to have SSHP values higher. A construction heuristic is developed based on this scheme. An improvement heuristic that uses the solution of the construction heuristic is also proposed. Finally, all methods are tested on forty defense scenarios. Two fastest solution methods, the linear model and the construction heuristic, are compared on a large scenario and proposed as appropriate solution techniques for the weapon-target allocation problems.