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In this thesis, an error analysis based method is proposed to calculate single shot hit probability (PSSH) values of a fire control system. The proposed method considers that a weapon and a threat are located in three dimensional space. They may or may not have relative motion in three dimensions with respect to each other. The method accounts for the changes in environmental conditions. It is applicable in modeling and simulation as well as in top down design of a fire control system to reduce the design cost. The proposed method is applied to a specific fire control system and it is observed that PSSH values highly depend on the distance between the weapon and the threat, hence they are time varying. Monte Carlo simulation is used to model various defense scenarios in order to evaluate a heuristic developed by G&uuml / lez (2007) for weapon-threat assignment and scheduling of weapons&rsquo / shots. The heuristic uses the proposed method for PSSH and time of flight computation. It is observed that the difference between the results of simulation and heuristic depends on the scenario used.

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.