This thesis is concerned with the targeting problem and the fire sequencing problem. The main decision process of firing consists of two phases. Initially, we decide the weapon-target allocation by solving the targeting problem. Then, we schedule the firing sequence so as to minimize the timespan. Two phase approachgives flexibility to the plan officers. That means the plan officers can handle each problem separately under various tactical and operational constraints.
We consider the problem of assigning weapons to targets so that the total cost is minimized while satisfying various tactical and operational constraints. Given a set of weapon systems and a set of targets, we need to assign weapons to targets and determine the number of rounds that each weapon may fire on the targets. A target may be fired on by more than one weapon systems and a weapon may fire on more than one targets. The constraints include the amount of ammunition available for each weapon, the desired destroy level on each target, restriction on the number of targets that a weapon system can fire, and the upper bound on the number of rounds that can be fired for each weapon-target pair.
The targeting problem can be modeled as a nonlinear integer programming problem, which can be transformed into a linear integer programming problem by linearizing the nonlinear constraints. Even though targeting problem is NP-hard, we try to solve the problem to optimality within a reasonable amount of time.
In the basic targeting problem, we consider the minimum tactical and operational restrictions required to plan the targeting operation. To solve the basic targeting problem, we apply the Lagrangian relaxation and the branch-and-bound method. In the Lagrangian relaxation, a primal heuristic is developed so as to obtain the feasible solution from the infeasible solution obtained by solving the relaxed problem. Three different branching strategies are adopted and evaluated in the branch-and-bound method....