We study the weapon-target assignment (WTA) problem which has wideapplications in the area of defense-related operations research. This problem calls forfinding a proper assignment of weapons to targets such that the total expected damagedvalue of the targets to be maximized. The WTA problem can be formulated as a nonlinearinteger programming problem which is known to be NP-complete. There does notexist any exact method for the WTA problem even small size problems, although severalheuristic methods have been proposed. In this paper, Lagrange relaxation method isproposed for the WTA problem. The method is an iterative approach which is to decomposethe Lagrange relaxation into two subproblems, and each subproblem can be easyto solve to optimality based on its specific features. Then, we use the optimal solutionsof the two subproblems to update Lagrange multipliers and solve the Lagrange relaxationproblem iteratively. Our computational efforts signify that the proposed methodis very effective and can find high quality solutions for the WTA problem in reasonableamount of time.
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