The importance of the weapon target assignment problem is increasing as weapon systems are expected to become intelligent and unmanned on the future battlefield. This study discusses the weapon-target assignment in small-scale ground force combat, which has not been addressed much in other studies. In ground combat, target assignment means the start of an engagement, so assignment should be made taking into account not only the probability of killing an enemy but also the probability of surviving friendly forces. We introduce the WTAG (WTA ground) model that reflects these characteristics and describes methodologies for solving the problem including mixed integer nonlinear problems and Lagrangian relaxation approaches. Our finding is that the algorithm presented can efficiently provide the bounds of the problem in a practical size.