In this work we optimize an effect-based weapon-target assignment that does not exceed a predetermined upper bounds P 1 , P 2 ,. .. , P k for the collateral damage of k types of assets. That is, for given P 1 , P 2 ,. .. , P k we optimize weapon-target assignments with respect to kill overhead by minimizing overkill of targets and assuring that the kill probabilities of friendly asset types do not exceed P 1 , P 2 ,. .. , P k .