Optimal Defensive Missile Allocation: A Discrete Min-Max Problem

This paper considers the problem of choosing the discrete antiballistic missile ABM defense levels of reliable subtractive area and point defenses protecting a set of targets so as to minimize the total damage done to the targets by on optimal attack by a given number of reliable offensive missiles of one type. It assumes that the offensive side knows the ABM defense levels chosen and that the defensive side knows the number of missiles possessed by the offensive side. The cost of the defensive allocation chosen must not exceed a stated budget level; the cost function need not be continuous or separable. The 0-1 implicit enumeration scheme of Lawler and Bell is combined with a branch-and-bound procedure to effect a solution.