An Optimum Allocation of Different Weapons to a Target Complex

How best to allocate offensive weapons of various types to a group of targets in order to maximize the payoff constitutes a very important problem for optimizing strategies of defense. Solutions to the allocation problem, for the case where one type of weapon is involved, exist in the literature. Essentially these solutions fall into two categories digital solutions which yield integral results, and analytical solutions, based on the Lagrange Multipliers, which treat the number of weapons as a continuous variable and thus produce fractional answers. Whenever the number of weapons is large compared with the number of targets, analytical methods are preferred to digital ones because they achieve a saving in computer time at a negligible loss of accuracy. On the other hand, if the number of weapons is of the same order of magnitude as the number of targets, digital methods are preferable because they yield exact answers, as opposed to analytical solutions that produce rounding errors too large to render the results useful. The object of this paper is to generalize an analytical solution to the case where the attacker has more than one type of weapon available for assignment to an undefended or virtually undefended target complex. Defense strategies are not included. The paper presents a computational example where three types of weapons, each with a different number of attacking vehicles, are allocated to twenty targets. This example also permits a comparison between the fractional results of an analytical solution and the integral values obtained by a computer-oriented algorithm.