Theory of Measures of Effectiveness for General-Purpose Military Forces: Part II. Lagrange Dynamic Programming in Time-Sequential Combat Games

This paper develops a method for converting the overall objectives of a military campaign into specific time-dependent objectives, suitable for guiding strategic decisions during the evolution of the campaign. In a mathematical sense, the paper deals with time-sequential two-person zero-sum games, in which the feasible strategies in any period depend on the resources left by strategy choices in previous time periods. The technique produces time-dependent shadow values for the various types of combat forces. While these shadow values derive ultimately from the national values at stake in the war, they escalate exponentially as we move backward in time from the projected end of the war. Thus, at the start of a long war, the shadow values of military forces and equipment can completely dominate the intrinsic economic and political values, so that initial combat strategy is motivated almost exclusively by the goals of force preservation and the destruction of enemy forces. This sensitive time dependence of the values helps to explain past difficulties in assessing shadow values for general-purpose forces. However, it appears that the relative shadow values of different force types may be comparatively constant and may be quite useful.