Annihilation prediction for lanchester-type models of modern warfare with logistics constraints

Abstract

Force-annihilation-prediction conditions are developed for Lanchester-type equations of modern warfare in which an important type of logistics constraint (limited ammunition) has been incorporated into the attrition-rate coefficients. Conceptually, combat is decomposed into two processes: (1) attrition and (2) logistics (ammunition consumption). After a discussion of Lanchester-type modelling of logistics processes for different levels of combat operations, a Lanchester-type homogenous-force model of a fire fight in small-scale combat (during which there is assumed to be no redistribution of ammunition) is presented with limited ammunition for each combatant being represented by time-dependent attrition-rate coefficients with compact support. Since physical/operational considerations compel one to sometimes consider discontinous attrition-rate coefficients, previous force-annihilation-prediction conditions developed under more restrictive conditions are extended to the general case of nonnegative, integrable attrition-rate coefficients and applied to the logistics-constrained Lanchester-type model developed here. The qualitative structure of battle outcome as a function of the initial force ratio for such logistics-constrained battles is discussed and several numerical examples given, which show that the situation considered here is a special case of time-constrained combat. These results allow one to study a broader class of variable-coefficient combat models of considerable tactical interest (e.g., models of logistics-constrained combat) almost as easily and thoroughly as Lanchester's classic constant-coefficient model (without logistics constraints).