Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition

Abstract

Abstract:We address the problem of optimal decision-making in conflicts based on Lanchester square law attrition model where a defending force needs to be partitioned optimally, and allocated to two different attacking forces of differing strengths and capabilities. We consider a resource allocation scheme called the Time Zero Allocation with Redistribution (TZAR) strategy, where allocation is followed by redistribution of defending forces, on the occurrence of certain decisive events. Unlike previous work on Lanchester attrition model based tactical decision-making, which propose time sequential tactics through an optimal control approach, the present article focuses on obtaining simpler resource allocation tactics based on a static optimization framework, and demonstrates that the results obtained are similar to those obtained by the more complex dynamic optimal control solution. Complete solution for this strategy is obtained for optimal partitioning of resources of the defending forces.

Optimal military strength allocation for campaign between single-kind arms and multi-kind arms

“…Literatures on this subject can be found in [1][2][3][4][5][6][7][8][9][10][11][12]. SHA Ji-Chang(1993) [1] studied this problem by differential game theory, and he pointed out that the defending side should concentrate all of its strength to fight with the strongest attacker.…”

A model for geographically distributed combat interactions of swarming naval and air forces

“…McEnearey et al [18], Ghose et al [6], Barkdoll et al [1], Wei et al [29], Popken et al [23]; while others emphasize the ground war, cf. González et al [8], and Sheeba et al [26]. These models are more detailed than DICM.…”

The Task of Distribution of Accessory Resources of Forces in Conflict Situations.

“…Это теория получила широкое распространение для анализа реальных боевых действий, и определяет тактику в военной игре моделирования [4,5,6]. Оптимальное распределение ресурсов и модели перераспределения в военных конфликтах на основе квадратичного закона Ланчестера предложено в [7,8]. В работе Chen, Jing, Li [2] проблема распределения подкрепление ресурсов сил в конфликтных ситуациях изучалась на основе метода Лагранжа.…”