发表机构
Charles University, Faculty of Mathematics and Physics; Department of Mathematics & NTIS, Faculty of Applied Sciences, University of West Bohemia（查理大学数学物理学院; 西波希米亚大学应用科学学院数学与NTIS系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究固定兵力在多个独立战场上的最优分配问题，通过损失和生存函数建立通用框架，证明了凸损失下最优分配的存在性及NP难性，并给出整数情形下的精确算法及多种目标下的分配规则。
AI 中文摘要
我们研究在已知敌方兵力分布的情况下，将固定规模的兵力分配到独立战场上的问题。通过损失函数和生存函数来表述战场结果，使我们能够在不需要假设特定作战方程组的情况下建立分配结果。对于凸的敌方损失函数，存在一个最优分配，其中至多有一个战场部分饱和。我们证明了对于每一族满足端点归一化的严格凸、严格递增的损失函数，该问题是NP难的，并给出了当总兵力规模和饱和阈值为整数时的精确伪多项式算法。我们还推导了最大化成功交战次数、最大化己方幸存者数量以及最大化敌方损失与己方损失之比的分配规则。应用包括包含经典兰彻斯特、游击战和混合作战模型的幂律族，以及具有隐式定义结果的模型。
英文摘要
We study the allocation of a force of a fixed size across independent battlefields against a known distribution of opposing forces. Formulating battlefield outcomes through loss and survival functions allows us to establish allocation results without assuming a specific system of combat equations. For convex enemy loss functions, an optimal allocation exists with at most one partially saturated battlefield. We prove NP-hardness for every prescribed family of strictly convex, strictly increasing loss functions satisfying an endpoint normalization, and give an exact pseudopolynomial algorithm for the special case when the total force size and saturation thresholds are integers. We also derive allocation rules for maximizing successful engagements, maximizing own survivors, and maximizing the ratio of enemy losses to own losses. Applications include a power-law family containing the classical Lanchester, guerrilla, and mixed combat models, as well as models with implicitly defined outcomes.
Comments26 pages, 3 figures
