人力资源配置与随机AI资源容量的联合优化
Joint Optimization of Human Headcount and Stochastic AI Resource Capacity
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中文总结 AI 辅助
本文针对生成式AI工具带来的成本压力，构建联合分配模型优化人力资源与AI令牌容量，得出相关最优解及替代关系反转的实证检验条件。
中文摘要 AI 辅助
生成式AI工具正迅速成为编码及其他业务运营的标准配置，虽能提升生产力，但其不可预测且往往高昂的成本给企业带来严重财务压力。企业管理层需在固定预算中分配人力资源配置与生成式AI令牌容量，而标准确定性规划忽略了令牌消耗的重尾波动性及审核AI生成输出的认知成本。我们将经认知摩擦调整的生产函数与机会约束随机预算前沿结合，构建联合分配模型，假设每位工程师的令牌使用量为独立同分布、非负且右偏的随机变量，不设定参数族，仅使用其均值、方差和偏度进行分析。通过带Cornish-Fisher偏度校正的中心极限定理，将机会约束转化为确定性等价形式，求解所得拉格朗日函数可得到闭式最优人力资源配置、最优人均令牌强度的超越条件，以及对任意合理波动-人力资源配置比均成立的边海森二阶条件。比较静态分析显示，个体令牌波动性上升会提高最优人均令牌强度同时缩减人力资源配置，尽管人力与令牌在生产中为互补品，但随机预算使其在边际上为替代品；个体使用偏度作为纯粹无谓损失会缩减预算且不改变替代动态，上述结论均预设使用离散度与计划均值分配无关。若离散度随均值成比例缩放，替代关系会反转，因此适用哪种机制是可实证检验的关键问题。
英文摘要
Generative AI tools are rapidly becoming standard for coding and other business operations. However, while these tools can drive productivity, their unpredictable, and often significant, costs are putting severe financial strain on organizations. The leadership of such organizations must split a fixed budget between human headcount and generative-AI token capacity, yet standard deterministic planning ignores both the heavy-tailed volatility of token consumption and the cognitive cost of auditing AI-generated output. We model the joint allocation by intersecting a cognitive-friction-adjusted production function with a chance-constrained stochastic budget frontier. Per-engineer token usage is treated as i.i.d., non-negative, and right-skewed; no parametric family is assumed, as only its mean, variance, and skewness enter the analysis. The chance constraint is reduced to a deterministic equivalent via the Central Limit Theorem with a Cornish--Fisher skewness correction. Solving the resulting Lagrangian yields a closed-form optimal headcount, a transcendental condition for optimal per-capita token intensity, and a bordered-Hessian second-order condition that holds for any reasonable volatility-to-headcount ratio. Comparative statics show that rising individual token volatility raises optimal per-capita token intensity while contracting headcount: although human labor and tokens are complements in production, the stochastic budget makes them substitutes at the margin. Individual usage skewness acts as a pure deadweight tax that shrinks the budget without altering the substitution dynamics. Both conclusions presuppose that usage dispersion is invariant to the planned mean allocation. In the case where dispersion instead scales proportionally with the mean, the substitution reverses, so which regime applies is a sharp, empirically testable question.
