使用前向-后向随机微分方程的约束深度库存管理
Constrained Deep Inventory Management Using Forward-Backward SDEs
- University of Washington（华盛顿大学）
- Amazon（亚马逊）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于前向-后向随机微分方程和深度学习的多产品库存管理方法，处理路径wise总运营约束，扩展高相对阶控制障碍函数至混合约束，实现安全最优补货决策。
AI中文摘要：
我们研究在路径wise（而非期望）施加的总运营限制下的多产品补货问题。现有库存和在途库存、仓库容量以及排放配额定义了一个安全集，由此产生的多产品缺货问题被建模为一个安全随机最优控制问题。Hamilton-Jacobi-Bellman (HJB) 方程被表示为前向-后向随机微分方程 (FBSDEs) 系统，并通过学习值函数及其梯度来求解，在每个决策时刻求解一个由控制障碍函数 (CBF) 推导出的二次规划。由于采购订单仅进入在途管道，在途约束的相对阶为一，而现有库存约束的相对阶为二。我们将 (Clark, 2021) 的随机高相对阶构造从单一障碍扩展到四个混合相对阶的耦合总约束，并通过设计确立了其初始条件要求。
英文摘要：
We study multi-product replenishment subject to aggregate operating limits imposed pathwise in place of expectation. On-hand and in-transit inventory, warehouse capacity and an emission allowance define a safe set, and the resulting multi-product lost-sales problem is posed as a safe stochastic optimal control problem. The Hamilton--Jacobi--Bellman (HJB) equation is represented as a system of forward--backward stochastic differential equations (FBSDEs) and solved by learning the value function and its gradient, with a quadratic program derived by control barrier function (CBF) is solved at each decision epoch. Because purchase orders enter the in-transit pipeline only, the in-transit constraints have relative degree one while the on-hand constraints have relative degree two. We extend the stochastic high-relative-degree construction of (Clark, 2021) from a single barrier to four coupled aggregate constraints of mixed relative degree, and we establish its initial-condition requirement by design.
