用深度学习解决50个商品的随机补货难题
A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions
- 将高维补货问题转为连续时间脉冲控制，用神经网络求解
- 在50维场景下性能优于现有最佳基准方法
- 适合需要大规模多品类库存优化的电商与供应链场景
针对一类高维随机联合补货问题，本文提出一种离散时间模型。首先将问题近似为连续时间脉冲控制问题，利用脉冲控制、带跳的后向随机微分方程（BSDEs）与随机目标问题之间的关联，构建了一种基于模拟和深度神经网络的新型计算方法。基于该方法求解结果，设计出可实施的原始（离散时间）随机联合补货问题的库存控制策略，并在一系列测试问题中与现有最优基准进行对比。实验表明，所提方法在目前已研究的问题中达到或超越最佳基准性能，且在至少50维（即50个库存单位，SKUs）下仍具备计算可行性。
原文摘要 · Abstract (English)
We consider a discrete-time formulation for a class of high-dimensional stochastic joint replenishment problems. First, we approximate the problem by a continuous-time impulse control problem. Exploiting connections among the impulse control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions -- that is, 50 stock-keeping units (SKUs).
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。