用神经网络快速预测复杂库存系统的长期性能。
Supervised Learning for the (s,S) Inventory Model with General Interarrival Demands and General Lead Times
- 基于神经网络，用分布的低阶矩作输入逼近库存状态。
- 可秒级预测库存分布、周期时长和缺货概率，误差小。
- 适合需要快速分析复杂库存模型的研究者与从业者。
连续审查的(s,S)库存模型是随机库存理论的核心，但当需求到达间隔和订货提前期服从非马尔可夫分布时，其分析变得解析不可解。此时，评估长期性能通常依赖昂贵的模拟。本文提出一种基于神经网络的监督学习框架，用于近似具有通用分布的需求到达间隔和订货提前期（在缺货损失情境下）的(s,S)库存系统的稳态性能度量。首先通过模拟生成训练标签，随后训练神经网络。训练后，神经网络几乎即时提供系统各项指标的预测，如库存水平的稳态分布、期望周期时间及缺货概率。我们发现，仅使用分布的少量低阶矩作为输入，即可有效训练网络并准确捕捉稳态分布。大量数值实验表明，在广泛系统参数范围内均具高精度。该方法有效替代了重复且昂贵的模拟运行。本框架易于扩展至其他库存模型，为分析复杂随机系统提供了高效快速的替代方案。
原文摘要 · Abstract (English)
The continuous-review (s,S) inventory model is a cornerstone of stochastic inventory theory, yet its analysis becomes analytically intractable when dealing with non-Markovian systems. In such systems, evaluating long-run performance measures typically relies on costly simulation. This paper proposes a supervised learning framework via a neural network model for approximating stationary performance measures of (s,S) inventory systems with general distributions for the interarrival time between demands and lead times under lost sales. Simulations are first used to generate training labels, after which the neural network is trained. After training, the neural network provides almost instantaneous predictions of various metrics of the system, such as the stationary distribution of inventory levels, the expected cycle time, and the probability of lost sales. We find that using a small number of low-order moments of the distributions as input is sufficient to train the neural networks and to accurately capture the steady-state distribution. Extensive numerical experiments demonstrate high accuracy over a wide range of system parameters. As such, it effectively replaces repeated and costly simulation runs. Our framework is easily extendable to other inventory models, offering an efficient and fast alternative for analyzing complex stochastic systems.
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