arXiv:2411.08631stat.MLcs.LG2024-11

用深度生成模型联合优化定价与库存,无需假设需求分布。

Deep Generative Demand Learning for Newsvendor and Pricing

  • 基于条件生成模型学习价格与特征下的需求分布。
  • 可精准估算利润并求解最优定价与库存决策。
  • 适用复杂场景,尤其适合有文本特征的现实问题。

我们研究基于特征的报童问题中的数据驱动库存与定价决策,其中需求受价格和上下文特征影响,且不作结构假设。未知的需求分布导致具有挑战性的条件随机优化问题,还涉及决策依赖的不确定性及特征融合。受深度生成学习进展启发,我们提出一种新方法,利用条件深度生成模型(cDGMs)学习需求分布,并在给定价格和特征条件下生成概率性需求预测。该生成式方法支持精确利润估计,进而设计出两类核心算法:(1) 针对任意价格的最优库存优化;(2) 联合确定最优定价与库存水平。我们提供了理论保证,包括利润估计的一致性和决策收敛至最优解。大量模拟实验——涵盖从简单到复杂的多种场景,含文本特征案例——以及一个真实世界案例研究验证了方法的有效性。本方法为管理科学与运筹学开辟新范式,可拓展至报童与定价问题的各类变体,并有望解决其他条件随机优化问题。

原文摘要 · Abstract (English)

We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand distribution results in a challenging conditional stochastic optimization problem, further complicated by decision-dependent uncertainty and the integration of features. Inspired by recent advances in deep generative learning, we propose a novel approach leveraging conditional deep generative models (cDGMs) to address these challenges. cDGMs learn the demand distribution and generate probabilistic demand forecasts conditioned on price and features. This generative approach enables accurate profit estimation and supports the design of algorithms for two key objectives: (1) optimizing inventory for arbitrary prices, and (2) jointly determining optimal pricing and inventory levels. We provide theoretical guarantees for our approach, including the consistency of profit estimation and convergence of our decisions to the optimal solution. Extensive simulations-ranging from simple to complex scenarios, including one involving textual features-and a real-world case study demonstrate the effectiveness of our approach. Our method opens a new paradigm in management science and operations research, is adaptable to extensions of the newsvendor and pricing problems, and holds potential for solving other conditional stochastic optimization problems.

报童问题生成模型定价优化数据驱动

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