Optimal Policies for Dynamic Pricing and Inventory Control with Nonparametric Censored Demands
Optimal Policies for Dynamic Pricing and Inventory Control with Nonparametric Censored Demands
复制标题
具有非参数审查需求的动态定价和库存控制的最优策略
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Yuanshuo Zhou
中科院分区：
文献类型：
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作者：
Boxiao Chen;Yining Wang;Yuanshuo Zhou
我们研究了T个连续审查期内销售损失的联合定价和库存控制的经典模型。企业不知道需求分布的先验，需要学习它从历史审查的需求数据。我们开发了非参数在线学习算法，以最快的速度收敛到千里眼的最优策略。根本的挑战依赖于，无论是零阶或一阶反馈是可访问的公司和奖励在任何单一的价格是不可观察的，由于需求审查。我们提出了一种新的反演方法的基础上的经验措施，一致地估计在两个价格的瞬时奖励函数的差异，直接解决审查需求带来的根本挑战。基于这一技术创新，我们设计了对分和三分搜索方法，在奖励函数为凹的情况下获得[公式：见文字]遗憾，并且我们设计了主动锦标赛淘汰方法，在奖励函数为非凹的情况下获得[公式：见文字]遗憾。我们用一个匹配的[Formula：see text]后悔下限来补充[Formula：see text]后悔上限。下界是由一个新的信息理论参数的基础上广义平方Hellinger距离，这是显着不同的传统参数的基础上Kullback-Leibler分歧。基于“差分估计”的上界技术和基于广义Hellinger距离的下界技术在文献中都是新的，并且可以潜在地应用于解决其他涉及学习的库存或截尾需求类型的问题。这篇论文被运营管理部的珍内特宋接受。补充材料：数据文件和在线附录可在https://doi.org/10.1287/mnsc.2023.4859上获得。
We study the classic model of joint pricing and inventory control with lost sales over T consecutive review periods. The firm does not know the demand distribution a priori and needs to learn it from historical censored demand data. We develop nonparametric online learning algorithms that converge to the clairvoyant optimal policy at the fastest possible speed. The fundamental challenges rely on that neither zeroth-order nor first-order feedbacks are accessible to the firm and reward at any single price is not observable due to demand censoring. We propose a novel inversion method based on empirical measures to consistently estimate the difference of the instantaneous reward functions at two prices, directly tackling the fundamental challenge brought by censored demands. Based on this technical innovation, we design bisection and trisection search methods that attain an [Formula: see text] regret for the case with concave reward functions, and we design an active tournament elimination method that attains [Formula: see text] regret when the reward functions are nonconcave. We complement the [Formula: see text] regret upper bound with a matching [Formula: see text] regret lower bound. The lower bound is established by a novel information-theoretical argument based on generalized squared Hellinger distance, which is significantly different from conventional arguments that are based on Kullback-Leibler divergence. Both the upper bound technique based on the “difference estimator” and the lower bound technique based on generalized Hellinger distance are new in the literature, and can be potentially applied to solve other inventory or censored demand type problems that involve learning. This paper was accepted by Jeannette Song, operations management. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2023.4859 .
通过需求学习保护隐私的动态个性化定价
影响因子：
5.4
作者：
Chen, Xi;Simchi-Levi, David;Wang, Yining
通讯作者：
Wang, Yining