基于线性规划的可重用资源实时分类在线策略

Yiding Feng, Rad Niazadeh, A. Saberi
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引用次数: 33

摘要

在电子商务租赁服务应用的激励下,我们考虑了可重复使用产品的实时分类。在我们的模型中,具有异构类型的到达消费者从提供的分类中选择租赁产品,支付租赁费用,并在租赁时间后将产品归还给平台。消费者类型指定了他们对各种产品的选择型号、租赁费用和租赁时间分布。我们的目标是针对无先验设置和贝叶斯设置设计竞争性在线策略,前者类型是任意的(或对抗性的),后者类型是独立于已知分布的。我们的贡献是三重的。我们首先在这两种设置中引入离线线性规划基准,它们使用时变库存约束来捕获租金下策略的可行性,并且只需要在期望中满足这些约束。其次,在无先验设置中,我们基于引入的LP开发了一个随机原始对偶框架,以解决当产品租赁时间随时间固定时,Golrezaei等人(2014)的库存平衡策略获得与不可重复使用资源相同的(渐近最优)竞争比率。作为推论,当库存较大时,我们得到最优竞争比为(1−1/e)。我们还表明,在i.i.d(随时间)随机租赁时间下,这一系列政策具有恒定的竞争力。第三,我们通过引入使用预期LP解决方案作为指导的基于仿真的策略,将齿轮转向贝叶斯设置。通过使用原始对偶分析,我们获得了针对一般类型变化的租赁时间分布和租赁费用的预期LP的(1/2)竞争简单静态模拟策略。我们进一步展示了针对相同基准的最优(1−1/ (cmin+3)0.5)竞争性自适应策略,其中cmin是最小的产品库存。我们的分析扩展了先知不等式文献中的工具,以设计丢弃阈值规则,这些规则在贝叶斯实时分类中保持基于仿真的策略的可行性。我们进一步使用数值模拟来证明我们所建议的政策的收入表现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Linear Programming Based Online Policies for Real-Time Assortment of Reusable Resources
Motivated by applications of rental services in e-commerce, we consider real-time assortment of reusable products. In our model, arriving consumers with heterogeneous types choose rental products from the offered assortment, pay the rental fees, and return the product to the platform after a rental time. Consumers' types specify their choice models, rental fees and rental time distributions for various products. Our goal is to design competitive online policies against an appropriate benchmark for both the prior-free setting, in which types are arbitrary (or adversarial), and the Bayesian setting, in which types are drawn independently from known distributions. Our contribution is threefold. We first introduce offline linear programming benchmarks in both settings, that use time-varying inventory constraints to capture feasibility of a policy under rentals, and are required to satisfy these constraints only in expectation. Second, in the prior-free setting, we develop a randomized primal-dual framework based on our introduced LP to settle that inventory balancing policies of Golrezaei et al. (2014) obtain same (asymptotically optimal) competitive ratios as with non-reusable resources when product rental times are fixed over time. As a corollary, we obtain the optimal competitive ratio of (1 − 1/e) when inventories are large. We also show this family of policies are constant competitive under i.i.d. (over time) stochastic rental times. Third, we change gear to the Bayesian setting by introducing simulation-based policies that use the expected LP solution as guidance. By using primal-dual analysis, we obtain a (1/2)-competitive simple and static simulation-based policy against the expected LP for general type-varying rental time distributions and rental fees. We further show optimal (1 − 1/ (cmin+3)0.5)-competitive adaptive policies against the same benchmark when rental times are infinite, where cmin is the smallest product inventory. Our analysis extends tools in the literature on prophet inequalities to design discarding threshold rules that maintain feasibility of a simulation-based policy in the Bayesian real-time assortment. We further justify the revenue performance of our proposed policies using numerical simulations.
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