The content discusses dynamic assortment optimization problems, which involve deciding the optimal assortment of products to offer and the inventory levels for each product in the presence of finite inventory and dynamic stockout-based substitution effects.
The authors consider two settings: 1) the dynamic assortment optimization (DA) problem, where customers see all available products, and 2) the dynamic assortment optimization with personalization (DAP) problem, where the seller can choose to offer a subset of available products to each customer.
The authors develop a unified algorithmic framework to address both DA and DAP problems under the Multinomial Logit (MNL) choice model. Key highlights:
For DA, the authors improve the best-known approximation ratio from 0.122-ϵ to 0.194-ϵ for distributions with the Increasing Failure Rate (IFR) property. Their algorithm is also significantly faster than prior work.
For DAP with deterministic number of customers (T), the authors achieve an approximation ratio of 1/2(1-1/e)-ϵ, surpassing the current best guarantee of 1/4(1-1/e).
For DAP with stochastic T following an arbitrary distribution, the authors provide a (0.25-ϵ)-approximation, addressing an open problem.
The authors establish novel structural properties of the fluid relaxations, including the submodular order property, which enables the development of efficient threshold-based approximation algorithms.
Overall, the work provides a unified and efficient algorithmic framework for dynamic assortment optimization under the MNL choice model, with improved approximation guarantees compared to prior work.
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by Shuo Sun,Raj... at arxiv.org 04-05-2024
https://arxiv.org/pdf/2404.03604.pdfDeeper Inquiries