Near-Optimal Bayesian Online Assortment of Reusable Resources

2025-12-07

AI Summary

This paper studies online revenue management of reusable resources in e-commerce leasing settings: given multiple customer types arriving independently from known heterogeneous distributions, how to design a Bayesian online algorithm with a high competitive ratio to maximize expected revenue. We propose a novel parallel framework—“discarding policy + post-processing selection”—that explicitly decouples the dynamic inventory coupling induced by resource reuse. Integrating an expected linear programming (LP) benchmark, independent randomized rounding, and a prophet-inequality-inspired post-processing mechanism, our approach achieves theoretical guarantees. When initial inventory is $c_0$, the algorithm attains a competitive ratio of $1 - minleft(frac{1}{2}, frac{sqrt{log c_0}}{c_0} ight)$; in the non-reusable special case, it improves to $1 - frac{1}{sqrt{c_0 + 3}}$. Synthetic experiments validate both effectiveness and robustness.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Motivated by the applications of rental services in e-commerce, we consider revenue maximization in online assortment of reusable resources for a stream of arriving consumers with different types. We design competitive online algorithms with respect to the optimum online policy in the Bayesian setting, in which types are drawn independently from known heterogeneous distributions over time. In the regime where the minimum of initial inventories $c_0$ is large, our main result is a near-optimal $1-minleft(frac{1}{2},sqrt{log(c_0)/c_0} ight)$ competitive algorithm for the general case of reusable resources. Our algorithm relies on an expected LP benchmark for the problem, solves this LP, and simulates the solution through an independent randomized rounding. The main challenge is obtaining point-wise inventory feasibility in a computationally efficient fashion from these simulation-based algorithms. To this end, we use several technical ingredients to design $ extit{discarding policies}$ -- one for each resource. These policies handle the trade-off between the inventory feasibility under reusability and the revenue loss of each of the resources. However, discarding a unit of a resource changes the future consumption of other resources. To handle this new challenge, we also introduce $ extit{post-processing}$ assortment procedures that help with designing and analyzing our discarding policies as they run in parallel, which might be of independent interest. As a side result, by leveraging techniques from the literature on prophet inequality, we further show an improved near-optimal $1-1/sqrt{c_0+3}$ competitive algorithm for the special case of non-reusable resources. We finally evaluate the performance of our algorithms using the numerical simulations on the synthetic data.

Problem

• Designs competitive online algorithms for revenue maximization in reusable resource assortment
• Addresses inventory feasibility challenges in computationally efficient simulation-based algorithms
• Develops discarding policies and post-processing procedures to manage resource reusability trade-offs

Innovation

• Uses expected LP benchmark with independent randomized rounding
• Implements discarding policies for each resource to ensure feasibility
• Introduces post-processing assortment procedures for parallel policy analysis