Technical Note—Near-Optimal Bayesian Online Assortment of Reusable Resources

Abstract

Near-Optimal Bayesian Online Assortment of Reusable Resources Motivated by rental services in e-commerce, we consider revenue maximization in the online assortment of reusable resources for different types of arriving consumers. We design competitive online algorithms compared with the optimal online policy in the Bayesian setting, where consumer types are drawn independently from known heterogeneous distributions over time. In scenarios with large initial inventories, our main result is a near-optimal competitive algorithm for reusable resources. Our algorithm relies on an expected linear programming (LP) benchmark, solves this LP, and simulates the solution through independent randomized rounding. The main challenge is achieving inventory feasibility efficiently using these simulation-based algorithms. To address this, we design discarding policies for each resource, balancing inventory feasibility and revenue loss. Discarding a unit of a resource impacts future consumption of other resources, so we introduce postprocessing assortment procedures to design and analyze our discarding policies. Additionally, we present an improved competitive algorithm for nonreusable resources and evaluate our algorithms using numerical simulations on synthetic data.