*Result*: Technical Note—Near-Optimal Bayesian Online Assortment of Reusable Resources.

*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. 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 min is large, our main result is a near-optimal 1 − min (1 2 , log (c min) / c min ) 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 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 postprocessing 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 / c min + 3 competitive algorithm for the special case of nonreusable resources. We finally evaluate the performance of our algorithms using the numerical simulations on the synthetic data. Funding: R. Niazadeh's research is partially supported by an Asness Junior Faculty Fellowship from the University of Chicago Booth School of Business. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2020.0687. [ABSTRACT FROM AUTHOR]

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