Joint Inventory and Assortment Optimization with Reusable Resources

You can download the paper here: SSRN

Abstract: In this paper, we study the joint inventory and online assortment optimization problem, where a decision maker first selects initial inventory levels for a set of products and then offers personalized assortments to customers arriving sequentially over a finite selling horizon. Customers make purchase decisions according to a multinomial logit choice model. The objective is to maximize expected revenue by the end of the horizon. We introduce and analyze this joint decision framework in the novel context of reusable resources, where each unit, upon rental or purchase, is used for a random duration before becoming available again. Our central contribution is a constant-factor approximation scheme under the assumption that usage durations exhibit the increasing failure rate (IFR) property. We leverage submodularity within a fluid approximation that approximates IFR-distributed durations using geometric random variables. A key technical result establishes a novel connection between the cumulative distribution functions of geometric and IFR distributions, which has potential applicability beyond our specific setting.