Basic Reusability and Beyond: Joint Inventory and Online Assortment Optimization with Reusable Resources

Abstract

In this work, we study the joint inventory and online assortment problem,  wherein a decision maker (DM) must first select initial inventory levels for a collection of available products or resources, and then offer personalized assortments to customers who arrive over a finite selling horizon, and who make purchasing decisions according to a multinomial logit choice model.  The goal across both sets of decisions is to maximize the expected revenue earned by the end of the selling horizon.   We are the first to consider this joint optimization framework when the resources are reusable.  That is, upon purchase or rental, each unit is consumed for a random duration, after which it returns to the DM for future use. Our cornerstone result when reusability is modeled in its classic form, is a constant factor approximation scheme when the usage duration distributions satisfy the increasing failure rate (IFR) property.  In a nutshell, our approach exploits notions of submodularity within a fluid approximation of the original problem.  This fluid problem approximates the IFR-based usage durations with appropriately defined geometric random variables.  To show that this approximate approach is indeed valid requires establishing a novel link between the CDFs of geometric and IFR-distributed random variables, which may find broader applications beyond those considered in this paper.  Next, we consider our joint optimization problem under an augmented version of basic reusability, wherein consumed resources can return to the DM as transformed versions of their original selves.  The intent of this novel modeling feature is to capture reusability settings where the identity of a product can possibly change due to its consumption (a product purchased online and returned to the seller may become damaged during the try-on process) or through the very nature of a return (a bike rented at one dock may be returned to a different one).  In this so-called network reusability setting,  we propose a novel  inventory refinement process that iteratively adjusts inventory decisions based on feedback from the online assortment stage. We ultimately establish a strong performance bound for our overall approach, which is network dependent. Through numerical experiments, we show that our approximation strategies perform nearly optimally across a wide range of reusability scenarios, demonstrating the robustness and practicality of our approach.