Online Allocation of Reusable Resources via Algorithms Guided by Fluid Approximations

TL;DR

This paper introduces a fluid approximation-guided online algorithm for allocating reusable resources in an adversarial setting, achieving near-optimal competitive performance and addressing stochastic reusability and customer choice.

Contribution

It presents a novel fluid approximation-based approach for online resource allocation with reusable resources, achieving a $(1-1/e)$ competitive ratio in large inventory scenarios.

Findings

Achieves $(1-1/e)$ competitiveness for general usage distributions.

Introduces a relaxed online algorithm guided by fluid approximations.

Provides a general framework for stochastic elements in resource allocation.

Abstract

We consider the problem of online allocation (matching and assortments) of reusable resources where customers arrive sequentially in an adversarial fashion and allocated resources are used or rented for a stochastic duration that is drawn independently from known distributions. Focusing on the case of large inventory, we give an algorithm that is $(1-1/e)$ competitive for general usage distributions. At the heart of our result is the notion of a relaxed online algorithm that is only subjected to fluid approximations of the stochastic elements in the problem. The output of this algorithm serves as a guide for the final algorithm. This leads to a principled approach for seamlessly addressing stochastic elements (such as reusability, customer choice, and combinations thereof) in online resource allocation problems, that may be useful more broadly.