Allocation Problems in Ride-Sharing Platforms: Online Matching with Offline Reusable Resources

TL;DR

This paper introduces a new model for online bipartite matching with reusable offline resources, providing an LP-based algorithm with provable competitive guarantees and demonstrating practical relevance to ride-sharing platforms.

Contribution

The paper proposes the OM-RR-KAD model for online matching with reusable resources, along with an LP-based adaptive algorithm and practical heuristics, extending prior work on disposable resources.

Findings

LP-based algorithm achieves 1/2 - eps competitive ratio

No non-adaptive algorithm can surpass 1/2 + o(1) ratio

Model effectively captures ride-sharing and taxi dispatching scenarios

Abstract

Bipartite matching markets pair agents on one side of a market with agents, items, or contracts on the opposing side. Prior work addresses online bipartite matching markets, where agents arrive over time and are dynamically matched to a known set of disposable resources. In this paper, we propose a new model, Online Matching with (offline) Reusable Resources under Known Adversarial Distributions (OM-RR-KAD), in which resources on the offline side are reusable instead of disposable; that is, once matched, resources become available again at some point in the future. We show that our model is tractable by presenting an LP-based adaptive algorithm that achieves an online competitive ratio of 1/2 - eps for any given eps greater than 0. We also show that no non-adaptive algorithm can achieve a ratio of 1/2 + o(1) based on the same benchmark LP. Through a data-driven analysis on a massive openly-available dataset, we show our model is robust enough to capture the application of taxi dispatching services and ride-sharing systems. We also present heuristics that perform well in practice.