A Decomposition Algorithm to Solve the Multi-Hop Peer-to-Peer Ride-Matching Problem

TL;DR

This paper introduces a decomposition algorithm for efficiently solving the multi-hop P2P ride-matching problem, enabling optimal solutions and practical application in dynamic ride-sharing scenarios.

Contribution

It presents a novel decomposition approach with preprocessing and heuristics for solving large-scale multi-hop ride-matching problems optimally and efficiently.

Findings

Algorithm achieves computational efficiency in numerical tests.

Proposed heuristics reduce solution times with acceptable accuracy.

Method is applicable to real-world dynamic ride-matching contexts.

Abstract

In this paper, we mathematically model the multi-hop Peer-to-Peer (P2P) ride-matching problem as a binary program. We formulate this problem as a many-to-many problem in which a rider can travel by transferring between multiple drivers, and a driver can carry multiple riders. We propose a pre-processing procedure to reduce the size of the problem, and devise a decomposition algorithm to solve the original ride-matching problem to optimality by means of solving multiple smaller problems. We conduct extensive numerical experiments to demonstrate the computational efficiency of the proposed algorithm and show its practical applicability to reasonably-sized dynamic ride-matching contexts. Finally, in the interest of even lower solution times, we propose heuristic solution methods, and investigate the trade-offs between solution time and accuracy.