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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 amany-to-many problem in which a rider can travel by transferring betweenmultiple drivers, and a driver can carry multiple riders. We propose apre-processing procedure to reduce the size of the problem, and devise adecomposition algorithm to solve the original ride-matching problem tooptimality by means of solving multiple smaller problems. We conduct extensivenumerical experiments to demonstrate the computational efficiency of theproposed algorithm and show its practical applicability to reasonably-sizeddynamic ride-matching contexts. Finally, in the interest of even lower solutiontimes, we propose heuristic solution methods, and investigate the trade-offsbetween solution time and accuracy.

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