Abstract
In this paper, the authors mathematically model the multi-hop Peer-to-Peer (P2P) ride-matching problem as a binary program. The authors 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. The authors 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. The authors 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, the authors propose heuristic solution methods, and investigate the trade-offs between solution time and accuracy.