A decomposition algorithm to solve the multi-hop Peer-to-Peer ride-matching problem

- A computationally efficient and exact algorithm for the multi-hop P2P ride-matching problem.
- The multi-hop property of the proposed formulation allows it to be used in multi-modal networks.
- The algorithm is capable of solving real-life sized dynamic ride-matching problems.

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 my 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.