Optimality-guaranteed algorithms on the dynamic shared-taxi problem

Shared mobility has attracted increasing attention due to its advantages in relieving traffic congestion and low-carbon environmental protection. This paper studies the dynamic shared-taxi problem of the on-demand shared-taxi system, where we introduce a rescheduling ratio to measure the proportion of requests that can be rescheduled in the total scheduled requests. To match vehicles and passengers in the on-demand platforms with high quality and efficiency, we formulate the problem into a mixed-integer model and develop two optimality-guaranteed algorithms, the branch-and-price algorithm and the Lagrangian relaxation algorithm. The two algorithms share a common subproblem which is solved by dynamic programming in parallel to speed up the solving. Computational results reveal that the branch-and-price algorithm and the Lagrangian relaxation algorithm are significantly superior to the commercial solver (Gurobi) in terms of the solution quality, solvable problem size, and the computational time. Specifically, the branch-and-price algorithm is superior in solution quality, while the Lagrangian relaxation algorithm can obtain high-quality solutions for several large-scale instances faster. After that, we further compare the proposed algorithms with several commonly used heuristic algorithms to verify the necessity of developing optimality-guaranteed algorithms. Finally, sensitivity analyses of the rescheduling ratio factor are carried out to provide several insights for the shared-taxi platform on balancing the relationship between the system-wide profit and user experience.