A Label-correcting Algorithm for Constrained One-to-Many K-shortest Path Problem with Replenishment

The constrained one to many K-shortest path problem with replenishment (CKSPR) is an important variant of the classical shortest path problem with wide-range applications in transportation and logistics. In CKSPR, the objective is to find K number of shortest paths between an origin and multiple destinations, considering limitations on vehicle driving range and the availability of refueling resources along the paths. We propose a solution to the CKSPR using a mixed integer linear program (MILP); however, it is NP-complete and solving large-scale networks is computationally challenging. To tackle this, we introduce an efficient algorithm building upon Bellman’s classic dynamic programming approach. Our algorithm focuses on identifying K-shortest paths while considering driving range constraints, allowing vehicles to recharge en route and extend their reach. Numerical experiments demonstrate that the algorithm outperforms the MILP solvers with time limit, providing scalable solutions for large-scale networks. The analysis highlights the significant impact of large number of vertices on the problem difficulty. The source code is available at https://gitlab.com/AmirDavatgari/ckspr.