We formalize the problem of multi-agent path finding with deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within a given deadline, without colliding with each other. We first show that the MAPF-DL problem is NP-hard to solve optimally. We then present an optimal MAPF-DL algorithm based on a reduction of the MAPF-DL problem to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network.
@article{arxiv.1805.04961,
title = {Multi-Agent Path Finding with Deadlines: Preliminary Results},
author = {Hang Ma and Glenn Wagner and Ariel Felner and Jiaoyang Li and T. K. Satish Kumar and Sven Koenig},
journal= {arXiv preprint arXiv:1805.04961},
year = {2018}
}