**7. Conclusions**

In this work, we addressed FQRP-G, where a set of vehicles has to be routed on a grid network according to a set of nonstop collision-free Manhattan paths that minimizes the overall number of required horizontal lanes. Such paths can be seamlessly operated with no further control logic for collision and deadlock detection and avoidance, leaving a sensor network as the only task to guarantee safe operations against an unexpected vehicle or infrastructure disruptions during the real-time execution.

We have presented an integer linear programming formulation of FQRP-G, called ILP, and three heuristics, showing that:


Further research is needed towards heuristic algorithms that, like B1 or B2, do not rely on one-way lanes and on simple Manhattan paths, which, according to the theoretical results reviewed in this work, is mandatory to enable a smaller number of required levels for the instances that are critical for Heuristic A. Possible lines for future studies could also involve exact solution methods for FQRP-G, based on either the model proposed in this work or alternative mathematical programming formulations, and the extension of FQRP-G and related solution approach to more and more realistic settings, e.g., considering arbitrary vehicle origins and destinations or more general grids.

**Author Contributions:** Conceptualization, G.A., C.D.F. and L.D.G.; methodology, G.A., C.D.F. and L.D.G.; software, C.D.F. and L.D.G.; validation, G.A., C.D.F. and L.D.G.; formal analysis, G.A., C.D.F. and L.D.G.; data curation, G.A., C.D.F. and L.D.G.; writing—original draft preparation, G.A., C.D.F. and L.D.G.; writing—review and editing, G.A., C.D.F. and L.D.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data are available from the corresponding authors.

**Conflicts of Interest:** The authors declare no conflict of interest.
