The Mothership and Drone Routing Problem

The mothership and drone routing problem (MDRP) considers the routing of a two-vehicle tandem. The larger vehicle, which may be a ship or an airplane, is called the mothership; the smaller vehicle, which may be a small boat or unmanned aerial vehicle, is called the drone. We assume that there exists a set of target locations T. For each t in T, the drone must launch from the mothership, visit t, and then return to the mothership to refuel. The drone has a limited range of R time units. In the MDRP, we assume that both mothership and drone operate in the open seas (i.e., using the Euclidean metric). We also introduce the mothership and infinite-capacity drone routing problem (MDRP-IC), where a drone launches from the mothership and visits one or more targets consecutively before returning to the mothership. Our exact approach uses branch and bound, where each node of the branch-and-bound tree corresponds to a potential subsequence of the order of target visits. A lower bound at each node is given by solving a second-order cone program, which optimally chooses a launch point and landing point for each target in the subsequence. A set of heuristics that also uses a second-order cone program as an embedded procedure is presented. We show that our schemes are flexible to accommodate a variety of additional constraints and/or objective functions. Computational results and interesting variants of the MDRP and MDRP-IC are also presented.