Optimizing Drone Delivery Paths from Shared Bases: A Location-Routing Problem with Realistic Energy Constraints

Recently, Amazon patented fulfillment centers for drones on a large scale in densely populated areas. A network of such shared centers can be used for landing and launching drones as an alternative to the traditional private bases in near future. This paper studies how a user of such a shared delivery infrastructure can optimally determine the required bases among the existing bases to perform her delivery tasks. To this end, a location-routing problem is studied where the problem determines the drone launching centers and their routes to deliver parcels. A realistic energy function is used that incorporates the effect of load weight for calculating energy consumption in all flight phases including take-off, level flight, hovering, and landing. Although the energy consumption is nonlinear, the problem is formulated as a mixed-integer linear programming model and strengthened by valid inequalities and a pre-processing algorithm that enables us to solve instances with up to 100 customers using off-the-shelf optimization solvers. Moreover, a heuristic method is presented to solve instances with up to 200 customers. Results indicate the importance of incorporating the load-dependent energy formula in contrast to using fixed flight duration constraints for drones. The value of allowing multiple visits on each trip versus only simple back-and-forth trips is also assessed. The advantage of using an integrated location-routing approach is shown over the sequential approach in which the locations of bases are decided first and the routes are constructed next. Moreover, to manage future demand uncertainty, the model is extended for the case that a number of demand scenarios are given.