Parcel delivery by vehicle and drone in ordered customer neighborhoods

Abstract

We consider a last-mile parcel delivery problem where a vehicle with a companion drone visits a set of ordered neighborhoods, following a line of travel that starts and ends at the depot. The decision-maker restricts the drone to fly within the neighborhood being serviced by the vehicle and seeks to optimize the vehicle and drone operations so that the total time to return to the depot, upon completing all deliveries, is minimized. The problem is formulated as a mixed-integer program, which is enhanced via cut-set constraints and valid inequalities derived using the Reformulation-Linearization Technique (RLT). Further, we investigate the logistical and computational effects of optionally imposing street precedence rules, based on training data from numerous optimized solutions for instances constructed in Amherst, MA (USA). Our study examines the computational tractability of the baseline model, the usefulness of imposing valid inequalities, and the impact of enforcing street precedence rules. Remarkably, enforcing RLT-based valid inequalities enables, in our experience, optimal solutions for instances having up to 200 customers within manageable times, thereby yielding a practical optimization-based framework for decision-makers.