Trucks and drones cooperation in the last‐mile delivery process

Abstract

We address the problem of routing a fleet of trucks equipped with unmanned aerial vehicles, commonly known as drones, to perform deliveries in last-mile delivery process. The customers can be served by either a truck or a drone within the respective time window of each. Each capacitated truck carries drones that can be launched to perform deliveries. The drone takes off from a truck located either at a customer or at the depot and it must land on the same truck after visiting a customer to be served. The aim is to serve all customers at minimum cost, under time window, capacity, and flying endurance constraints. We formulate the problem as a mixed integer linear program (MILP) and develop a heuristic procedure where a two-phase strategy is embedded in a multi-start framework. The computational results are carried out on instances generated by starting from vehicle routing problem with time windows benchmarks. We analyze the behavior of the considered transportation system by mean of the solutions provided by the MILP. The proposed formulation is able to solve instances with up to 15 customers. The solutions of the MILP are used as benchmark to assess the effectiveness of the proposed heuristic procedure.

Truck and drone routing problem with synchronization on arcs

“…Schermer et al (2019a), Sacramento et al (2019), Kitjacharoenchai et al (2020), and Euchi and Sadok (2021) proposed solution methods for the VRPD. Di Puglia Pugliese and Guerriero (2017), Di Puglia Pugliese et al (2020), and Das et al (2020) introduced the VRPD with time windows. Schermer et al (2019b) introduced the VRPD with en route operations.…”

The vehicle routing problem with drones and drone speed selection

“…As for the problem with one tandem, several heuristic algorithms, e.g. [11,17,24,26,38,39,45], and exact approaches, e.g. [16,40,43,47], have been presented for the VRPD and several related problems.…”

“…[16,40,43,47], have been presented for the VRPD and several related problems. Several approaches consider time windows [16,17], allow multiple visits to customers on the same flight [26,47], or enable the launch and retrieval of drones at discrete points on an arc [39]. However, only the approach presented by Liu et al [26] considers a range that is not limited by a maximum time or distance.…”

“…Variables u are used in constraints (17) to set precedence variables p. If p f ij = 1, then node j is visited after node i by truck f and u f j is larger than u f i + 1. Equations ( 18) and ( 19) guarantee that the depot precedes (node 0) and succeeds (node c + 1) customer i on the route of truck f if and only if customer i is visited by truck f .…”

A Scalable Last-Mile Delivery Service: From Simulation to Scaled Experiment

“…Recent efforts in this area include ant colony optimization to solve mTSP with capacity and time window constraints for vehicle routing [13], fuzzy logic approaches for multiobjective mTSP [18], and data-driven graph-theoretic approaches to bus scheduling [19]. Other efforts have proposed augmenting last-mile delivery with cargo bicycles [20] and drones [21], [22] to decrease the number of cars and vans required and further reduce delivery times. However, to the best of our knowledge, validation of a last-mile delivery service in a physical experiment has not yet been reported in the literature.…”