Optimization Approaches for the Traveling Salesman Problem with Drone

Abstract

The fast and cost-efficient home delivery of goods ordered online is logistically challenging. Many companies are looking for new ways to cross the last-mile to their customers. One technology-enabled opportunity that recently has received much attention is the use of a drone to support deliveries. An innovative last-mile delivery concept in which a truck collaborates with a drone to make deliveries gives rise to a new variant of the traveling salesman problem (TSP) that we call the TSP with drone. In this paper, we model this problem as an IP and develop several fast route first-cluster second heuristics based on local search and dynamic programming. We prove worst-case approximation ratios for the heuristics and test their performance by comparing the solutions to the optimal solutions for small instances. In addition, we apply our heuristics to several artificial instances with different characteristics and sizes. Our experiments show that substantial savings are possible with this concept in comparison to truck-only delivery.

When UAVs coexist with manned airplanes: Large‐scale aerial network management using ADS‐B

“…The f(t 0 , t, ΔM) is generated by our collected data set from the previous 102 days (from June 10 to September 18). The UAVs' flying time is randomly chosen between [20,40] minutes, with an average flight time of 30 minutes. One UAV flight's starting time (i s (n)) is randomly distributed during 10:00 and 17:20.…”

On the min-cost Traveling Salesman Problem with Drone

“…Recently, an objective function that minimizes the transportation cost was studied by Mathew et al [19] for a related problem called the Heterogeneous Delivery Problem (HDP). However, unlike in [12], [20] and [14], the problem is modelled on a directed physical street network where a truck cannot achieve direct delivery to the customer. Instead, from the endpoint of 95 an arc, the truck can launch a drone that will service the customers.…”

“…The authors use the Nood-Bean Transformation available in Matlab to reduce a GTSP to a TSP, which is then solved by a heuristic proposed in the study. To the best of our knowledge, the min-cost 100 objective function has not been studied for TSP-D when the problem is defined in a more realistic way-similarly to [12], [20], and [14]. Consequently, this gap in the literature provides a strong motivation for studying TSP-D with the min-cost objective function.…”

Routing of Carrier-vehicle Systems with Dedicated Last-stretch Delivery Vehicle and Fixed Carrier Route

“…Another related problem is the Traveling Salesman Problem with Drone (TSP-D) in the work of Agatz et al [1], where they work on the combination of a single truck and a single drone to c 2017 Information Processing Society of Japan find the shortest tour in terms of time, to serve all customer locations by either the truck or the drone. They assume that both the truck and the drone travel on the road network, and the drone's speed is a constant α times higher than the truck's speed.…”

“…Furthermore, Ha et al [7] studied a variant of the TSP-D as introduced in the work of Agatz et al [1], albeit with a formulation that excludes the possibility to have a launch and rendezvous in the same point. They called their problem the Min-Cost TSP-D.…”