An exact algorithm for the two-echelon vehicle routing problem with drones

Zhou, Hang; Qin, Hu; Cheng, Chun; Rousseau, Louis-Martin

doi:10.1016/j.trb.2023.01.002

Cited by 48 publications

(17 citation statements)

References 49 publications

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“…Tamke and Buscher [46] tackled the VRP with Drones and Drone Speed Selection (VRPD-DSS), proposing a model that considers speed-dependent energy consumption for cost-saving in rural deliveries. Zhou et al [47] focused on the Two-Echelon VRP with Drones (2E-VRP-D), optimizing last-mile deliveries with a collaborative truck-drone system. Xia et al [48] proposed the VRP with Load-Dependent Drones (VRPLD), emphasizing the importance of energy consumption modeling for routing and hub placement.…”

Section: Figure 2 Combined Working Patterns Of Drones and Vehicles (O...mentioning

confidence: 99%

Capacitated Multi Drone Assisted Vehicle Routing Problem

Kavlak,

İşleyen,

Toklu

2024

Gazi University Journal of Science

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Transportation is developing rapidly with today’s technology. By following different methods in every field, sustainable and low-cost transportation systems are tried to be created. Vehicle routing problems (VRP), which differ according to the fields, have been defined to produce solutions for these purposes. These differences occur according to the vehicles, nodes, and time limitations in the system. In much of the literature on VRPs, transportation varies according to the modes used, and these are referred to as air, land, and water transport. However, transportation modes that can operate as a hybrid, that is, integrated at the same time, have emerged with the development of technology. In this study, new generation vehicle routing problems integrated with emerging technology have been studied and, unlike other studies, a mixed integer programming model has been developed for the Multiple-Drone Assisted Capacitated Vehicle Routing Problem (mDroneCVRP), which minimizes the time of the last vehicle arriving at the warehouse. As the most important contribution, the assumption that drones take off from the same vehicle and land on the same vehicle in other studies has been stretched, thus providing the opportunity to take off and land from different vehicles. A constructive heuristic based on a greedy procedure is also developed and its solutions are compared with the MIP solution to analyze the performance of the algorithm.

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Section: Figure 2 Combined Working Patterns Of Drones and Vehicles (O...mentioning

confidence: 99%

Capacitated Multi Drone Assisted Vehicle Routing Problem

Kavlak,

İşleyen,

Toklu

2024

Gazi University Journal of Science

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“…For sake of completeness, we also mention a number of studies on the further generalization to the multiple trucks case: among other ones, Kitjacharoenchai et al (2019), Bakir and Tinic ¸ (2020), Tamke andBuscher (2021), andZhou et al (2022). From the theoretical side, Wang, Poikonen, and Golden (2017) provided several worst-case bounds on the optimal value, involving the number of vehicles and their relative speed.…”

Section: Morandi Et Almentioning

confidence: 99%

The Traveling Salesman Problem with Drones: The Benefits of Retraversing the Arcs

Morandi

Leus

Matuschke

et al. 2023

Transportation Science

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In the traveling salesman problem with drones (TSP-mD), a truck and multiple drones cooperate to serve customers in the minimum amount of time. The drones are launched and retrieved by the truck at customer locations, and each of their flights must not consume more energy than allowed by their batteries. Most problem settings in the literature restrict the feasible truck routes to cycles (i.e., closed paths), which never visit a node more than once. Revisiting a node, however, may lower the time required to serve all the customers. Additionally, we observe that optimal solutions for the TSP-mD may retraverse arcs (i.e., optimal truck routes may contain the same arcs multiple times). We refer to such solutions as arc retraversing and include them in our solution space by modeling the truck route as a closed walk. We describe Euclidean instances where all the optimal solutions are arc retraversing. The necessity of arc retraversals does not seem to have been investigated in previous studies, and those that allow node revisits seem to assume that there always exists an optimal solution without arc retraversals. We prove that under certain conditions, which are commonly met in the literature, this assumption is correct. When these conditions are not met, however, excluding arc-retraversing solutions might result in an increase of the optimal value; we identify cases where a priori and a posteriori upper bounds hold on such increase. Finally, we prove that there is no polynomial-time heuristic that can approximate the metric TSP-mD within a constant factor, unless P = NP. We identify a (nonconstant) approximation factor explicitly when the truck can visit all the nodes.

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“…It is related to the two-echelon vehicle routing problem (2E-VRP), see (Sluijk et al, 2023), as we can consider the deliveries of the trucks as a first echelon, and the deliveries of the drones as a second echelon. In this context, Zhou et al (2023) recently proposed a branch-and-price approach that optimally solves instances of up to 30 customers in less than 3 hours for the 2E-VRP-D. Given that real-world last mile delivery problems commonly contain a higher number of customers to serve it is necessary to be able to solve larger instances in a reasonable time.…”

Section: Introductionmentioning

confidence: 99%

“…We also show the benefit of the improvements proposed. Six new sets of medium-size instances with 40, 100, 120, 130, 140 and 150 customers extending the dataset of small-size instances proposed in (Zhou et al, 2023) and based on (Chen et al, 2021), (Solomon, 1987) and (Gehring and Homberger, 1999).…”

Section: Introductionmentioning

confidence: 99%

A Branch-Cut-And-Price Approach for the Two-Echelon Vehicle Routing Problem with Drones

Lichau,

sadykov,

François

et al. 2024

Preprint

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An exact algorithm for the two-echelon vehicle routing problem with drones

Cited by 48 publications

References 49 publications

Capacitated Multi Drone Assisted Vehicle Routing Problem

Capacitated Multi Drone Assisted Vehicle Routing Problem

The Traveling Salesman Problem with Drones: The Benefits of Retraversing the Arcs

A Branch-Cut-And-Price Approach for the Two-Echelon Vehicle Routing Problem with Drones

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