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Journal ArticleDOI

The vehicle routing problem with drones: several worst-case results

01 Apr 2017-Optimization Letters (Springer Berlin Heidelberg)-Vol. 11, Iss: 4, pp 679-697
TL;DR: The VRPD is motivated by a number of highly influential companies such as Amazon, DHL, and Federal Express, actively involved in exploring the potential use of commercial drones for package delivery.
Abstract: In this paper, we introduce the vehicle routing problem with drones (VRPD). A fleet of trucks equipped with drones delivers packages to customers. Drones can be dispatched from and picked up by the trucks at the depot or any of the customer locations. The objective is to minimize the maximum duration of the routes (i.e., the completion time). The VRPD is motivated by a number of highly influential companies such as Amazon, DHL, and Federal Express, actively involved in exploring the potential use of commercial drones for package delivery. After stating our simplifying assumptions, we pose a number of questions in order to study the maximum savings that can be obtained from using drones; we then derive a number of worst-case results. The worst-case results depend on the number of drones per truck and the speed of the drones relative to the speed of the truck.
Citations
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Journal ArticleDOI
01 Dec 2018-Networks
TL;DR: This article describes the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning, and provides insights into widespread and emerging modeling approaches to civil applications of UAVs.
Abstract: Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult-to-access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.

576 citations


Cites background from "The vehicle routing problem with dr..."

  • ...The limited capacity of the energy unit is usually modeled as maximal operation time [274, 292], maximal flying distance [104, 244], or the limited number of addresses a drone can visit during one flight [75, 237]....

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  • ...[287] Decentral H, EmpCS, Exp several drones, UGVs a general framework: no specific drone characteristics are formulated other (environmental protection and disaster management) [292] P several drones, several trucks limited flight time, delivery of 1 package per sortie transport...

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  • ...4) Synchronization [89,158,312] [262] [3,37,41,58,106,140,186,215,287,292] No synchronization [81,165–167,274] [78,122,141,200,243,244,248] [82,186,212,271,281,296] et al....

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  • ...Battery swaps and refueling usually require assistance of a human operator [292]; however, there exist fully automated platforms able to exchange or to recharge the battery of a drone in just a couple of minutes [53, 268, 269, 275]....

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  • ...Also in this operation type, most common objectives aim at minimizing the makespan (eg, completion time of a route) [3, 41, 186, 243, 271, 292] and the cost [37, 167, 271], such as energy consumption [287] or the number of required drones [122]....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors proposed a new variant of the traveling salesman problem TSP that they call the TSP with drone, and developed several fast route-first, cluster-second heuristics based on local search and dynamic programming.
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 drones 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 integer program 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 compared to truck-only delivery. The online appendix is available at https://doi.org/10.1287/trsc.2017.0791 .

414 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a new variant of the traveling salesman problem (TSP) called the TSP with drone, and formulated this problem as an MIP model and developed several fast route first-cluster second heuristics based on local search and dynamic programming.
Abstract: The fast and cost-effcient 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 formulate this problem as an MIP model 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 numerical analysis shows that substantial savings are possible with this concept in comparison to truck-only delivery.

388 citations

Journal ArticleDOI
TL;DR: In this article, a new variant of the traveling salesman problem, called TSP with drone (TSP-D), is proposed to minimize operational costs including total transportation cost and one created by waste time a vehicle has to wait for the other.
Abstract: Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called “last-mile delivery”. In this novel approach, they are deployed alongside trucks to deliver goods to customers to improve the quality of service and reduce the transportation cost. This approach gives rise to a new variant of the traveling salesman problem (TSP), called TSP with drone (TSP-D). A variant of this problem that aims to minimize the time at which truck and drone finish the service (or, in other words, to maximize the quality of service) was studied in the work of Murray and Chu (2015). In contrast, this paper considers a new variant of TSP-D in which the objective is to minimize operational costs including total transportation cost and one created by waste time a vehicle has to wait for the other. The problem is first formulated mathematically. Then, two algorithms are proposed for the solution. The first algorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu (2015), in which an optimal TSP solution is converted to a feasible TSP-D solution by local searches. The second algorithm, a Greedy Randomized Adaptive Search Procedure (GRASP), is based on a new split procedure that optimally splits any TSP tour into a TSP-D solution. After a TSP-D solution has been generated, it is then improved through local search operators. Numerical results obtained on various instances of both objective functions with different sizes and characteristics are presented. The results show that GRASP outperforms TSP-LS in terms of solution quality under an acceptable running time.

324 citations

Journal ArticleDOI
TL;DR: It is demonstrated that the improvement in efficiency of a delivery system in which an unmanned aerial vehicle UAV provides service to customers while making return trips to a truck that is itself moving is proportional to the square root of the ratio of the speeds of the truck and the UAV.
Abstract: We determine the efficiency of a delivery system in which an unmanned aerial vehicle UAV provides service to customers while making return trips to a truck that is itself moving. In other words, a UAV picks up a package from the truck which continues on its route, and after delivering the package, the UAV returns to the truck to pick up the next package. Although the hardware for such systems already exists, the extent to which such an approach can actually provide a significantly improved quality of service is not yet understood. By combining a theoretical analysis in the Euclidean plane with real-time numerical simulations on a road network, we demonstrate that the improvement in efficiency is proportional to the square root of the ratio of the speeds of the truck and the UAV. The online supplement is available at https://doi.org/10.1287/mnsc.2017.2824 . This paper was accepted by Vishal Gaur, operations management.

236 citations

References
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BookDOI
01 Jan 2008
TL;DR: In this article, the authors present a survey of the state-of-the-art approaches for solving the Capacitated Vehicle Routing Problem on trees and using a genetic algorithm to solve the generalized orienteering problem.
Abstract: Overviews and Surveys- Routing a Heterogeneous Fleet of Vehicles- A Decade of Capacitated Arc Routing- Inventory Routing- The Period Vehicle Routing Problem and its Extensions- The Split Delivery Vehicle Routing Problem: A Survey- Challenges and Advances in A Priori Routing- Metaheuristics for the Vehicle Routing Problem and Its Extensions: A Categorized Bibliography- Parallel Solution Methods for Vehicle Routing Problems- Recent Developments in Dynamic Vehicle Routing Systems- New Directions in Modeling and Algorithms- Online Vehicle Routing Problems: A Survey- Modeling and Solving the Capacitated Vehicle Routing Problem on Trees- Using a Genetic Algorithm to Solve the Generalized Orienteering Problem- An Integer Linear Programming Local Search for Capacitated Vehicle Routing Problems- Robust Branch-Cut-and-Price Algorithms for Vehicle Routing Problems- Recent Models and Algorithms for One-to-One Pickup and Delivery Problems- One-to-Many-to-One Single Vehicle Pickup and Delivery Problems- Challenges and Opportunities in Attended Home Delivery- Chvatal-Gomory Rank-1 Cuts Used in a Dantzig-Wolfe Decomposition of the Vehicle Routing Problem with Time Windows- Vehicle Routing Problems with Inter-Tour Resource Constraints- From Single-Objective to Multi-Objective Vehicle Routing Problems: Motivations, Case Studies, and Methods- Practical Applications- Vehicle Routing for Small Package Delivery and Pickup Services- Advances in Meter Reading: Heuristic Solution of the Close Enough Traveling Salesman Problem over a Street Network- Multiperiod Planning and Routing on a Rolling Horizon for Field Force Optimization Logistics- Health Care Logistics, Emergency Preparedness, and Disaster Relief: New Challenges for Routing Problems with a Focus on the Austrian Situation- Vehicle Routing Problems and Container Terminal Operations - An Update of Research

976 citations

Journal ArticleDOI
TL;DR: Two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery are provided, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels.
Abstract: Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.

851 citations


"The vehicle routing problem with dr..." refers background in this paper

  • ...Three recent papers are Murray and Chu [7], Agatz et al. [1], and Gambella et al. [5]....

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  • ...Three recent papers are Murray and Chu [7], Agatz et al....

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Book
05 Dec 2014
TL;DR: The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area.
Abstract: Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Operations researchers have made significant developments in the algorithms for their solution, and Vehicle Routing: Problems, Methods, and Applications, Second Edition reflects these advances. The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area; it emphasizes methodology related to specific classes of vehicle routing problems and, since vehicle routing is used as a benchmark for all new solution techniques, contains a complete overview of current solutions to combinatorial optimization problems. It also includes several chapters on important and emerging applications, such as disaster relief and green vehicle routing. Audience: This book is intended for both researchers and graduate level students in operations research and applied mathematics. Practitioners will find this book particularly useful. Readers need a basic knowledge of the main methods for the solution of combinatorial optimization problems.

756 citations

01 Jan 2007

434 citations


"The vehicle routing problem with dr..." refers background in this paper

  • ...The vehicle routing problem (VRP) is a well-studied problem [6,10]....

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Journal ArticleDOI
TL;DR: In this article, the authors proposed a new variant of the traveling salesman problem (TSP) called the TSP with drone, and formulated this problem as an MIP model and developed several fast route first-cluster second heuristics based on local search and dynamic programming.
Abstract: The fast and cost-effcient 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 formulate this problem as an MIP model 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 numerical analysis shows that substantial savings are possible with this concept in comparison to truck-only delivery.

388 citations