Same-Day Delivery with Drone Resupply
TL;DR: A novel way to exploit drones in same-day home delivery settings: drone resupply is introduced, which considers a home delivery system in which delivery trucks are regularly resupplied by drones.
Abstract: Unmanned aerial vehicles, commonly referred to as drones, have recently seen an increased level of interest as their potential use in same-day home delivery has been promoted and advocated by large...
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TL;DR: This work proposes a mixed integer programming model, and develops a branch-and-price algorithm for routing trucks and drones in an integrated manner, and shows good computational performance of the proposed algorithm.
Abstract: The vehicle routing problem with drones (VRPD) is an extension of the classic capacitated vehicle routing problem, where not only trucks but drones are used to deliver parcels to customers. One distinctive feature of the VRPD is that a drone may travel with a truck, take off from its stop to serve customers, and land at a service hub to travel with another truck as long as the flying range and loading capacity limitations are satisfied. Routing trucks and drones in an integrated manner makes the problem much more challenging and different from classical vehicle routing literature. We propose a mixed integer programming model, and develop a branch-and-price algorithm. Extensive experiments are conducted on the instances randomly generated in a practical setting, and the results demonstrate the good computational performance of the proposed algorithm. We also conduct sensitivity analysis on a key factor that may affect the total cost of a solution.
216 citations
TL;DR: This work focuses on routing problems with drones, mostly in the context of parcel delivery, and surveys and classify the existing works and provides perspectives for future research.
Abstract: The interest in using drones in various applications has grown significantly in recent years. The reasons are related to the continuous advances in technology, especially the advent of fast microprocessors, which support intelligent autonomous control of several systems. Photography, construction, and monitoring and surveillance are only some of the areas in which the use of drones is becoming common. Among these, last-mile delivery is one of the most promising areas. In this work we focus on routing problems with drones, mostly in the context of parcel delivery. We survey and classify the existing works and we provide perspectives for future research.
189 citations
TL;DR: This paper surveys established and novel last-mile concepts and puts special emphasis on the decision problems to be solved when setting up and operating each concept, and systematically record the alternative delivery concepts in a compact notation scheme.
Abstract: In the wake of e-commerce and its successful diffusion in most commercial activities, last-mile distribution causes more and more trouble in urban areas all around the globe. Growing parcel volumes to be delivered toward customer homes increase the number of delivery vans entering the city centers and thus add to congestion, pollution, and negative health impact. Therefore, it is anything but surprising that in recent years many novel delivery concepts on the last mile have been innovated. Among the most prominent are unmanned aerial vehicles (drones) and autonomous delivery robots taking over parcel delivery. This paper surveys established and novel last-mile concepts and puts special emphasis on the decision problems to be solved when setting up and operating each concept. To do so, we systematically record the alternative delivery concepts in a compact notation scheme, discuss the most important decision problems, and survey existing research on operations research methods solving these problems. Furthermore, we elaborate promising future research avenues.
169 citations
TL;DR: This paper surveys the state-of-the-art optimization approaches in the civil application of drone operations (DO) and drone-truck combined operations (DTCO) including construction/infrastructure, agriculture, transportation/logistics, security/disaster management, entertainment/media, etc.
158 citations
TL;DR: This research introduces a new routing model that considers a synchronized truck-drone operation by allowing multiple drones to fly from a truck, serve one or multiple customers, and return to the same truck for a battery swap and package retrieval.
126 citations
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ILOG1
TL;DR: In this paper, a local search method called Large Neighbourhood Search (LNS) is used to solve vehicle routing problems, analogous to the shuffling technique of job shop scheduling.
Abstract: We use a local search method we term Large Neighbourhood Search (LNS) to solve vehicle routing problems. LNS is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology. LNS explores a large neighbourhood of the current solution by selecting a number of "related" customer visits to remove from the set of planned routes, and re-inserting these visits using a constraint-based tree search. Unlike similar methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We analyse the performance of our method on benchmark problems. We demonstrate that results produced are competitive with Operations Research meta-heuristic methods, indicating that constraint-based technology is directly applicable to vehicle routing problems.
1,207 citations
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
"Same-Day Delivery with Drone Resupp..." refers background in this paper
...Murray and Chu (2015) introduced the flying sidekick traveling salesman problem (FSTSP), in which a set of customers must be served exactly once by either a delivery vehicle or a drone operating in conjunction with the delivery vehicle....
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...For example, in the last few years, several papers on models and algorithms to support this operational use of drones have appeared (Murray and Chu, 2015; Agatz et al., 2016; Campbell et al., 2017)....
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...Murray and Chu (2015) also consider a simpler version of the problem, in which the deliveries are divided into two groups, one set delivered by the delivery vehicle and the other set delivered by the drone traveling out-and-back from the distribution center....
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01 Jan 2017
TL;DR: In this paper, the authors propose two multi-trip vehicle routing problems (VRPs) specifically for drone delivery scenarios, one minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to budget constraint.
Abstract: Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs.
752 citations
TL;DR: A survey of vehicle routing problems with multiple synchronization constraints, which presents a classification of different types of synchronization and discusses the central issues related to the exact and heuristic solution of such problems.
Abstract: This paper presents a survey of vehicle routing problems with multiple synchronization constraints. These problems exhibit, in addition to the usual task covering constraints, further synchronization requirements between the vehicles, concerning spatial, temporal, and load aspects. They constitute an emerging field in vehicle routing research and are becoming a “hot” topic. The contribution of the paper is threefold: (i) It presents a classification of different types of synchronization. (ii) It discusses the central issues related to the exact and heuristic solution of such problems. (iii) It comprehensively reviews pertinent literature with respect to applications as well as successful solution approaches, and it identifies promising algorithmic avenues.
417 citations
"Same-Day Delivery with Drone Resupp..." refers background in this paper
...Synchronization, another characteristic that has attracted a lot of attention in the routing and scheduling community recently, see e.g., Drexl (2012), is the most challenging feature, as the delivery vehicle and the drone need to meet at a particular location for resupply to take place....
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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