The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery

https://doi.org/10.1016/j.trc.2015.03.005Get rights and content

Highlights

  • Two new optimization problems related to parcel delivery by drone are defined.

  • These problems are inspired by Amazon’s, Google’s, and DHL’s drone delivery programs.

  • In one problem, a drone may be launched from a traditional delivery truck.

  • Mixed integer programming formulations for these problems are provided.

  • Efficient, yet effective, heuristics are proposed to solve these NP-hard problems.

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.

Introduction

Amazon CEO Jeff Bezos recently captured headlines when he announced on the CBS broadcast of 60 Minutes that his company has developed a fleet of unmanned aerial vehicles (UAVs) for small parcel delivery (Rose, 2013). The plan set forth by Bezos would use UAVs to deliver parcels from distribution centers (warehouses) directly to customers via Amazon’s Prime Air UAV, pictured in Fig. 1a. In the warehouse-to-customer operation, parcels are loaded into a container that is held by the UAV, also known as a drone, unmanned aircraft system (UAS), and remotely piloted aircraft (RPA). The UAV departs from the warehouse and travels to the customer location, where it navigates via the onboard global positioning system (GPS). The container (with parcel inside) is dropped off near the customer’s front door and the UAV returns to the warehouse. All of this takes place without human intervention or guidance.

While some dismissed this announcement as a publicity stunt (Carlson, 2013 notes that the story aired the night before “Cyber Monday,” one of the busiest online shopping days annually), Amazon is not alone in the race towards delivery-by-drone. German postal and logistics group Deutsche Post DHL recently announced that their Parcelcopter, pictured in Fig. 1b, has been authorized to deliver medical supplies to a car-free island off the coast of Germany (Bryan, 2014). Australian textbook distributor Zookal has begun testing delivery-by-drone in Australia, Singapore, and Malaysia, with hopes of entering the U.S. market in 2015 (Welch, 2013). UPS is also said to be considering the use of drones for moving packages within, or between, warehouses (Stern, 2013). More recently, Google entered the arena with the announcement of their Project Wing, featuring a vertical-takeoff-and-landing aircraft with a wing-shaped body (Madrigal, 2014).

The use of UAVs for “last-mile” parcel delivery promises to change the landscape of the logistics industry. However, there remain several significant regulatory and technological barriers to overcome before drones realize widespread adoption in the commercial sector. In the United States, Federal Aviation Administration (FAA) rules currently prohibit the use of UAVs for commercial purposes (although other countries have less restrictive regulations). The FAA also requires UAVs to be operated under a ceiling of 400-feet and within the “pilot’s” line-of-sight, severely limiting their effective range and forcing a human operator to be occupied throughout the flight. However, while Amazon’s fleet of drones remains grounded for now, the FAA has cleared oil and gas company BP (formerly British Petroleum) to fly UAVs at sea and over Alaska (Jansen, 2014). This move may signal that companies like Amazon could be given the green-light soon, as the FAA is expected to provide updated guidance on the use of commercial UAVs in 2015.

From the technical perspective, researchers are working to improve the endurance and safety of UAVs. Because UAVs of the size appropriate for small parcel delivery are battery operated, one such research area involves the improvement of battery energy storage. Limited battery capacity impacts the flight endurance of these aircraft, which can also be affected by flight speed and payload. Additionally, for safety and reliability purposes, these UAVs may require redundant systems (e.g., additional motors and sensors) that further reduce flight endurance. Furthermore, UAVs rely on GPS, which has a limited accuracy of about 10 m without corrective technologies (Arnold and Zandbergen, 2011). UAVs operating in heavily forested areas or so-called urban canyons may lose contact with a GPS signal. As such, there is increased interest in localization and navigation approaches that enable UAVs to function in GPS-denied environments (c.f., Clark and Bevly, 2008, Marais et al., 2014). Similar research is also being conducted to combat GPS “spoofing,” whereby false signals are broadcast to enable the hijacking of a UAV (c.f., Humphreys, 2012, Faughnan et al., 2013). Even with perfect localization information, (semi-)autonomous UAVs require the ability to perform obstacle detection and avoidance. This is a fertile research area in robotics, where vision-, sonar-, and laser-based methodologies are being improved (c.f., Jimenez and Naranjo, 2011, Merz and Kendoul, 2013, Apatean et al., 2013, Pestana et al., 2014, Park and Kim, 2014). Given the potential for UAV applications, it is not surprising that a recent market study by the Teal Group forecasted that UAV spending will more than double over the next decade, with cumulative worldwide expenditures exceeding $89 billion. Although much of this research will be for military purposes, small UAVs (those weighing less than 55 lb) of the type suitable for commercial applications represent the highest growth potential (Teal Group, 2014).

While research related to overcoming the aforementioned technical issues is abundant, we are aware of no studies addressing the operational challenges. For example, consider the direct warehouse-to-customer operation proposed by Amazon. The Prime Air UAV has a range of 10 miles (Gross, 2013). Thus, UAV deliveries must originate from distribution centers located in close proximity to customers. This may require a relocation of existing distribution centers, or the construction of new ones. To enjoy economies of scale, these distribution centers (DCs) would presumably be located near densely populated urban areas where, paradoxically, customers tend to live in high-rise housing with no “front door” on which to receive deliveries via UAV. Furthermore, although Amazon indicates that 86% of its deliveries weigh less than the five-pound payload capacity of its Prime Air UAVs (Gross, 2013), the remaining percentage of deliveries would still require delivery by traditional means. Such a system is depicted in Fig. 2b, where circular nodes indicate customers whose parcels cannot be delivered via UAV.

Depending upon the number of available UAVs, as well as the performance characteristics of the fleet, it may not be optimal to deliver-by-drone to all eligible customers. For example, in Fig. 2c the total time required to deliver to all customers is decreased if the truck delivers parcels to some of the customers that could feasibly be served by the UAV.

In cases where the distribution center is located far from the customers, an alternative is to pair the UAV with a traditional delivery truck, as depicted in Fig. 3b. The delivery truck departs from the DC carrying a UAV and all customer parcels. As the driver makes deliveries, the UAV is launched from the truck, carrying parcels for individual customers. While the UAV is en route, it needs no intervention from the delivery driver (autonomous flight). The UAV then returns to the truck, which has moved to a new customer location. The driver is required to load packages, replace batteries, and to recover the UAV to be secured aboard the truck while in transit.

There are several advantages associated with this unique approach to using UAVs for last-mile delivery. Primarily, by transporting the UAV closer to customer locations onboard the truck, the UAV may be launched within flight range of more customers, increasing the effective flight range of the UAV. Additionally, this system leverages the ground vehicle’s much larger cargo capacity, with the truck serving dual roles as both a mobile depot and a delivery resource. Furthermore, as Ralph Rio of the ARC Advisory Group notes, in the event that the UAV experiences technical difficulties, the delivery driver is nearby to address the issue (Banker, 2013). While AMP Electric Vehicles has teamed with researchers at the University of Cincinnati to develop a working prototype of a drone that takes off from, and returns to, a delivery truck (Wohlsen, 2014), we are aware of no published algorithms that optimize delivery scheduling for UAV/truck tandems.

The primary contribution of this paper is to introduce a new variant of the traditional traveling salesman problem (TSP) that addresses the challenge of determining optimal customer assignments for a UAV working in tandem with a delivery truck. We term this problem, as depicted in Fig. 3b, the flying sidekick traveling salesman problem (FSTSP). A review of the literature related to the FSTSP is presented in Section 2. This is followed by a formal definition of the FSTSP in Section 3, where a mixed integer linear programming formulation is provided. Owing to the NP-hard nature of this problem, an efficient heuristic is proposed to solve large-scale FSTSP instances of the size that may be encountered by a parcel delivery service.

Secondarily, we also introduce the problem associated with devising optimal truck and UAV assignments in the case of a DC located in close proximity to customers (i.e., as depicted in Fig. 2b and c). We term this the parallel drone scheduling TSP (PDSTSP), and provide a formal definition, mathematical programming formulation, and heuristic solution approach in Section 4. We demonstrate empirically, via an extensive numerical analysis in Section 5, the effectiveness of the proposed heuristics and highlight the benefits of last-mile parcel delivery by a UAV/truck tandem over the traditional truck-only operation. Also provided in Section 5 is an analysis of the trade-offs between UAV speed and endurance. Finally, a summary and overview of the myriad future research opportunities related to the FSTSP and PDSTSP are highlighted in Section 6.

Section snippets

Related literature

There is a vast body of literature on the TSP and the vehicle routing problem (VRP). While these foundational problems are not directly applicable to the problems at hand, the interested reader is referred to the recent TSP surveys by Golden et al., 2008, Eksioglu et al., 2009, the book on the VRP and its extensions by Toth and Vigo (Eds.), the survey on the multiple TSP (mTSP) provided by Bektas (2006), the survey on automated guided vehicles provided by Vis (2006), and the review of

The flying sidekick TSP

The FSTSP considers a set of c customers, each of whom must be served exactly once by either a driver-operated delivery truck or an unmanned aircraft operating in coordination with the truck. Because some customer requests may be infeasible to fulfill by the UAV (e.g., parcels that exceed the UAV’s payload capacity, parcels requiring a signature, or customer locations not amenable to safely landing the UAV), these customers must be served by the truck only.

The truck and UAV must depart from,

The parallel drone scheduling TSP

The FSTSP is applicable to scenarios in which the DC is relatively far from the customer locations and a single UAV is available to operate in synchronization with a delivery truck. However, in the event that a significant proportion of customers are located within a UAV’s flight range from the DC, a different problem arises. The parallel drone scheduling TSP (PDSTSP) may be formally defined as follows, where the notation from the FSTSP is adopted unless stated otherwise.

A single depot exists,

Empirical results

A series of numerical experiments were conducted to assess the effectiveness of the proposed FSTSP and PDSTSP heuristics, and to gain insights into potential strategies for future enhancements. In addition to assessing the proposed heuristics, a study was conducted to explore the trade-offs between increased UAV flight speed and longer flight endurance. All computational work was conducted on an HP 8100 Elite desktop PC with a quad-core Intel i7–860 processor and 4 GB RAM running Ubuntu Linux

Discussion and future research

Recent demonstrations by Amazon, Google, and DHL (among others) have shown the potential of UAVs for small parcel delivery. While extensive research efforts have focused on the technical aspects of UAVs, this paper seeks to provide new algorithms designed to optimize the operational elements of a delivery-by-drone logistics system.

In particular, two new problems have been formally defined. The FSTSP seeks to coordinate a traditional delivery truck with a UAV that may be launched from the truck.

Acknowledgements

The authors thank Eddie Robison Rivera for his editorial support. We are grateful to Editor-in-Chief Yafeng Yin and the two anonymous reviewers whose helpful suggestions have improved the quality of this research.

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