Abstract
Recently, Amazon patented fulfillment centers for drones on a large scale in densely populated areas. A network of such shared centers can be used for landing and launching drones as an alternative to the traditional private bases in near future. This paper studies how a user of such a shared delivery infrastructure can optimally determine the required bases among the existing bases to perform her delivery tasks. To this end, a location-routing problem is studied where the problem determines the drone launching centers and their routes to deliver parcels. A realistic energy function is used that incorporates the effect of load weight for calculating energy consumption in all flight phases including take-off, level flight, hovering, and landing. Although the energy consumption is nonlinear, the problem is formulated as a mixed-integer linear programming model and strengthened by valid inequalities and a pre-processing algorithm that enables us to solve instances with up to 100 customers using off-the-shelf optimization solvers. Moreover, a heuristic method is presented to solve instances with up to 200 customers. Results indicate the importance of incorporating the load-dependent energy formula in contrast to using fixed flight duration constraints for drones. The value of allowing multiple visits on each trip versus only simple back-and-forth trips is also assessed. The advantage of using an integrated location-routing approach is shown over the sequential approach in which the locations of bases are decided first and the routes are constructed next. Moreover, to manage future demand uncertainty, the model is extended for the case that a number of demand scenarios are given.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Data Availability
Not applicable.
References
Stolaroff, J.K., Samaras, C., O’Neill, E.R., Lubers, A., Mitchell, A.S., Ceperley, D.: Energy use and life cycle greenhouse gas emissions of drones for commercial package delivery. Nat. Commun. 9(1), 409 (2018)
Sung, I., Nielsen, P.: Zoning a service area of unmanned aerial vehicles for package delivery services. J. Intell. Robot. Syst. 97, 719–731 (2020)
Kim, S.J., Lim, G.J.: A real-time rerouting method for drone flights under uncertain flight Time. J. Intell. Robot. Syst. 100, 1355–1368 (2020)
Kim, S.J., Lim, G.J.: Drone-aided border surveillance with an electrification line battery charging system. J. Intell. Robot. Syst. 92, 657–670 (2018)
Ahmadian, N., Lim, G.J., Torabbeigi, M., Kim, S.J.: Smart border patrol using drones and wireless charging system under budget limitation. Comput. Ind. Eng. 164, 107891 (2022)
Li, L., Liang, H., Wang, J., et al.: Online routing for autonomous vehicle cruise systems with fuel constraints. J. Intell. Robot. Syst. 104, 68 (2022)
Sundar, K., Rathinam, S.: Algorithms for heterogeneous, multiple depot, multiple unmanned vehicle path planning problems. J. Intell. Robot. Syst. 88, 513–526 (2017)
Liu, X., Peng, Z.R., Zhang, L.Y.: Real-time UAV rerouting for traffic monitoring with decomposition based multi-objective optimization. J. Intell. Robot. Syst. 94, 491–501 (2019)
Ramasamy, S., Reddinger, J.P.F., Dotterweich, J.M., et al.: Coordinated route planning of multiple fuel-constrained unmanned aerial systems with recharging on an unmanned ground vehicle for mission coverage. J. Intell. Robot. Syst. 106, 30 (2022)
Park, H.J., Mirjalili, R., Côté, M.J., et al.: Scheduling Diagnostic Testing Kit Deliveries with the Mothership and Drone Routing Problem. J. Intell. Robot. Syst. 105, 38 (2022)
Curlander, J.C., Gilboa-Amir, A., Kisser, L.M., Koch, R.A., Welsh, R.D.: Multi-level fulfillment center for unmanned aerial vehicles. U.S. Patent No. US9777502B2. Washington, DC: U.S. Patent and Trademark Office (2017)
Salhi, S., Rand, G.K.: The effect of ignoring routes when locating depots. Eur. J. Oper. Res. 39, 150–156 (1989)
Lang, F.: World's first triple-drop delivery drone takes off. https://interestingengineering.com/innovation/first-triple-drop-delivery-drone-takes-off (2021, April 28)
Ahmadi-Javid, A., Seyedi, P., Syam, S.S.: A survey of healthcare facility location. Comput. Oper. Res. 79, 223–263 (2017)
Al-Rabiaah, S., Hosny, M., AlMuhaideb, S.: An efficient greedy randomized heuristic for the maximum coverage facility location problem with drones in healthcare. Appl. Sci. 12(3), 1403 (2022)
Toth, P., Vigo, D.: The vehicle routing problem. SIAM (2002)
Prodhon, C., Prins, C.: A survey of recent research on location-routing problems. Eur. J. Oper. Res. 238(1), 1–17 (2014)
Schneider, M., Drexl, M.: A survey of the standard location-routing problem. Ann. Oper. Res. 259, 389–414 (2017)
Janinhoff, L., Klein, R., Sailer, D., Schoppa, J.M.: Out-of-home delivery in last-mile logistics: A review. Comput. Oper. Res. 168, 106686 (2024)
Chauhan, D., Unnikrishnan, A., Figliozzi, M.: Maximum coverage capacitated facility location problem with range constrained drones. Trans. Res. Part C Emerging. Technol. 99, 1–18 (2019)
Kim, D., Lee, K., Moon, I.: Stochastic facility location model for drones considering uncertain flight distance. Ann. Oper. Res. 283, 1283–1302 (2019)
Kim, S.J., Lim, G.J., Cho, J., et al.: Drone-aided healthcare services for patients with chronic diseases in rural areas. J. Intell. Robot. Syst. 88, 163–180 (2017)
Torabbeigi, M., Lim, G.J., Kim, S.J.: Drone Delivery scheduling optimization considering payload-induced battery consumption rates. J. Intell. Robot. Syst. 97, 471–487 (2020)
Yakıcı, E.: Solving location and routing problem for UAVs. Comput. Ind. Eng. 102, 294–301 (2016)
Liu, Y., Liu, Z., Shi, J., Wu, G., Chen, C.: Optimization of base location and patrol routes for unmanned aerial vehicles in border intelligence, surveillance, and reconnaissance. J. Adv. Trans. (2019)
Yılmaz, O., Yakıcı, E., Karatas, M.: A UAV location and routing problem with spatio-temporal synchronization constraints solved by ant colony optimization. J. Heuristics. 25, 673–701 (2019)
Langelaan, J.W., Schmitz, S., Palacios, J., Lorenz, R.D.: Energetics of rotary-wing exploration of Titan. In Proceedings of 2017 IEEE Aerospace Conference, pp.1–11 (2017)
Ahmadi-Javid, A., & Meskar, M. Delivery by drones with arbitrary energy consumption models: A new formulation approach. arXiv preprint, arXiv:2211.00842. https://doi.org/10.48550/arXiv.2211.00842 (2022)
Zhang, J., Campbell, J.F., Sweeney, D.C., II., Hupman, A.C.: Energy consumption models for delivery drones: A comparison and assessment. Transp. Res. Part D: Transp. Environ. 90, 102668 (2021)
Dukkanci, O., Campbell, J. F., & Kara, B. Y. Facility location decisions for drone delivery with riding: A literature review. Comput. Oper. Res. 106672 (2024)
Vichitkunakorn, P., Emde, S., Masae, M., Glock, C.H., Grosse, E.H.: Locating charging stations and routing drones for efficient automated stocktaking. Eur. J. Oper. Res. 316, 1129–1145 (2024)
Ahmadi-Javid, A., Amiri, E., Meskar, M.: A profit-maximization location-routing-pricing problem: A branch-and-price algorithm. Eur. J. Oper. Res. 271(3), 866–881 (2018)
Ahmadi-Javid, A., Azad, N.: Incorporating location, routing and inventory decisions in supply chain network design. Trans. Res. Part E Logis. Trans. Rev. 46, 582–597 (2010)
Mara, S.T.W., Kuo, R.J., Asih, A.M.S.: Location-routing problem: A classification of recent research. Int. Trans. Oper. Res. 28(6), 2941–2983 (2021)
Funding
The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Author information
Authors and Affiliations
Contributions
Methodology, Formal analysis, Software, Data Curation, Writing-original draft preparation: [Mahla Meskar]. Supervision, Conceptualization, Methodology, Formal analysis, Writing reviewing and editing: [Amir Ahmadi-Javid]. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Ethics Approval
Not applicable.
Consent to Participate
Informed consent was obtained from all individual participants included in the study.
Consent to Publish
All authors agreed with the content and all gave explicit consent to submit.
Competing interests
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Meskar, M., Ahmadi-Javid, A. Optimizing Drone Delivery Paths from Shared Bases: A Location-Routing Problem with Realistic Energy Constraints. J Intell Robot Syst 110, 142 (2024). https://doi.org/10.1007/s10846-024-02129-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-024-02129-9
Keywords
- Unmanned Aerial Vehicles (UAVs)
- Drone delivery
- Location-Routing Problems (LRPs)
- Shared fulfillment centers
- Energy constraints
- Battery consumption