Mathematical Investigation on the Sustainability of UAV Logistics
Abstract
1. Introduction
2. Literature Review
2.1. Routing with UAVs
2.2. Sustainable VRPs
3. System Description and Methodologies
3.1. System Description
3.2. Research Approaches
3.2.1. Phase I: Mathematical Optimization with Multiple Depots & Trips
3.2.1.1. Notation
System Parameters | ||
i,j | : | Indices for customer tasks; |
: | Index for depots; | |
: | Index for delivery vehicles; | |
: | Index for multiple trips; | |
: | Number of customer tasks; | |
: | Number of delivery vehicles in the system; | |
: | Number of depots; | |
: | Maximum number of trips per delivery vehicle during the time horizon; | |
: | Large positive number; | |
: | Location (latitude, longitude) of task ; | |
: | Distance () from task (depot) i to task (depot); | |
: | Maximum travelling time (minutes) of vehicle ; | |
: | Loadable capacity () of vehicle ; | |
: | Travel speed of vehicle ; | |
: | Initial depot of vehicle ; | |
: | Demand for task ; | |
: | Processing time of task or replenishment time at depot ; | |
: | Earliest start time of task ; | |
: | Latest start time of task . | |
Sets | ||
≔ | , set of tasks; | |
≔ | , set of start depots; | |
≔ | , set of end depots; | |
≔ | , set of all tasks and depots; | |
≔ | , set of vehicles; | |
≔ | set of delivery trips. | |
Decision variables | ||
: | Binary decision variable, equal to 1 if vehicle processes task or refuel/reload at depot after processing task or refuel/reload at depot , during the rth trip; 0, otherwise; | |
: | Binary decision variable, equal to 1 if is task is assigned to vehicle during its rth trip; 0 otherwise; | |
: | Real number decision variable, start time of task by the rth trip of vehicle . |
3.2.1.2. Mathematical Model
3.2.2. Phase II: Environmental Analysis
4. Case study
4.1. Case Study Description
4.2. Result of Phase I
4.3. Result of Phase II
5. Concluding Remarks
Author Contributions
Acknowledgments
Conflicts of Interest
Appendix A
Component | Latitude | Longitude | Ai (kg) | Ei (time) | Li (time) | Pi (min) |
---|---|---|---|---|---|---|
AFC 1 (OAK4) | 37.745554 | −121.405899 | − | − | − | 3 |
AFC 2 (SJC7) | 37.724946 | −121.529487 | − | − | − | 3 |
C1 | 37.758957 | −121.533522 | 0.5 | 14:05 | 14:08 | 2 |
C2 | 37.733929 | −121.519634 | 1.0 | 14:10 | 14:15 | 1 |
C3 | 37.715911 | −121.520369 | 0.3 | 14:20 | 14:26 | 1 |
C4 | 37.722765 | −121.544745 | 0.3 | 14:23 | 14:28 | 1 |
C5 | 37.726434 | −121.488956 | 1.1 | 14:25 | 14:30 | 2 |
C6 | 37.748291 | −121.482774 | 0.3 | 14:30 | 14:36 | 2 |
C7 | 37.734170 | −121.470416 | 0.4 | 14:34 | 14:40 | 1 |
C8 | 37.726698 | −121.449134 | 0.8 | 14:38 | 14:45 | 1 |
C9 | 37.749915 | −121.455130 | 0.4 | 14:43 | 14:48 | 1 |
C10 | 37.745974 | −121.444830 | 0.5 | 14:48 | 14:53 | 2 |
C11 | 37.756825 | −121.422498 | 0.2 | 14:53 | 14:57 | 1 |
C12 | 37.748816 | −121.425940 | 0.2 | 14:58 | 15:04 | 1 |
C13 | 37.735515 | −121.433507 | 0.7 | 15:05 | 15:09 | 2 |
C14 | 37.727368 | −121.431281 | 0.4 | 15:10 | 15:15 | 2 |
C15 | 37.735640 | −121.414277 | 0.6 | 15:13 | 15:18 | 1 |
C16 | 37.734443 | −121.410023 | 0.2 | 15:17 | 15:22 | 2 |
C17 | 37.745062 | −121.428390 | 0.2 | 15:21 | 15:24 | 1 |
C18 | 37.734207 | −121.439899 | 0.7 | 15:26 | 15:29 | 1 |
C19 | 37.741537 | −121.43835 | 0.4 | 15:30 | 15:34 | 1 |
C20 | 37.735574 | −121.483496 | 0.3 | 15:37 | 15:41 | 2 |
C21 | 37.733535 | −121.512674 | 0.2 | 15:43 | 15:46 | 2 |
C22 | 37.737334 | −121.517482 | 0.2 | 15:45 | 15:50 | 1 |
C23 | 37.725357 | −121.518890 | 0.5 | 15:50 | 15:54 | 1 |
C24 | 37.733093 | −121.528331 | 0.4 | 15:53 | 15:57 | 1 |
C25 | 37.729156 | −121.535539 | 0.6 | 15:56 | 16:00 | 2 |
References
- Banker, S.; Amazon and drones. Here Is Why it Will Work. Forbes Magazine. Available online: https://www.forbes.com/sites/stevebanker/2013/12/19/amazon-drones-here-is-why-it-will-work (accessed on 26 August 2019).
- Perlow, B. Amazon Completes 1st Drone Delivery. ABC News. Available online: https://abcnews.go.com/US/amazon-completes-drone-delivery/story?id=44185981 (accessed on 26 August 2019).
- Bryan, V. Drone Delivery: DHL ‘Parcelcopter’ Flies to German Isle. Reuters. Available online: www.reuters.com/article/us-deutsche-post-drones/drone-deliverydhl-parcelcopter-flies-to-german-isle-idUSKCN0HJ1ED20140924 (accessed on 26 August 2019).
- Teal Group. 2019 World Civil Unmanned Aerial Systems Market Profile & Forecast. Available online: http://tealgroup.com/images/TGCTOC/WCUAS2019TOC_EO.pdf (accessed on 26 August 2019).
- Business Insider. The Most Staggering Part About Amazon’s Upcoming Drone Delivery Service. Available online: https://www.businessinsider.com/cost-savings-from-amazon-drone-deliveries-2016-6 (accessed on 26 August 2019).
- Nex, F.; Remondino, F. UAV for 3D mapping applications: A review. Appl. Geomat. 2014, 6, 1–15. [Google Scholar] [CrossRef]
- Siebert, S.; Teizer, J. Mobile 3D mapping for surveying earthwork projects using an Unmanned Aerial Vehicle (UAV) system. Automat. Constr. 2014, 41, 1–14. [Google Scholar] [CrossRef]
- Carlsson, J.G.; Song, S. Coordinated logistics with a truck and a drone. Manag. Sci. 2018, 64, 3971–4470. [Google Scholar] [CrossRef]
- Murray, C.C.; Chu, A.G. The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery. Transp. Res. Part C Emerg. Technol. 2015, 54, 86–109. [Google Scholar] [CrossRef]
- Jeong, H.Y.; Song, B.D.; Lee, S. Truck-drone hybrid delivery routing: Payload-energy dependency and No-Fly zones. Int. J. Prod. Econ. 2019, 214, 220–233. [Google Scholar] [CrossRef]
- Dantzig, G.B.; Ramser, J.H. The truck dispatching problem. Manag. Sci. 1959, 6, 80–91. [Google Scholar] [CrossRef]
- Shima, T.; Schumacher, C. Assignment of cooperating UAVs to simultaneous tasks using genetic algorithms. In Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA, USA, 15–18 August 2005; p. 5829. [Google Scholar] [CrossRef][Green Version]
- Zeng, J.; Yang, X.; Yang, L.; Shen, G. Modeling for UAV resource scheduling under mission synchronization. J. Syst. Eng. Electron. 2010, 21, 821–826. [Google Scholar] [CrossRef]
- Weinstein, A.; Schumacher, C. UAV scheduling via the vehicle routing problem with time windows. In Proceedings of the AIAA Infotech@ Aerospace 2007 Conference and Exhibit, Rohnert Park, CA, USA, 7–10 May 2007; p. 2839. [Google Scholar] [CrossRef]
- Kim, Y.; Gu, D.W.; Postlethwaite, I. Real-time optimal mission scheduling and flight path selection. IEEE Trans. Autom. Control 2007, 52, 1119–1123. [Google Scholar] [CrossRef]
- Alidaee, B.; Wang, H.; Landram, F. A note on integer programming formulations of the real-time optimal scheduling and flight path selection of UAVs. IEEE Trans. Control Syst. Technol. 2009, 17, 839–843. [Google Scholar] [CrossRef]
- Guerriero, F.; Surace, R.; Loscri, V.; Natalizio, E. A multi-objective approach for unmanned aerial vehicle routing problem with soft time windows constraints. Appl. Math. Model 2014, 38, 839–852. [Google Scholar] [CrossRef]
- Sundar, K.; Rathinam, S. Algorithms for routing an unmanned aerial vehicle in the presence of refueling depots. IEEE Trans. Autom. Control 2013, 11, 287–294. [Google Scholar] [CrossRef]
- Troudi, A.; Addouche, S.A.; Dellagi, S.; Mhamedi, A. Sizing of the drone delivery fleet considering energy autonomy. Sustainability 2018, 10, 3344. [Google Scholar] [CrossRef]
- Liu, M.; Liu, X.; Zhu, M.; Zheng, F. Stochastic Drone Fleet Deployment and Planning Problem Considering Multiple-Type Delivery Service. Sustainability 2019, 11, 3871. [Google Scholar] [CrossRef]
- Kim, J.; Song, B.D.; Morrison, J.R. On the scheduling of systems of UAVs and fuel service stations for long-term mission fulfillment. J. Intell. Robot. Syst. 2013, 70, 347–359. [Google Scholar] [CrossRef]
- Song, B.D.; Kim, J.; Morrison, J.R. Rolling horizon path planning of an autonomous system of UAVs for persistent cooperative service: MILP formulation and efficient heuristics. J. Intell. Robot. Syst. 2016, 84, 241–258. [Google Scholar] [CrossRef]
- Song, B.D.; Park, K.; Kim, J. Persistent UAV delivery logistics: MILP formulation and efficient heuristic. Comput. Ind. Eng. 2018, 120, 418–428. [Google Scholar] [CrossRef]
- Erdoğan, S.; Miller-Hooks, E. A green vehicle routing problem. Transp. Res. Part E 2012, 48, 100–114. [Google Scholar] [CrossRef]
- Chiang, W.-C.; Li, Y.; Shang, J.; Urban, T.L. Impact of drone delivery on sustainability and cost: Realizing the UAV potential through vehicle routing optimization. Appl. Energy 2019, 242, 1164–1175. [Google Scholar] [CrossRef]
- Poonthalir, G.; Nadarajan, R. Green vehicle routing problem with queues. Expert Syst. Appl. 2019, 138, 112823. [Google Scholar] [CrossRef]
- Bektas, T.; Laporte, G. The pollution-routing problem. Transp. Res. B Methodol. 2011, 45, 1232–1250. [Google Scholar] [CrossRef]
- Lin, C.; Choy, K.L.; Ho, G.T.S.; Chung, S.H.; Lam, H.Y. Survey of green vehicle routing problems: Past and future trends. Expert Syst. Appl. 2014, 41, 1118–1138. [Google Scholar] [CrossRef]
- US Department of Energy. Fuel Economy Guide. Available online: http://www.fueleconomy.gov (accessed on 11 October 2019).
- European Commission. Directorate-General Transp. In MEET: Methodology for Calculating Transport Emissions and Energy Consumption; European Commission: Brussels, Belgium, 1999; ISBN 978-92-8286-785-3. [Google Scholar]
- Naderipour, M.; Alinaghian, M. Measurement, evaluation and minimization of CO2, NOx, and CO emissions in the open time dependent vehicle routing problem. Measurement 2016, 90, 443–452. [Google Scholar] [CrossRef]
- Kara, I.; Kara, B.Y.; Yetis, M.K. Energy minimizing vehicle routing problem. In Proceedings of the International Conference on Combinatorial Optimization and Applications, Xian, China, 14–16 August 2007; pp. 62–71. [Google Scholar]
- Kuo, Y. Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Comput. Ind. Eng. 2010, 59, 157–165. [Google Scholar] [CrossRef]
- Kuo, Y.; Wang, C.C. Optimizing the VRP by minimizing fuel consumption. Manag. Environ. Qual. Int. J. 2011, 22, 440–450. [Google Scholar] [CrossRef]
- Malandraki, C.; Daskin, M.S. Time dependent vehicle routing problems: Formulations, properties and heuristic algorithms. Transp. Sci. 1992, 26, 185–200. [Google Scholar] [CrossRef]
- Jabali, O.; Van Woensel, T.; De Kok, A.G. Analysis of travel times and CO2 emissions in time-dependent vehicle routing. Prod. Oper. Manag. 2012, 21, 1060–1074. [Google Scholar] [CrossRef]
- Zhou, Y.; Lee, G. A Lagrangian relaxation-based solution method for a green vehicle routing problem to minimize greenhouse gas emissions. Sustainability 2017, 9, 776. [Google Scholar] [CrossRef]
- Shen, L.; Tao, F.; Wang, S. Multi-depot open vehicle routing problem with time windows based on carbon trading. Int. J. Environ. Res. Public Health 2018, 15, 2025. [Google Scholar] [CrossRef]
- Dekker, R.; Fleischmann, M.; Inderfurth, K.; van Wassenhove, L.N. (Eds.) Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains; Springer Science & Business Media: Berlin, Germany, 2013. [Google Scholar]
- D’Andrea, R. Guest editorial can drones deliver? IEEE Trans. Autom. Sci. Eng. 2014, 11, 647–648. [Google Scholar] [CrossRef]
- Schneider, M.; Stenger, A.; Goeke, D. The electric vehicle-routing problem with time windows and recharging stations. Transp. Sci. 2014, 48, 500–520. [Google Scholar] [CrossRef]
- Lin, J.; Zhou, W.; Wolfson, O. Electric vehicle routing problem. Transp. Res. Procedia 2016, 12, 508–521. [Google Scholar] [CrossRef]
- Goeke, D.; Schneider, M. Routing a mixed fleet of electric and conventional vehicles. Eur. J. Oper. Res. 2015, 245, 81–99. [Google Scholar] [CrossRef]
- Macrina, G.; Pugliese, L.D.P.; Guerriero, F.; Laporte, G. The green mixed fleet vehicle routing problem with partial battery recharging and time windows. Comput. Oper. Res. 2019, 101, 183–199. [Google Scholar] [CrossRef]
- Goodchild, A.; Toy, J. Delivery by drone: An evaluation of unmanned aerial vehicle technology in reducing CO2 emissions in the delivery service industry. Transp. Res. Part D Transp. Environ. 2018, 61, 58–67. [Google Scholar] [CrossRef]
- Coelho, B.N.; Coelho, V.N.; Coelho, I.M.; Ochi, L.S.; Haghnazar, R.; Zuidema, D.; Lima, M.S.F.; da Costa, A.R. A multi-objective green UAV routing problem. Comput. Oper. Res. 2017, 88, 306–315. [Google Scholar] [CrossRef]
- Dukkanci, O.; Kara, B.Y.; Bektas, T. The Drone Delivery Problem. Available online: https://ssrn.com/abstract=3314556 (accessed on 10 January 2019).
- Park, J.; Kim, S.; Suh, K. A comparative analysis of the environmental benefits of drone-based delivery services in urban and rural areas. Sustainability 2018, 10, 888. [Google Scholar] [CrossRef]
- Kim, S.; Moon, I. Traveling salesman problem with a drone station. IEEE Trans. Syst. Man Cybern. Syst. 2018, 49, 42–52. [Google Scholar] [CrossRef]
- Coutinho, W.P.; Battarra, M.; Fliege, J. The unmanned aerial vehicle routing and trajectory optimisation problem, a taxonomic review. Comput. Ind. Eng. 2018, 120, 116–128. [Google Scholar] [CrossRef]
- Song, B.D.; Kim, J.; Kim, J.; Park, H.; Morrison, J.R.; Shim, D.H. Persistent UAV service: An improved scheduling formulation and prototypes of system components. J. Intell. Robot. Syst. 2014, 74, 221–232. [Google Scholar] [CrossRef]
- Lee, D.; Amazon to Deliver by Drone ‘within Months’. BBC NEWS. Available online: https://www.bbc.com/news/technology-48536319 (accessed on 26 August 2019).
- 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. 2018, 9, 409. [Google Scholar] [CrossRef]
UAV | Delivery Routes | Starting AFC | Assigned Tasks | Ending AFC |
---|---|---|---|---|
1 | 1 | 1 | 11, 12, 13, 18, 19 | 1 |
2 | 1 | − | 1 | |
2 | 1 | 1 | 8, 14, 15, 16 | 1 |
2 | 1 | − | 1 | |
3 | 1 | 2 | 1, 2, 4 | 2 |
2 | 2 | 6, 7, 9, 10, 17 | 1 | |
4 | 1 | 2 | 3, 5, 20, 21, 22 | 2 |
2 | 2 | 23, 24, 25 | 2 | |
Total travelling distance: 56.270 km (CPU time: 653.71 seconds) |
GV | Delivery Routes | Starting AFC | Assigned Tasks | Ending AFC |
---|---|---|---|---|
1 | 1 | 1 | 11, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25 | 2 |
2 | − | − | − | |
2 | 1 | 2 | 1, 2, 4, 3, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16 | 1 |
2 | − | − | − | |
Total travelling distance: 47.633 km (CPU time: 6.34 seconds) |
GV | UAV | ||
---|---|---|---|
Traveled Distance (km/h) | 47.633 | 56.270 | |
GV speed | WAER | CO2 emissions (kg) | Allowable AER (Wh/km) |
40 | 0.7831 | 37.3019 | 1775.807 |
50 | 0.7298 | 34.7605 | 1654.822 |
60 | 0.6826 | 32.3135 | 1547.848 |
70 | 0.6483 | 30.8785 | 1470.013 |
80 | 0.6246 | 29.7516 | 1416.364 |
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Eun, J.; Song, B.D.; Lee, S.; Lim, D.-E. Mathematical Investigation on the Sustainability of UAV Logistics. Sustainability 2019, 11, 5932. https://doi.org/10.3390/su11215932
Eun J, Song BD, Lee S, Lim D-E. Mathematical Investigation on the Sustainability of UAV Logistics. Sustainability. 2019; 11(21):5932. https://doi.org/10.3390/su11215932
Chicago/Turabian StyleEun, Joonyup, Byung Duk Song, Sangbok Lee, and Dae-Eun Lim. 2019. "Mathematical Investigation on the Sustainability of UAV Logistics" Sustainability 11, no. 21: 5932. https://doi.org/10.3390/su11215932
APA StyleEun, J., Song, B. D., Lee, S., & Lim, D.-E. (2019). Mathematical Investigation on the Sustainability of UAV Logistics. Sustainability, 11(21), 5932. https://doi.org/10.3390/su11215932