Abstract
This paper addresses the design of a parcel delivery system using drones, which includes the strategic planning of the system and operational planning for a given region. The amount of payload affects the battery consumption rate (BCR), which can cause a disruption in delivery of goods if the BCR was under-estimated in the planning stage or cause unnecessarily higher expenses if it was over-estimated. Hence, a reliable parcel delivery schedule using drones is proposed to consider the BCR as a function of payload in the operational planning optimization. A minimum set covering approach is used to model the strategic planning and a mixed integer linear programming problem (MILP) is used for operational planning. A variable preprocessing algorithm and primal and dual bound generation methods are developed to improve the computational time for solving the operational planning model. The optimal solution provides the least number of drones and their flight paths to deliver parcels while ensuring the safe return of the drones with respect to the battery charge level. Experimental data show that the BCR is a linear function of the payload amount. The results indicate the impact of including the BCR in drone scheduling, 3 out of 5 (60%) flight paths are not feasible if the BCR is not considered. The numerical results show that the sequence of visiting customers impacts the remaining charge.
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References
Amazon Inc., Amazon prime air, (access date: July, 2018). [Online]. Available: www.amazon.com/primeair
Keeney, T.: How can amazon charge $1 for drone delivery? (access date: July, 2018). [Online]. Available: https://ark-invest.com/research/drone-delivery-amazon
Mercedes-Benz co., Vans & drones in zurich, (access date: July, 2018). [Online]. Available: https://www.mercedes-benz.com/en/mercedes-benz/vehicles/transporter/vans-drones-in-zurich/
McFarland, M.: Ups drivers may tag team deliveries with drones, 2007 (access date: July, 2018). [Online]. Available: http://money.cnn.com/2017/02/21/technology/ups-drone-delivery/index.html
DHL, Successful trial integration of dhl parcelcopter into logistics chain, 2016 (access date: July, 2018). [Online]. Available: http://www.dhl.com/en/press/releases/releases_2016/all/parcel_ecommerce/successful_trial_integration_dhl_parcelcopter_logistics_chain.html
Omidshafiei, S., Agha-mohammadi, A. -a., Amato, C., Liu, S. -Y., How, J. P., Vian, J. L.: Health-aware multi-uav planning using decentralized partially observable semi-markov decision processes. In: AIAA infotech@ aerospace, 2016 p (1407)
Enright, J., Frazzoli, E., Savla, K., Bullo, F.: On multiple uav routing with stochastic targets: Performance bounds and algorithms. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, pp. 5830 (2005)
Oberlin, P., Rathinam, S., Darbha, S.: Today’s traveling salesman problem. IEEE Robot. Autom. Mag. 17(4), 70–77 (2010)
Kim, S. J., Lim, G. J., Cho, J., Côté, M. J.: Drone-aided healthcare services for patients with chronic diseases in rural areas. J. Intell. Robot. Syst. 88(1), 163–180 (2017)
Kim, Y., Gu, D. -W., Postlethwaite, I.: Real-time optimal mission scheduling and flight path selection. IEEE Trans. Autom. Control 52(6), 1119–1123 (2007)
Murray, C. C., Chu, A. G.: The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery. Transportation Research Part C: Emerging Technologies 54, 86–109 (2015)
Ha, Q. M., Deville, Y., Pham, Q. D., Hà, M. H.: On the min-cost traveling salesman problem with drone. Transportation Research Part C: Emerging Technologies 86, 597–621 (2018)
Carlsson, J. G., Song, S.: Coordinated logistics with a truck and a drone, Management Science (2017)
Papadimitriou, C. H., Steiglitz, K.: Combinatorial optimization: algorithms and complexity, Courier Corporation (1998)
Torabbeigi, M., Lim, G. J., Kim, S. J.: Drone delivery schedule optimization considering the reliability of drones. In: 2018 international conference on unmanned aircraft systems (ICUAS). IEEE, pp. 1048–1053 (2018)
Kim, S. J., Lim, G. J.: Drone-aided border surveillance with an electrification line battery charging system, Journal of Intelligent & Robotic Systems, pp. 1–14 (2018)
Kim, S., Lim, G.: A hybrid battery charging approach for drone-aided border surveillance scheduling. Drones 2(4), 38 (2018)
Hong, I., Kuby, M., Murray, A. T.: A range-restricted recharging station coverage model for drone delivery service planning. Transportation Research Part C: Emerging Technologies 90, 198–212 (2018)
Yurek, E. E., Ozmutlu, H. C.: A decomposition-based iterative optimization algorithm for traveling salesman problem with drone. Transportation Research Part C: Emerging Technologies 91, 249–262 (2018)
Olivares, V., Cordova, F., Sepúlveda, J. M., Derpich, I.: Modeling internal logistics by using drones on the stage of assembly of products. Proc. Comput. Sci. 55, 1240–1249 (2015)
Kim, S. J., Ahmadian, N., Lim, G. J., Torabbeigi, M.: A rescheduling method of drone flights under insufficient remaining battery duration. In: 2018 international conference on unmanned aircraft systems (ICUAS). IEEE, pp. 468–472 (2018)
Lim, G. J., Kim, S., Cho, J., Gong, Y., Khodaei, A.: Multi-uav pre-positioning and routing for power network damage assessment. IEEE Trans. Smart Grid 9(4), 3643–3651 (2018)
Scott, J., Scott, C.: Drone delivery models for healthcare. In: Hawaii international conference on system sciences, pp. 3297–3304 (2017)
Kim, S. J., Lim, G. J., Cho, J.: Drone flight scheduling under uncertainty on battery duration and air temperature. Comput. Ind. Eng. 117, 291–302 (2018)
Zachariadis, E. E., Tarantilis, C. D., Kiranoudis, C. T.: The load-dependent vehicle routing problem and its pick-up and delivery extension. Transp. Res. B 71, 158–181 (2015)
Xiao, Y., Zhao, Q., Kaku, I., Xu, Y.: Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput. Oper. Res. 39(7), 1419–1431 (2012)
Dorling, K., Heinrichs, J., Messier, G. G., Magierowski, S.: Vehicle routing problems for drone delivery. IEEE Trans. Syst. Man Cybern. Syst 47(1), 1–16 (2017)
Abdilla, A., Richards, A., Burrow, S.: Power and endurance modelling of battery-powered rotorcraft. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, pp. 675–680 (2015)
Liu, Z., California, B., Kurzhanskiy, A.: A power consumption model for multi-rotor small unmanned aircraft systems. In: International conference on unmanned aircraft systems (ICUAS), pp. 310–315 (2017)
Cheng, F., Hua, W., Pin, C.: Rotorcraft flight endurance estimation based on a new battery discharge model. Chin. J. Aeronaut. 30(4), 1561–1569 (2017)
L. SZ DJI Technology Co., Phantom 4 pro, (access date: July, 2018). [Online]. Available: https://www.dji.com/phantom-4-pro
Handbook: Helicopter flying, FAA-H-8083-21A (2012)
Pirhooshyaran, M., Snyder, L. V.: Optimization of inventory and distribution for hip and knee joint replacements via multistage stochastic programming. In: Modeling and optimization: Theory and applications, pp 139–155. Springer, Cham (2017)
Miller, C. E., Tucker, A. W., Zemlin, R. A.: Integer programming formulation of traveling salesman problems. J. ACM 7(4), 326–329 (1960)
Caric, T., Gold, H.: Vehicle routing problem. In-Teh, 2008
Wolsey, L. A.: Integer programming. IIE Trans. 32(273-285), 2–58 (2000)
Bron, C., Kersch, J.: Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16(9), 575–577 (1973)
Korte, B., Vygen, J.: Combinatorial optimization: Theory and algorithms. Algorithms and Combinatorics (2006)
MATLAB and Statistics Toolbox Release R2016a The MathWorks, Inc., Natick, MA, USA
GAMS Development Corporation. General Algebraic Modeling System (GAMS) Release 24.7.3. Washington, DC, USA, 2016. [Online]. Available: http://www.gams.com/
IBM ILOG, CPLEX reference manual, vol. 12.6.3.0, Released: July 2016. [Online]. Available: http://www.ilog.com
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Appendices
Appendix A
Appendix B
The data was collected when the battery’s SOC was between 95% and 15%. For example, it took 2.35 minutes for the battery charge to drop from 95% to 85% when the payload was 0.22 lb.
Appendix C
The parameter M should be large enough that does not eliminate any feasible solution. This parameter appears in Constraints (16) and (17).
The same for the Constraint (17).
Appendix D
In the test case problem, there are 5 candidate locations to open depots. Table 13 shows whether a customer is within the covering range of each candidate location (value of 1) or not (value of 0).
Appendix E
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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). https://doi.org/10.1007/s10846-019-01034-w
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DOI: https://doi.org/10.1007/s10846-019-01034-w