Skip to main content
SpringerLink
Log in

An Optimization Approach to Minimize the Expected Loss of Demand Considering Drone Failures in Drone Delivery Scheduling

  • Regular Paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This study proposes a drone-based delivery schedul- ing method considering drone failures to minimize the expected loss of demand (ELOD). An optimization model (DDS-F) is developed to determine the assignment of each drone to a subset of customers and the corresponding delivery sequence. Because solving the optimization model is computationally challenging, a Simulated Annealing (SA) heuristic algorithm is developed to reduce the computational time. The proposed SA features a fast initial solution generation based on the Petal algorithm, a binary integer programming model for path selection, and a local neigh- borhood search algorithm to find better solutions. Numerical results showed that the proposed approach outperformed the well-known Makespan problem in reducing the ELOD by 23.6% on a test case. Several case studies are conducted to illustrate the impact of the failure distribution function on the optimal flight schedules. Furthermore, the proposed approach was able to obtain the exact solutions for the test cases studied in this paper. Numerical results also showed the efficiency of the proposed algorithm in reducing the computational time by 44.35%, on average, compared with the exact algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cho, J., Lim, G., Biobaku, T., Kim, S., Parsaei, H.: Safety and security management with unmanned aerial vehicle (UAV) in oil and gas industry. Procedia Manuf. 3, 1343–1349 (2015)

    Article  Google Scholar 

  2. G. J. Lim, S. Kim, J. Cho, Y. Gong, and A. Khodaei, “Multi-UAV Pre-Positioning and Routing for Power Network Damage Assessment,” IEEE Transactions on Smart Grid, 2016

  3. Varghese, A., Gubbi, J., Sharma, H., Balamuralidhar, P.: “Power infrastructure monitoring and damage detection using drone captured images,” in 2017 International Joint Conference on Neural Networks (IJCNN). IEEE. 1681–1687 (2017)

  4. 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 Robotic Syst. 88(1), 163–180 (2017)

    Article  Google Scholar 

  5. Ackerman, E., Strickland, E.: Medical delivery drones take flight in east africa. IEEE Spectr. 55(1), 34–35 (2018)

    Article  Google Scholar 

  6. Kim, S.J., Lim, G.J.: Drone-aided border surveil- lance with an electrification line battery charging system. J Intell Robotic Syst. 92(3–4), 657–670 (2018)

    Article  Google Scholar 

  7. Kim, S., Lim, G.: A hybrid battery charging approach for drone-aided border surveillance scheduling. Drones. 2(4), (2018)

  8. Kim, S.J., Lim, G.J., Cho, J.: Drone relay statisons for supporting wireless communication in military operations. Adv Intell Syst Comput Adv Human Factors Robots Unmanned Syst. 123–130 (2017)

  9. Torabbeigi, M., Lim, G.J., Kim, S.J.: Drone delivery scheduling optimization considering payload- induced battery consumption rates. J Intell Robotic Syst. 1–17 (2019)

  10. S. J. Kim, N. Ahmadian, G. J. Lim, and M. Torabbeigi, “A rescheduling method of drone flights under insuffi- cient remaining battery durationduration,” in 2018 International Conference on Unmanned Aircraft Systems (ICUAS) IEEE, 2018, pp. 468–472

  11. Keeney, T.: “Drone delivery: How can amazon charge $1 for drone delivery?” May 2016. [Online]. Available: https://ark-invest.com/research/drone-delivery-amazon

  12. Shi, Z., Ng, W.K.: “A collision-free path planning algorithm for unmanned aerial vehicle delivery,” in 2018 International Conference on Unmanned Aircraft Systems (ICUAS). IEEE. 358–362 (2018)

  13. Amazon.com Inc., “Amazon prime air.”[Online]. Available: http://www.amazon.com/primeair

  14. Bryan, V.: “Drone delivery: DHL ‘parcelcopter’ flies to german isle,” Sep 2014. [Online]. Available: http://www.reuters.com/article/us-deutsche- post-drones-idUSKCN0HJ1ED20140924

  15. Stern, J.: “Like amazon, ups also considering using unmanned flying vehicles,” Dec 2013. [Online]. Available: http://abcnews.go.com/Technology/amazon- ups-drone-delivery-options/story?id=21086160

  16. Sawadsitang, S., Niyato, D., Tan, P.-S., Wang, P.: Joint ground and aerial package delivery services: a stochastic optimization approach. IEEE Trans. Intell. Transp. Syst. 20(6), 2241–2254 (2018)

    Article  Google Scholar 

  17. Ahmadian, N., Lim, G.J., Torabbeigi, M., Kim, S.J.: “Collision-free multi-UAV flight scheduling for power network damage assessment,” in 2019 International Con- ference on Unmanned Aircraft Systems (ICUAS). IEEE. 794–798 (2019)

  18. Kharchenko, V., Torianyk, V.: “Cybersecurity of the internet of drones: Vulnerabilities analysis and imeca based assessment,” in 2018 IEEE 9th International Con- ference on Dependable Systems, Services and Technologies (DESSERT). IEEE. 364–369 (2018)

  19. King, D.W., Bertapelle, A., Moses, C.: “UAV failure rate criteria for equivalent level of safety,” in International Helicopter Safety Symposium, Montreal. 9, (2005)

  20. 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. 1048–1053 (2018)

  21. F. Schenkelberg, “How reliable does a delivery drone have to be?” in 2016 Annual Reliability and Maintain- ability Symposium (RAMS), 2016, pp. 1–5

  22. Zhao, Z., Quan, Q., Cai, K.-Y.: A health evaluation method of multicopters modeled by stochastic hybrid system. Aerosp. Sci. Technol. 68, 149–162 (2017)

    Article  Google Scholar 

  23. Lu, P., van Kampen, E.-J., de Visser, C., Chu, Q.: Nonlinear aircraft sensor fault reconstruction in the presence of disturbances validated by real flight data. Control. Eng. Pract. 49, 112–128 (2016)

    Article  Google Scholar 

  24. Rafaralahy, H., Richard, E., Boutayeb, M., Za-sadzinski, M.: “Simultaneous observer based sensor diagno- sis and speed estimation of unmanned aerial vehicle,” 2008. 47th IEEE Conf Decision Control. (2008)

  25. Ansari, A., Bernstein, D.S.: “Aircraft sensor fault detection using state and input estimation,” in 2016 American Control Conference (ACC). IEEE. 5951–5956 (2016)

  26. Heredia, G., Ollero, A., Bejar, M., Mahtani, R.: Sensor and actuator fault detection in small autonomous helicopters. Mechatronics. 18(2), 90–99 (2008)

    Article  Google Scholar 

  27. E. C. Larson, B. E. Parker, and B. R. Clark, “Model- based sensor and actuator fault detection and isolation,” in Proceedings of the 2002 American Control Conference (IEEE Cat. No. CH37301), vol. 5. IEEE, 2002, pp. 4215–4219

  28. A. Freddi, S. Longhi, and A. Monteriu, “A model-based fault diagnosis system for a mini-quadrotor,” in 7th workshop on Advanced Control and Diagnosis, 2009, pp. 19–20

  29. S. Bhattacharya and T. Basar, “Game-theoretic analysis of an aerial jamming attack on a UAV communication network,” Proceedings of the 2010 American Control Conference, 2010

  30. Saha, B., Koshimoto, E., Quach, C.C., Hogge, E.F., Strom, T.H., Hill, B.L., Vazquez, S.L., Goebel, K.: Battery health management system for electric UAVs. Aerospace Conference. 2011 (2011)

  31. Zhao, Z., Wang, X., Xu, J., Yu, J.: A performance evaluation algorithm of stochastic hybrid systems based on fuzzy health degree and its application to quadrotors. IEEE Access. 6, 37 581–37 594 (2018)

    Article  Google Scholar 

  32. P. Toth and D. Vigo, The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, 2002

  33. S. S. Fazeli, S. Venkatachalam, and J. M. Smereka, “Efficient algorithms for autonomous electric vehicles’ minmax routing problem,” arXiv preprint arXiv:2008.03333, 2020

  34. Iida, Y.: Basic concepts and future directions of road network reliability analysis. J Adv Trans. 33(2), 125–134 (1999)

    Article  Google Scholar 

  35. L. Tang, W. Cheng, and J. Liang, “Vehicle Routing Problem Research Based on Road Network Reliability,” International Conference on Transportation Engineering, 2009

  36. J. Gao, “Optimization of distribution routing problem based on travel timereliability,” 2009 International Con- ference on Information Management, Innovation Man- agement and Industrial Engineering, 2009

  37. X. Zhang, Y. Pu, H. Liu, and D. Yang, “Vehicle Routing Optimization Considering Dynamic Reliability during Last- Ing Period of Traffic Incidents,” International Conference of Logistics Engineering and Management (ICLEM), American Society of Civil Engineers, 2010

  38. Ando, N., Taniguchi, E.: Travel time reliability in vehicle routing and scheduling with time windows. Netw. Spat. Econ. 6(3–4), 293–311 (2006)

    Article  MathSciNet  Google Scholar 

  39. “Fact sheet – smalls unmanned aircraft regulations (part 107).” [Online]. Available: https://www.faa.gov/news/fact_sheets/news_story.cfm?newsId=22615

  40. R. N. Allan et al., Reliability Evaluation of Power Sys- Tems. Springer Science & Business Media, 2013

    Google Scholar 

  41. Gillett, B.E., Miller, L.R.: A heuristic algorithm for the vehicle-dispatch problem. Oper. Res. 22(2), 340–349 (1974)

    Article  Google Scholar 

  42. Ryan, D.M., Hjorring, C., Glover, F.: Extensions of the petal method for vehicle routeing. J Operat Res Soc. 44(3), 289–296 (1993)

    Article  Google Scholar 

  43. Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J ACM (JACM). 7(4), 326–329 (1960)

    Article  MathSciNet  Google Scholar 

  44. T. Caric and H. Gold, Vehicle Routing Problem. IntechOpen, 2008

  45. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science. 220(4598), 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  46. Dorling, K., Heinrichs, J., Messier, G.G., Magierowski, S.: Vehicle routing problems for drone delivery. IEEE Trans Syst, Man, Cybernetics: Syst. 47(1), 1–16 (2017)

    Article  Google Scholar 

  47. A. Ponza, “Optimization of Drone-Assisted Parcel Delivery,” Master’s thesis, University of Padua, 2016

  48. Mu, D., Wang, C., Zhao, F., Sutherland, J.W.: Solving vehicle routing problem with simultaneous pickup and delivery using parallel simulated annealing algorithm. Int J Ship Transport Logistics. 8(1), 81–106 (2016)

    Article  Google Scholar 

  49. Lim, G.J., Kardar, L., Cao, W.: A hybrid framework for optimizing beam angles in radiation therapy planning. Ann. Oper. Res. 217(1), 357–383 (2014)

    Article  MathSciNet  Google Scholar 

  50. G. Van Rossum and F. L. Drake, Python 3 Reference Manual. CreateSpace, 2009

  51. “Python interface,” access date: August, 2019. [Online]. Available: https://www.gurobi.com/documentation/8.1/quickstart_windows/py_python_interface.html#section: Python

  52. Bistouni, F., Jahanshahi, M.: Evaluating failure rate of fault-tolerant multistage interconnection networks using weibull life distribution. Reliability Eng Syst Safety. 144, 128–146 (2015)

    Article  Google Scholar 

  53. Jozefowiez, N., Semet, F., Talbi, E.-G.: Multiobjective vehicle routing problems. Eur. J. Oper. Res. 189(2), 293–309 (2008)

    Article  Google Scholar 

  54. Augerat, P., Belenguer, J.M., Benavent, E., Corberán, A., Naddef, D., Rinaldi, G.: Computational results with a branch and cut code for the capacitated vehicle routing problem. IMAG. 34, (1995)

  55. Jain, A., Jain, S.K.: Formulation and optimization of temozolomide nanoparticles by 3 factor 2 level factorial design. Biomatter. 3(2), e25102 (2013)

    Article  Google Scholar 

  56. Kenny, Q.Y., et al.: Indicator function and its application in two-level factorial designs. Ann. Stat. 31(3), 984–994 (2003)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, University of Houston, Houston, TX, USA

    Maryam Torabbeigi & Gino J. Lim

  2. Bayer Crop Science, 700 W Chesterfield Pkwy W, Chesterfield, MO, 63017, USA

    Navid Ahmadian

  3. Republic of Korea Army, Gyeryong, South Korea

    Seon Jin Kim

Authors
  1. Maryam Torabbeigi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gino J. Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Navid Ahmadian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Seon Jin Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gino J. Lim.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Torabbeigi, M., Lim, G.J., Ahmadian, N. et al. An Optimization Approach to Minimize the Expected Loss of Demand Considering Drone Failures in Drone Delivery Scheduling. J Intell Robot Syst 102, 22 (2021). https://doi.org/10.1007/s10846-021-01370-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01370-w

Keywords

Search

Navigation