Annals of Operations Research

, Volume 283, Issue 1–2, pp 1283–1302 | Cite as

Stochastic facility location model for drones considering uncertain flight distance

  • Dongwook Kim
  • Kyungsik Lee
  • Ilkyeong MoonEmail author
S.I. : Applications of OR in Disaster Relief Operations, Part II


This paper developed a stochastic modelling framework to determine the locations and transport capacities of drone facilities for effectively coping with a disaster. The developed model is applicable to emergency planning that incorporates drones into humanitarian logistics while taking into account the uncertain characteristics of drone operating conditions. Because of the importance of speedy decision making in disaster management, a heuristic algorithm was developed using Benders decomposition, which generates time-efficient high-quality solutions. The linear programming rounding method was used to make the algorithm efficient. Computational experiments demonstrated the superiority of the developed algorithm, and a sensitivity analysis was carried out to gain additional insights.


Humanitarian logistics Facility location Stochastic programming Drone 



The authors are grateful for the valuable comments from anonymous reviewers. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT and Future Planning (MSIT) [NRF-2017R1A2B2007812]; the Basic Science Research Program through the NRF funded by the Ministry of Education (NRF-2015R1D1A1A01057719).


  1. Agatz, N., Bouman, P., & Schmidt, M. (2018). Optimization approaches for the traveling salesman problem with drone. Transportation Science. Scholar
  2. Ahmadi-Javid, A., Seyedi, P., & Syam, S. S. (2017). A survery of healthcare facility location. Computers & Operations Research,79, 223–263.CrossRefGoogle Scholar
  3. Beckmann, M. J. (1999). Lectures on location theory. Berlin: Springer.CrossRefGoogle Scholar
  4. Berman, O., Krass, D., & Drezner, Z. (2003). The gradual covering decay location problem on a network. European Journal of Operational Research,151(3), 474–480.CrossRefGoogle Scholar
  5. Boonmee, C., Arimura, M., & Asada, T. (2017). Facility location optimization model for emergency humanitarian logistics. International Journal of Disaster Risk Reduction,24, 485–498.CrossRefGoogle Scholar
  6. Burdakov, O., Kvarnstrom, J., & Doherty, P. (2017). Optimal scheduling for replacing perimeter guarding unmanned aerial vehicles. Annals of Operations Research,249, 163–174.CrossRefGoogle Scholar
  7. Chowdhury, S., Emelogu, A., Marufuzzaman, M., Nurre, S. G., & Bian, L. (2017). Drones for disaster response and relief operations: A continuous approximation model. International Journal of Production Economics,188, 167–184.CrossRefGoogle Scholar
  8. Chu, Y., & Xia, Q. (2004). Generating benders cuts for a general class of integer programming problems. In J. C. Régin & M. Rueher (Eds.) Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (Vol. 3011, pp. 127–141). CPAIOR 2004. Lecture notes in computer science. Berlin: Springer.Google Scholar
  9. Evers, L., Dollevoet, T., Barros, A. I., & Monsuur, H. (2014). Robust UAV planning. Annals of Operations Research,222, 293–315.CrossRefGoogle Scholar
  10. Farahani, R. Z., Asgari, N., Heidari, N., Hosseininia, M., & Goh, M. (2012). Covering problems in facility location: A review. Computers & Industrial Engineering,62, 368–407.CrossRefGoogle Scholar
  11. Geoffrion, A. M. (1972). Generalized benders decomposition. Journal of Optimization Theory and Applications,10(4), 237–260.CrossRefGoogle Scholar
  12. Geoffrion, A. M., & Graves, G. W. (1974). Multicommodity distribution system design by benders decomposition. Management Science,20(5), 822–844.CrossRefGoogle Scholar
  13. Goldberg, J., Dietrich, R., Chen, J., Mitwasi, G., Valenzuela, T., & Criss, L. (1990). Validating and applying a model for locating emergency medical vehicles in Tucson. Arizona, European Journal of Operational Research,49(3), 308–324.CrossRefGoogle Scholar
  14. Grass, E., Fischer, K., & Rams, A. (2018). An accelerated L-shaped method for solving two-stage stochastic programs in disaster management. Annals of Operations Research. Scholar
  15. Ham, A. M. (2018). Integrated scheduling of m-truck, m-drone, and m-depot constrained by time-window, drop-pickup, and m-visit using constraint programming. Transportation Research Part C: Emerging Technology,91, 1–14.CrossRefGoogle Scholar
  16. Karatas, M. (2017). A multi-objective facility location problem in the presence of variable gradual coverage performance and cooperative cover. European Journal of Operational Research,262, 1040–1051.CrossRefGoogle Scholar
  17. Khodaparasti, S., Bruni, M. E., Beraldi, P., Maleki, H. R., & Jahedi, S. (2018). A multi-period location-allocation model for nursing home network planning under uncertainty. Operations Research for Health Care,18, 4–15.CrossRefGoogle Scholar
  18. Kim, S.J., Lim, G.J., & Cho, J. (2017). A robust optimization approach for scheduling drones considering uncertainty of battery duration. In Proceedings of the 2017 industrial and systems engineering conference (pp. 187–192), Center Pittsburgh; United States.Google Scholar
  19. Lee, C., & Han, J. (2017). Benders-and-Price approach for electric vehicle charging station location problem under probabilistic travel range. Transportation Research Part B,106, 130–152.CrossRefGoogle Scholar
  20. Marín, A., Martínez-Merino, L. I., Rodríguez-Chía, A. M., & Saldanha-da-Gama, F. (2018). Multi-period stochastic covering location problems: Modeling framework and solution approach. European Journal of Operational Research,268, 432–449.CrossRefGoogle Scholar
  21. Meng, S., & Shia, B. C. (2013). Set covering location models with stochastic critical distances. Journal of the Operational Research Society,64, 945–958.CrossRefGoogle Scholar
  22. Merwaday, A., & Guvenc, I. (2015). UAV assisted heterogeneous networks for public safety communications. In Proceedings of 2015 IEEE wireless communications and networking conference workshops, WCNCW 2015 (pp. 329–334), New Orleans, United States.Google Scholar
  23. Murray, C. C., & Chu, C. C. (2015). The flying sidekick traveling salesman problem: optimization of drone-assisted parcel delivery. Transportation Research Part C: Emerging Technology,54, 86–109.CrossRefGoogle Scholar
  24. Otto, A., Agatz, N., Campbell, J., Golden, B., & Pesch, E. (2018). Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey. Networks,00, 1–48. Scholar
  25. Paul, J. A., & MacDonald, L. (2016). Location and capacity allocations decisions to mitigate the impacts of unexpected disasters. European Journal of Operational Research,251, 252–263.CrossRefGoogle Scholar
  26. Pereira, J., & Averbakh, I. (2013). The robust set covering problem with interval data. Annals of Operations Research,207, 217–235.CrossRefGoogle Scholar
  27. Shavarani, S. M., Nejad, M. G., Rismanchian, F., & Izbirak, G. (2018). Application of hierarchical facility location problem for optimization of a drone delivery system: a case study of Amazon prime air in the city of San Francisco. The International Journal of Advanced Manufacturing Technology,95, 3141–3153.CrossRefGoogle Scholar
  28. Shmoys, D., Tardos, E., & Aardal, K. (1997). Approximation algorithms for facility location problems. In Proceedings of the 29th ACM symposium on the theory of computing (pp. 265–274), Assoc. for Computing Machinery, Seattle, WA.Google Scholar
  29. Tayal, A., Gunasekaran, A., Singh, S. P., Dubey, R., & Papadopoulos, T. (2017). Formulating and solving sustainable stochastic dynamic facility layout problem: A key to sustainable operations. Annals of Operations Research,253, 621–655.CrossRefGoogle Scholar
  30. Zhang, B., Peng, J., & Li, S. (2017). Covering location problem of emergency service facilities in an uncertain environment. Applied Mathematical Modelling,51, 2017.Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Institute for Industrial Systems InnovationSeoul National UniversitySeoulKorea

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