Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지
DOI QR코드

DOI QR Code

A Mixed-Integer Programming Model for Effective Distribution of Relief Supplies in Disaster

재난 구호품의 효과적 분배를 위한 혼합정수계획 모형

  • Kim, Heungseob (Department of Industrial and Systems Engineering/Department of Smart Manufacturing Engineering Changwon National University)
  • 김흥섭 (창원대학교 산업시스템공학과/스마트제조융합협동과정)
  • Received : 2020.12.22
  • Accepted : 2021.01.04
  • Published : 2021.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

The topic of this study is the field of humanitarian logistics for disaster response. Many existing studies have revealed that compliance with the golden time in response to a disaster determines the success or failure of relief activities, and logistics costs account for 80% of the disaster response cost. Besides, the agility, responsiveness, and effectiveness of the humanitarian logistics system are emphasized in consideration of the disaster situation's characteristics, such as the urgency of life-saving and rapid environmental changes. In other words, they emphasize the importance of logistics activities in disaster response, which includes the effective and efficient distribution of relief supplies. This study proposes a mathematical model for establishing a transport plan to distribute relief supplies in a disaster situation. To determine vehicles' route and the amount of relief for cities suffering a disaster, it mainly considers the urgency, effectiveness (restoration rate), and uncertainty in the logistics system. The model is initially developed as a mixed-integer nonlinear programming (MINLP) model containing some nonlinear functions and transform into a Mixed-integer linear programming (MILP) model using a logarithmic transformation and piecewise linear approximation method. Furthermore, a minimax problem is suggested to search for breakpoints and slopes to define a piecewise linear function that minimizes the linear approximation error. A numerical experiment is performed to verify the MILP model, and linear approximation error is also analyzed in the experiment.

Keywords

References

  1. Balcik, B. and Beamon, B.M., Facility location in humanitarian relief, International Journal of Logistics, 2008, Vol. 11, No. 2, pp. 101-121. https://doi.org/10.1080/13675560701561789
  2. Cao, Z., Wang, W., Ma, D., Su, J., Gao, Z., and Han, Y., Optimum path analysis of post-earthquake transportation considering multi-objective based on GIS, In International Conference on Transportation Engineering 2009, 2009, pp. 1104-1109.
  3. Celik, M., Ergun, O., Johnson, B., Keskinocak, P., Lorca, A., Pekgun, P., and Swann, J., Humanitarian Logistics, INFORMS Tutorials in Operations Research, 2012, Vol. 9, pp. 18-49.
  4. Chang, M.S., Tseng, Y.L., and Chen, J.W., A scenario planning approach for the flood emergency logistics preparation problem under uncertainty, Transportation Research Part E : Logistics and Transportation Review, 2007, Vol. 43, No. 6, pp. 737-754. https://doi.org/10.1016/j.tre.2006.10.013
  5. Cheng, W. and Lu, J., Operational analysis on emergency logistics system and emergency response model, In 2008 IEEE International Conference on Service Operations and Logistics, and Informatics, 2008, Vol. 1, pp. 1323-1328.
  6. Choi, H. and Ha, H., The Priority of Supply Chain Designs for Humanitarian Relief with AHP(Analytic Hierarchy Process), Korean Journal of Logistics, 2013, Vol. 21, No. 3, pp. 121-134. https://doi.org/10.15735/KLS.2013.21.3.009
  7. Cozzolino, A., Humanitarian Logistics : Cross-Sector Cooperation in Disaster Relief Management, Springer Science & Business Media, 2012.
  8. Dudin, A. and Semenova, O., A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters, Journal of Applied Probability, 2004, Vol. 41, No. 1, pp. 547-556. https://doi.org/10.1239/jap/1082999085
  9. Economou, A., The compound Poisson immigration process subject to binomial catastrophes, Journal of Applied Probability, 2004, Vol. 41, No. 1, pp. 508-523. https://doi.org/10.1017/S0021900200014467
  10. Han, S., Jeong, H., Kim, K., and Park J., A Research on the Vehicle Routing Problem in the Disaster Scene, Korean Management Science Review, 2016, Vol. 33, No. 1, pp. 101-117. https://doi.org/10.7737/KMSR.2016.33.1.101
  11. Hsieh, P.H., A data-analytic method for forecasting next record catastrophe loss, The Journal of Risk and Insurance, 2004, Vol. 71, No. 2, pp. 309-322. https://doi.org/10.1111/j.0022-4367.2004.00091.x
  12. Huang, K., Jiang, Y., Yuan, Y., and Zhao, L., Modeling multiple humanitarian objectives in emergency response to large-scale disasters, Transportation Research Part E : Logistics and Transportation Review, 2015, Vol. 75, pp. 1-17. https://doi.org/10.1016/j.tre.2014.11.007
  13. Korea Meteorological Administration, Annual Earthquake, 2020.
  14. Kumar, S.K. and Tiwari, M.K., Supply chain system design integrated with risk pooling, Computers & Industrial Engineering, 2013, Vol. 64, No. 2, pp. 580-588. https://doi.org/10.1016/j.cie.2012.11.013
  15. Lima-Junior, F.R. and Carpinetti, L.C.R., Quantitative models for supply chain performance evaluation : A literature review, Computers & Industrial Engineering, 2017, Vol. 113, pp. 333-346. https://doi.org/10.1016/j.cie.2017.09.022
  16. Meixell, M.J. and Gargeya, V.B., Global supply chain design : A literature review and critique, Transportation Research Part E : Logistics and Transportation Review, 2005, Vol. 41, No. 6, pp. 531-550. https://doi.org/10.1016/j.tre.2005.06.003
  17. Ozdamar, L., Ekinci, E., and Kucukyazici, B., Emergency logistics planning in natural disasters, Annals of Operations Research, 2004, Vol. 129, pp. 217-245. https://doi.org/10.1023/B:ANOR.0000030690.27939.39
  18. Parragh, S.N., Doerner, K.F., Hartl, R.F., and Gandibleux, X., A heuristic two-phase solution approach for the multi-objective dial-a-ride problem, Networks : An International Journal, 2009, Vol. 54, No. 4, pp. 227-242. https://doi.org/10.1002/net.20335
  19. Roh, S.Y., Jang, H.M., and Han, C.H., Warehouse location decision factors in humanitarian relief logistics, The Asian Journal of Shipping and Logistics, 2013, Vol. 29, No. 1, pp. 103-120. https://doi.org/10.1016/j.ajsl.2013.05.006
  20. Ryu, K. and Hwang, T., Optimal Locations of Disaster Relief Warehouses Based on Connected Maximum Covering Problem, Journal of the Korea Society of Supply Chain Management, 2019, Vol. 19, No. 1, pp. 19-30. https://doi.org/10.25052/KSCM.2019.05.19.1.19
  21. Tatham, P., Pettit, S., Charles, A., Lauras, M., and Van Wassenhove L., A model to define and assess the agility of supply chains : building on humanitarian experience, International Journal of Physical Distribution & Logistics Management, 2010, Vol. 40, pp. 722-741. https://doi.org/10.1108/09600031011079355
  22. Trunick, P.A., Logistics when it counts, Logistics Today, 2005, Vol. 46, No. 2, p. 38.
  23. Van Wassenhove, L.N., Humanitarian aid logistics : supply chain management in high gear, Journal of the Operational research Society, 2006, Vol. 57, No. 5, pp. 475-489. https://doi.org/10.1057/palgrave.jors.2602125
  24. Yi, W. and Kumar, A., Ant colony optimization for disaster relief operations, Transportation Research Part E : Logistics and Transportation Review, 2007, Vol. 43, No. 6, pp. 660-672. https://doi.org/10.1016/j.tre.2006.05.004
  25. Yi, W. and Ozdamar, L., A dynamic logistics coordination model for evacuation and support in disaster response activities, European Journal of Operational Research, 2007, Vol. 179, No. 3, pp.1177-1193. https://doi.org/10.1016/j.ejor.2005.03.077
  26. Yoon, K., Kim, J., and Yang. C., A study of Innovational Logistics System's Preferential Order Decision for Disaster Response, using AHP, Korea Logistics Review, 2015, Vol. 25, No. 2, pp. 1-12.