Bi-level Scenario-based Location-allocation-inventory Models for Post-crisis Conditions and Solving with Electromagnetic and Genetic Algorithms

Document Type : Original Article


Department of Industrial Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran


Incidents that occur suddenly due to natural and human functions and impose hardships on society are called crises. As the Earth’s climate changes have increased the number of natural crises, including earthquakes, floods, hurricanes, etc., in recent years, human beings have felt the need for crisis management and the necessary planning in critical situations more than ever. This research aims to model and solve the problem of location, allocation, and inventory in post-crisis conditions. To meet this purpose, first, we have conducted a review of the previous papers. Then, we have identified the research gaps in management and planning in critical situations. In this study, uncertain budgets and demands and bi-level programming decision-making are the innovations. As a result, we have developed mixed-integer linear mathematical models to cover the research gaps. Finally, several problems have been solved in small dimensions by GAMS software and large-sized problems by genetic and electromagnetic meta-heuristic algorithms. Then, we analyzed the algorithms’ performance which indicates the genetic algorithm is better than the electromagnetic algorithm in this issue.


Main Subjects

  1. Rezaei-Malek, M., Tavakkoli-Moghaddam, R., Zahiri, B. and Bozorgi-Amiri, A., “An interactive approach for designing a robust disaster relief logistics network with perishable commodities”, Computers & Industrial Engineering, 94, (2016), 201-215, doi: 10.1016/j.cie.2016.01.014.
  2. Kohn, S., Eaton, J. L., Feroz, S. and Bainbridge, A. A., Hoolachan, J., Barnett, D. J., “Personal disaster preparedness: an integrative review of the literature”, Disaster medicine and Public Health Preparedness, Vol. 6, No. 3, (2012), 217-231, doi: 10.1001/dmp.2012.47.
  3. Boonmee, C., Arimura, M. and Asada, T., “Location and allocation optimization for integrated decisions on post-disaster waste supply chain management: On-site and off-site separation for recyclable materials”, International Journal of Disaster Risk Reduction, Vo. l31, (2018), 902-917,
  4. Habib, M. S. and Sarkar, B., “An integrated location-allocation model for temporary disaster debris management under an uncertain environment”, Sustainability, Vol. 9, (2017), 716,
  5. Lorca, Á., Çelik, M., Ergun, Ö. and Keskinocak, P., “An optimization‐based decision‐support tool for post‐disaster debris operations”, Production and Operations Management, Vol. 26, No. 6, (2017), 1076-1091, doi: 10.1111/poms.12643.
  6. Paul, J. A. and MacDonald, L., “Location and capacity allocations decisions to mitigate the impacts of unexpected disasters”, European Journal of Operational Research, Vol. 251, No. 1, (2016), 252-263,
  7. Ferreira, G. O., Arruda, E. F. and Marujo, L. G., “Inventory management of perishable items in long-term humanitarian operations using Markov decision processes”, International Journal of Disaster Risk Reduction, Vol. 31, (2018), 460-469,
  8. JICA, C. "The study on seismic microzoning of the Greater Tehran Area in the Islamic Republic of Iran.", Pacific Consultants International Report, OYO Cooperation, Japan, (2000), 291-390.
  9. Cozzolino, A., Rossi, S. and Conforti, A., “Agile and lean principles in the humanitarian supply chain: The case of the United Nations World Food Programme”, Journal of Humanitarian Logistics and Supply Chain Management, Vol. 2, No. 1, (2012), 16-33,
  10. Naji-Azimi, Z., Renaud, J., Ruiz, A. and Salari, M., “A covering tour approach to the location of satellite distribution centers to supply humanitarian aid”, European Journal of Operational Research, Vol. 222, No. 3, (2012), 596-605, doi: 10.1016/j.ejor.2012.05.001.
  11. Hu, Z. H. and Sheu, J. B., “Post-disaster debris reverse logistics management under psychological cost minimization”, Transportation Research Part B: Methodological, 55, (2013), 118-141,
  12. Bozorgi-Amiri, A., Jabalameli, M. S., Alinaghian, M. and Heydari, M., “A modified particle swarm optimization for disaster relief logistics under uncertain environment”, The International Journal of Advanced Manufacturing Technology, Vol. 60, No. 1-4, (2012), 357-371, doi: 10.1007/s00170-011-3596-8.
  13. Yu, W., “Reachability guarantee-based model for pre-positioning of emergency facilities under uncertain disaster damages”, International Journal of Disaster Risk Reduction, Vol. 42, (2020), 101335,
  14. Oksuz M. K. and Satoglu, S. I., “A two-stage stochastic model for location planning of temporary medical centers for disaster response”, International Journal of Disaster Risk Reduction, Vol. 44, (2020), 101426,
  15. Boonmee, C., Naotaka, I., Takumi, A. and Mikiharu, A., “Multi-model optimization for shelter-site selection: A case study in Banta municipality, Thailand”, The 53rd Japan Society of Civil Engineers Conference, Hokkaido University, Japan, (2017), 2175-2181.
  16. Chakravarty, A. K., “Humanitarian relief chain: Rapid response under uncertainty”, International Journal of Production Economics, Vol. 151, (2014), 146-157,
  17. Hong, X., Lejeune, M. A. and Noyan, N., “Stochastic network design for disaster preparedness”, IIE Transactions, Vol. 47, No. 4, (2015), 329-357,
  18. Mohammadi, R., Ghomi, S. F. and Jolai, F., “Prepositioning emergency earthquake response supplies: A new multi-objective particle swarm optimization algorithm”, Applied Mathematical Modelling, Vol. 40, No. 9-10, (2016), 5183-5199,
  19. Tofighi, S., Torabi, S. A. and Mansouri, S. A., “Humanitarian logistics network design under mixed uncertainty”, European Journal of Operational Research, Vol. 250, (2016), 239-250,
  20. Hu, S. L., Han, C. F. and Meng, L. P., “Stochastic optimization for joint decision making of inventory and procurement in humanitarian relief”, Computers & Industrial Engineering, Vol. 111, (2017), 39-49,
  21. Shen, Z., Dessouky, M. and Ordóñez, F., “Perishable inventory management system with a minimum volume constraint”, Journal of the Operational Research Society, 62, No. 19, (2011), 2063-2082,
  22. Manopiniwes, W., Nagasawa, K. and Irohara, T., “Humanitarian relief logistics with time restriction: Thai flooding case study”, Industrial Engineering & Management Systems, Vol. 13, No. 4, (2014), 398-407,
  23. Roni, M. S., EksiogluJin, M. and Mamun, S., “A hybrid inventory policy with split delivery under regular and surge demand”, International Journal of Production Economics, Vol. 172, (2016), 126-136, doi: 10.1016/j.ijpe.2015.11.015.
  24. Tavana, M., Abtahi, A. R., Di Caprio, D., Hashemi, R. and Yousefi-Zenouz, R., “An integrated location-inventory-routing humanitarian supply chain network with pre-and post-disaster management considerations”, Socio-Economic Planning Sciences, Vol. 64, (2018), 21-37.
  25. Celik, E., Aydin, N. and Gumus, A. T., “A stochastic location and allocation model for critical items to response large-scale emergencies: A case of Turkey”, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Vol. 7, No.1, (2016), 1-15, doi: 10.11121/ijocta.01.2017.00300.
  26. Loree, N. and Aros-Vera, F., “Points of distribution location and inventory management model for Post-Disaster Humanitarian Logistics”, Transportation Research Part E: Logistics and Transportation Review, Vol. 116, (2018), 1-24,
  27. Cavdur, F., Sebatli-Saglam, A. and Kose-Kucuk, M., “A spreadsheet-based decision support tool for temporary-disaster-response facilities allocation”, Safety Science, Vol. 124, (2020), 104581, doi: 10.1016/j.ssci.2019.104581.
  28. Baharmand, H., Comes, T. and Lauras, M., “Bi-objective multi-layer location–allocation model for the immediate aftermath of sudden-onset disasters”, Transportation Research Part E: Logistics and Transportation Review, Vol. 127, (2019), 86-110,
  29. Liu, A., Zhu, Q., Xu, L., Lu, Q. and Fan, Y., “Sustainable supply chain management for perishable products in emerging markets: An integrated location-inventory-routing model”, Transportation Research Part E: Logistics and Transportation Review, Vol. 150, (2021), 102319, doi: 10.1016/j.tre.2021.102319.
  30. Mahtab, Z., Azeem, A., Ali, S. M., Paul, S. K. and Fathollahi-Fard, A. M. “Multi-objective robust-stochastic optimisation of relief goods distribution under uncertainty: a real-life case study”, International Journal of Systems Science: Operations & Logistics, (2021), 1-22.
  31. Fetter, G. and Rakes, T., “Incorporating recycling into post-disaster debris disposal”, Socio-Economic Planning Sciences, Vol. 46, No. 1, (2012), 14-22,
  32. Kim, J., Deshmukh, A. and Hastak, M., “Selecting a temporary debris management site for effective debris removal”, 10th Annual Conference of the International Institute for Infrastructure Renewal and Reconstruction, (2014), 214-218, doi: 10.5703/1288284315362.
  33. Onan, K., Ülengin, F. and Sennaroğlu, B., “An evolutionary multi-objective optimization approach to disaster waste management: A case study of Istanbul, Turkey”, Expert Systems with Applications, 42, No. 22, (2015), 8850-8857,
  34. Pramudita, A., Taniguchi, E. and Qureshi, A. G., “Location and routing problems of debris collection operation after disasters with realistic case study”, Procedia-Social and Behavioral Sciences, Vol. 125, (2014), 445-458,
  35. Takeda, T., Mori, Y., Kubota, N. and Arai, Y., “A route planning for disaster waste disposal based on robot technology”, In 2014 IEEE Symposium on Robotic Intelligence in Informationally Structured Space (RiiSS), (2014), 1-6.
  36. Balcik, B. and Beamon, B. M., “Facility location in humanitarian relief”, International Journal of Logistics, Vol. 11, No. 2, (2008), 101-121,
  37. Garrido, R. A., Lamas, P. and Pino, F. J., “A stochastic programming approach for floods emergency logistics”, Transportation Research Part E: Logistics and Transportation Review, 75, (2015), 18-31, doi: 10.1016/j.tre.2014.12.002.
  38. Rabbani, M., Manavizadeh, N., Samavati, M. and Jalali, M., “Proactive and reactive inventory policies in humanitarian operations”, Uncertain Supply Chain Management, 3, (2015), 253-272, doi: 10.5267/j.uscm.2015.3.004.
  39. Renkli, Ç. and Duran, S., “Pre-positioning disaster response facilities and relief item”, Human and Ecological Risk Assessment: An International Journal, Vol. 21, 5, (2015), 1169-1185,
  40. Noyan, N., Balcik, B. and Atakan, S., “A stochastic optimization model for designing last mile relief networks”, Transportation Science, 50, (2015), 1092-1113,
  41. Escudero, L. F., Garín, M. A., Monge F. and Unzueta, A., “On preparedness resource allocation planning for natural disaster relief under endogenous uncertainty with time-consistent risk-averse management”, Computers & Operations Research, Vol. 98, (2018), 84-102, doi: 10.1016/j.cor.2018.05.010.
  42. Fallahpour, A., Wong, K. Y., Rajoo, S., Fathollahi-Fard, A. M., Antucheviciene, J. and Nayeri, S., “An integrated approach for a sustainable supplier selection based on Industry 4.0 concept”, Environmental Science and Pollution Research, (2021), 1-19.
  43. Fathollahi-Fard, A. M., Hajiaghaei-Keshteli, M., Tavakkoli-Moghaddam, R. and Smith, N. R. “Bi-level programming for home health care supply chain considering outsourcing”, Journal of Industrial Information Integration, Vol. 25, (2022), 100246.
  44. Pasha, J., Dulebenets, M. A., Fathollahi-Fard, A. M., Tian, G., Lau, Y. Y., Singh, P. and Liang, B. “An integrated optimization method for tactical-level planning in liner shipping with heterogeneous ship fleet and environmental considerations”, Advanced Engineering Informatics, Vol. 48, (2021), 101299.