Mathematical modeling for the distribution of relief items under uncertainty to control vehicle costs and downtime

Document Type : Original Article

Authors

1 Department of Industrial Management, AK.C., Islamic Azad University, Aliabad Katoul, Iran

2 Department of Industrial Engineering, AK.C., Islamic Azad University, Aliabad Katoul, Iran

3 Department of Accounting, AK.C., Islamic Azad University, Aliabad Katoul, Iran

10.22091/jemsc.2026.15874.1376

Abstract

This research focuses on designing a mathematical model for the location and routing of humanitarian aid distribution in humanitarian organizations, developed under conditions of uncertainty and with an approach to control costs and vehicle downtime. The goal of this research is to optimize the distribution process of essential items by providing a multi-objective model that simultaneously determines optimal locations and suitable distribution routes by controlling costs and time. To solve the model, the Epsilon Constraint (EC) method and the NSGA-II multi-objective genetic algorithm were used. The results show that the proposed model can select the shortest routes, minimize logistical costs, and optimally allocate vehicles according to their type to each destination. The model's validity was examined through a case study, and the results were compared with existing designs, demonstrating that the proposed model's performance is superior to current approaches. Overall, this research provides decision-makers with a scientific and data-driven tool to develop more effective disaster response strategies by reducing costs and optimizing resources.

Keywords

Main Subjects

References

Abdolhossein Zadeh, S., Zandieh, M., & Alam-Tabriz, A. (2025). E-Healthcare improvement through the design of a cloud-based blood supply chain: A system dynamics approach. Journal of Engineering Management and Soft Computing, 11(1), 47-1. https://doi.org/10.22091/jemsc.2025.11210.1201
Abolghasemian, M., Bigdeli, H., & Shamami, N. (2024). Locating Routing Problem (LRP) of distribution of priority support items to ground forces in war conditions. Engineering Management and Soft Computing, 10(1), 262-292. https://doi.org/10.22091/jemsc.2023.9453.1232
Abolghasemian, M., Ghane Kanafi, A., & Daneshmandmehr, M. (2020). A two-phase simulation-based optimization of hauling system in open-pit mine. Interdisciplinary Journal of Management Studies, 13(4), 705-732. https://doi.org/10.22059/ijms.2020.283100.673669
Anaya-Arenas, A. M., Ruiz, A., & Renaud, J. (2018). Importance of fairness in humanitarian relief distribution. Production Planning & Control, 29(14), 1145-1157. https://doi.org/10.1080/09537287.2018.1518557
Cao, C., Liu, Y., Tang, O., & Gao, X. (2021). A fuzzy bi-level optimization model for multi-period post-disaster relief distribution in sustainable humanitarian supply chains. International Journal of Production Economics, 235, 108081. https://doi.org/10.1016/j.ijpe.2021.108081
Cheng, C., Zhu, R., Costa, A. M., Thompson, R. G., & Huang, X. (2021). Multi-period two-echelon location routing problem for disaster waste clean-up. Transportmetrica A: Transport Science, 18(3), 1335-1365. https://doi.org/10.1080/23249935.2021.1916747
Du, J., Wang, X., Wu, X., Zhou, F., & Zhou, L. (2022). Multi-objective optimization for two-echelon joint delivery location routing problem considering carbon emission under online shopping. Transportation Letters, 15(7), 652-670. https://doi.org/10.1080/19427867.2022.2096781
Fallahtafti, A., Ardjmand, E., Young II, W. A., & Weckman, G. R. (2021). A multi-objective two-echelon location-routing problem for cash logistics: A metaheuristic approach. Applied Soft Computing, 111, 107685. https://doi.org/10.1016/j.asoc.2021.107685
Fathi, M. R., Saffarinia, A., & Pahlevanzadeh, M. J. (2026). Multi-objective green supply chain network design considering carbon emissions and electricity consumption. Journal of Engineering Management and Soft Computing, 12(1), 14-35. https://doi.org/10.22091/jemsc.2026.14628.1326
Gandra, V. M. S., Çalık, H., Wauters, T., Toffolo, T. A., Carvalho, M. A. M., & Berghe, G. V. (2021). The impact of loading restrictions on the two-echelon location routing problem. Computers & Industrial Engineering, 160, 107609. https://doi.org/10.1016/j.cie.2021.107609
Giedelmann-L, N., Guerrero, W. J., & Solano-Charris, E. L. (2022). System dynamics approach for food inventory policy assessment in a humanitarian supply chain. International Journal of Disaster Risk Reduction, 81, 103286. https://doi.org/10.1016/j.ijdrr.2022.103286
Hasanpour Jesri, Z. S., Eshghi, K., Rafiee, M., & Van Woensel, T. (2022). The multi-depot traveling purchaser problem with shared resources. Sustainability, 14(16), 10190. https://doi.org/10.3390/su141610190
Heidari, A., Imani, D. M., Khalilzadeh, M., & Sarbazvatan, M. (2022). Green two-echelon closed and open location-routing problem: Application of NSGA-II and MOGWO metaheuristic approaches. Environment, Development and Sustainability, 25, 11467–11503. https://doi.org/10.1007/s10668-022-02534-1
Izadi, E., Nikbakht, M., Feylizadeh, M., & Shahin, A. (2025). Ranking of criteria affecting humanitarian supply chain services based on blockchain platforms using multi-criteria decision-making methods. Journal of Engineering Management and Soft Computing, 10(2), 143-160. https://doi.org/10.22091/jemsc.2025.11552.1215
Jahangiri, S., Abolghasemian, M., Pourghader Chobar, A., Nadaffard, A., & Mottaghi, V. (2021). Ranking of key resources in the humanitarian supply chain in the emergency department of Iranian hospital: A real case study in COVID-19 conditions. Journal of Applied Research on Industrial Engineering, 8(5), 1-10. https://doi.org/10.22105/jarie.2021.275255.1263
Jahangiri, Sh., Abolghasemian, M., Ghasemi, P., & Pourghader Chobar, A. (2021). Simulation-based optimization: analysis of the emergency department resources under COVID-19 conditions. International Journal of Industrial and Systems Engineering, 39(4), 461-481. https://doi.org/10.1504/IJISE.2021.120358
Khan, S. A., & Ali, M. (2023). A robust multi-objective location-routing design for emergency medical supplies under deep uncertainty. International Journal of Disaster Risk Reduction, 92, 103745. https://doi.org/10.1016/j.ijdrr.2023.103745
Mamashli, Z., Bozorgi-Amiri, A., Dadashpour, I., Nayeri, S., & Heydari, J. (2021). A heuristic-based multi-choice goal programming for the stochastic sustainable-resilient routing-allocation problem in relief logistics. Neural Computing and Applications, 34, 15473–15499. https://doi.org/10.1007/s00521-021-06703-9
Mohamed, I. B., Klibi, W., Sadykov, R., Şen, H., & Vanderbeck, F. (2022). The two-echelon stochastic multi-period capacitated location-routing problem. European Journal of Operational Research, 303(2), 601-622. https://doi.org/10.1016/j.ejor.2022.02.046
Narimani, R., Motamedi, M., & Khalili, H. A. (2024). A mathematical programming model for the distribution of relief items in a humanitarian supply chain. Emergency Management, 13(1), 51-69. https://doi.org/10.22034/em.2024.19854.1082
Nozari, H., Tavakkoli-Moghaddam, R., & Gharemani-Nahr, J. (2022). A neutrosophic fuzzy programming method to solve a multi-depot vehicle routing model under uncertainty during the COVID-19 pandemic. International Journal of Engineering, 35(2), 360-371. https://doi.org/10.5829/ije.2022.35.02b.11
Peng, D., Ye, C., & Wan, M. (2022). A multi-objective improved novel discrete particle swarm optimization for emergency resource center location problem. Engineering Applications of Artificial Intelligence, 111, 104725. https://doi.org/10.1016/j.engappai.2022.104725
Rezaei Kallaj, M., Abolghasemian, M., Moradi Pirbalouti, S., Sabk Ara, M., & Pourghader Chobar, A. (2021). Vehicle routing problem in relief supply under a crisis condition considering blood types. Mathematical Problems in Engineering, 2021, 7217182. https://doi.org/10.1155/2021/7217182
Shao-hong, Y., Jia-yang, N., Tai-long, C., Qiu-tong, L., Cen, Y., Jia-qing, C., Zhi-zhen, F., & Jie, L. (2022). Location algorithm of transfer stations based on density peak and outlier detection. Applied Intelligence, 52, 14321–14333. https://doi.org/10.1007/s10489-022-03181-w
Silva, R. F., Santos, B. F., & Mota, C. M. (2024). Ensuring equity in humanitarian logistics: A stochastic multi-echelon vehicle routing model under demand fluctuations. European Journal of Operational Research, 315(2), 542-558. https://doi.org/10.1016/j.ejor.2023.11.039
Wang, B. C., Qian, Q. Y., Gao, J. J., Tan, Z. Y., & Zhou, Y. (2021). The optimization of warehouse location and resources distribution for emergency rescue under uncertainty. Advanced Engineering Informatics, 48, 101278. https://doi.org/10.1016/j.aei.2021.101278
Wang, Y., Sun, Y., Guan, X., Fan, J., Xu, M., & Wang, H. (2021). Two-echelon multi-period location routing problem with shared transportation resource. Knowledge-Based Systems, 226, 107168. https://doi.org/10.1016/j.knosys.2021.107168
Wang, L., & Zhang, Y. (2025). Fleet repositioning and breakdown management in dynamic humanitarian supply chains: A machine-learning-assisted metaheuristic approach. Transportation Research Part E: Logistics and Transportation Review, 184, 103412. https://doi.org/10.1016/j.tre.2024.103412
Wei, X., Qiu, H., Wang, D., Duan, J., Wang, Y., & Cheng, T. C. E. (2020). An integrated location-routing problem with post-disaster relief distribution. Computers & Industrial Engineering, 147, 106632. https://doi.org/10.1016/j.cie.2020.106632
Yofrido, F. M., & Harjana, L. T. (2019). Social-fairness perception in natural disaster, learn from Lombok: A phenomenological report. Indonesian Journal of Anesthesiology and Reanimation, 1(1), 1-7. https://doi.org/10.20473/ijar.V1I12019.1-7
Yu, X., Zhou, Y., & Liu, X. F. (2020). The two-echelon multi-objective location routing problem inspired by realistic waste collection applications: The composable model and a metaheuristic algorithm. Applied Soft Computing, 94, 106477. https://doi.org/10.1016/j.asoc.2020.106477
Marjani, M. R., Jabbari, M., & Aghaee, M. (2026). A Hybrid Approach Based on Data Density Analysis for Group Supplier Selection Problem Considering Multi-Level Risk Assessment: A Case Study. Journal of Data Analytics and Intelligent Decision-making, 2(3), 1-28. doi: 10.22091/jdaid.2026.16147.1066
Bahadori Jahromi, H. (2026). From Analytics to Agility: How Smart Contract Capability and Supply Chain Digitalization Strengthen Supply Chain Performance in Financial Services. Journal of Data Analytics and Intelligent Decision-making, 2(3), 29-54. doi: 10.22091/jdaid.2026.16727.1094
Kiani, M. S. (2026). Sports Law and Coaches' Responsibility: Challenges and New Approaches in Iran. Journal of Data Analytics and Intelligent Decision-making, 2(2), 1-9. doi: 10.22091/jdaid.2026.15415.1035
Molani Aghdam, M., & Ardeshir Larijani, I. (2026). Artificial neural network evaluating nonlinear evolutionary effect of cognitive and risk complexity in Ambidextrous strategy renewal. Journal of Data Analytics and Intelligent Decision-making, 2(2), 10-30. doi: 10.22091/jdaid.2026.15918.1050
Joshan, A. (2026). Analysis of Emerging Approaches in Cybersecurity for Internet of Things (IoT) Networks with an Emphasis on Smart Urban and Domestic Infrastructures. Journal of Data Analytics and Intelligent Decision-making, 2(1), 1-16. doi: 10.22091/jdaid.2026.15424.1036
Jamshidi Gahrouei, A., & Asgharian, R. (2026). AI-Driven Protection Schemes for Modern Power Grids: Technologies, Challenges, and Opportunities. Journal of Data Analytics and Intelligent Decision-making, 2(1), 17-30. doi: 10.22091/jdaid.2026.15133.1032
Shahabi, V., Sarhangi, R., & Mehdiabadi, A. (2025). Explaining IT Governance for Implementing Branchless Banking Through Digital Transformation. Journal of Data Analytics and Intelligent Decision-making, 1(4), 1-31. doi: 10.22091/jdaid.2026.14530.1018
Joshan, A. (2025). Towards a Human-Centric Industry 5.0 Enabled by the Convergence of Artificial Intelligence, Internet of Things, and Blockchain. Journal of Data Analytics and Intelligent Decision-making, 1(4), 32-49. doi: 10.22091/jdaid.2026.14749.1025
Riki, M., Mohammadi, F., & Eslami, E. (2025). Video Coding Machine Architecture for Smart Urban Traffic Optimization with Deep Learning. Journal of Data Analytics and Intelligent Decision-making, 1(3), 1-12. doi: 10.22091/jdaid.2025.14036.1003
Mansoori, A. (2025). The Application of Artificial Intelligence in Human Resource Performance Appraisal: A Conceptual Framework for Responsible Implementation. Journal of Data Analytics and Intelligent Decision-making, 1(3), 13-30. doi: 10.22091/jdaid.2025.14114.1009
Jafari, H., Etebari, A., & Jafari, M. (2025). Proposing a Developed Gram–Schmidt Algorithm to Construct Orthogonal Unit Vectors (A Mathematical and Practical Approach). Journal of Data Analytics and Intelligent Decision-making, 1(2), 61-78. doi: 10.22091/jdaid.2025.14004.1001
Hasani, M., Deiranlou, M., & Karimi, H. (2025). Designing an Efficient Bike-Sharing System for the University of Bojnord. Journal of Data Analytics and Intelligent Decision-making, 1(2), 79-89. doi: 10.22091/jdaid.2025.14320.1014
Tavakkoli-Moghaddam, R., Akbari, A. H., Tanhaeean, M., Moghdani, R., Gholian-Jouybari, F., & Hajiaghaei-Keshteli, M. (2024). Multi-objective boxing match algorithm for multi-objective optimization problems. Expert Systems with Applications, 239, 122394. https://doi.org/10.1016/j.eswa.2023.122394
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