System Engineering and Productivity

System Engineering and Productivity

Multi-objective Modeling for Cost Management in Optimal Allocation of Relief Supplies in Crisis Conditions

Articles in Press

Document Type : Research Paper

Authors
Somayeh Khoshnami 1
Elmira Mashayekhi 2
1 Ph.D. Student, Department of Industrial Management, Qa. C., Islamic Azad University, Qazvin, Iran
2 Corresponding author: Assistant Professor, Department of Industrial Management, Qa. C., Islamic Azad University, Qazvin, Iran
10.22034/sep.2025.2075536.1416
Abstract
This study examines multi-objective modeling for cost management in the optimal allocation of relief goods in crisis situations, focusing on the importance of time and resources in emergencies. The main goal is to develop a mathematical model for optimization that enables more effective and efficient allocation of relief goods by incorporating uncertainty in decision-making, reducing costs, and improving crisis response. The article presents a multi-objective, multi-period mathematical programming model for fair distribution of relief items and develops a multi-objective, multi-level humanitarian supply chain for equitable distribution of livelihood packages to counter crises. Additionally, a metaheuristic method is developed to solve the model for large-scale problems, and Pareto solutions are evaluated. The research examines four dimensions of humanitarian logistics indicators: access and transportation costs, unmet demand rate per period, the distance between the demand fill rate and the ideal satisfaction rate over the entire period, and environmental risks. The model is designed for allocating essential materials (water, food, medicine, equipment, clothing, and blankets) from multiple relief centers to various affected areas to ensure fair behavior and better alignment with real conditions. Results show that increasing epsilon up to a certain value causes negligible changes in objective function values, but beyond that, it leads to significant changes; the feasible region and improvement vector for objective functions are determined for epsilon values between 50 and 900, with optimal epsilon values for the first to fourth objective functions being 500, 150, 600, and 150 and 600, respectively. The proposed model is suitable for sudden large-scale local natural disasters (not national) occurring in urban areas with a certain resident population and cannot be directly used for storms or other low-impact, dispersed disasters. Ultimately, this research helps improve relief processes, reduce associated costs, and leads to saving human lives and mitigating crisis damages.

Highlights

  • Development of a multi-objective mathematical model under uncertainty for optimal allocation of relief resources
  • Use of advanced meta-heuristic method to solve multi-level and multi-period model 
  • Model design with the aim of ensuring fair distribution of livelihood packages
  • Model's ability to reduce costs and improve rapid response in local disasters

Keywords
Cost Management
Relief Distribution
Crisis Conditions
Epsilon Constraint
Multi-objective Modelling
Subjects

Copyright © Somayeh Khoshnami, Elmira Mashayekhi

 

License

This article is released under the Creative Commons Attribution (CC BY 4.0) license. Anyone is free to copy, share, translate, and adapt this article for any purpose, whether commercial or non-commercial, as long as proper citation is given to the authors and original publication.

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System Engineering and Productivity

Articles in Press, Accepted Manuscript
Available Online from 25 November 2025

  • Receive Date 11 September 2025
  • Revise Date 13 November 2025
  • Accept Date 24 November 2025
  • First Publish Date 25 November 2025
  • Publish Date 25 November 2025