A Multi-Stage Stochastic Programming Model for Relief Logistics in Simultaneous Crisis Situation

The critical importance of humanitarian relief during concurrent crises lies in the extensive and complex impacts these events have on societies. Concurrent crises often place significant demands on relief resources, requiring greater planning and coordination. In such situations, rapid and efficient relief operations can prevent human casualties, economic losses, and the escalation of social problems.



This study employs a scenario-based multi-objective stochastic programming approach to propose a model for resource allocation and distribution. A review of national and international research reveals that the issue of resource allocation in concurrent crises has received limited attention. To date, no mathematical model based on scenarios that considers the probabilities of various events in concurrent crises has been developed in the country. Therefore, this research focuses on developing a multi-objective model for resource allocation under different scenarios in concurrent crises.



A three-stage stochastic optimization model was developed to address the complexities of emergency logistics. The model focuses on three objectives: minimizing the total expected transportation time, minimizing the total expected costs, and minimizing the total expected unmet demand at each stage. The model was implemented using data from a real incident involving multiple natural disasters in North Khorasan Province, Iran, in 2016. On November 3, an earthquake of magnitude 4.0 struck, causing no casualties. The next day, heavy rainfall led to severe flooding, causing extensive damage to homes and infrastructure, as well as numerous casualties and displacements. Landslides, lightning strikes, and a severe storm followed, triggering fires and further destruction in urban and rural areas. In this study, the flood was treated as the primary disaster and the storm as the secondary disaster.



Two storage centers were designated for distributing emergency resources such as tents, drinking water, and food. Relief efforts were conducted via land, air, and boats. Thirty scenarios with varying probabilities were designed to analyze the likelihood of secondary disasters. The study highlights that scenario-based planning can significantly enhance the efficiency and effectiveness of humanitarian relief during multiple crises.



The results indicated that in scenarios considering only primary disasters, the resource supply rate in areas affected by primary disasters averaged over 75%. However, after resource allocation to these areas, only 90 tents, 1,500 units of drinking water, and 300 food rations remained. The shortage of remaining resources reduced the supply rate in other areas to an average of about 8%. Conversely, when secondary disasters were also included in the model, the average supply of resources, including food, water, and tents, improved significantly across all regions.



These findings underscore the importance of accounting for secondary disasters in the design of relief programs. Overall, the results demonstrated that the proposed model effectively optimized the allocation of emergency resources. Compared to traditional methods, the model provided a more adaptive and efficient resource distribution under crisis conditions. A key finding is that considering secondary disasters significantly enhanced the sustainability and efficiency of the resource distribution process, preventing new crises caused by unmet resource demands. Furthermore, the proposed approximate method reduced problem-solving time and minimized unmet demand under worst-case scenarios. In conclusion, this research highlights that incorporating more complex and realistic conditions, such as secondary disasters, can lead to substantial improvements in humanitarian relief processes.