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

Introduction: Efficient management of relief operations in situations involving concurrent disasters—particularly when secondary crises follow primary ones—constitutes one of the major challenges in humanitarian logistics planning. The complexity of such conditions is intensified by uncertainties in resource demand and the probability of various scenarios, highlighting the necessity of designing models that are both effective and sensitive to these fluctuations. The primary objective of this study is to develop a multi-objective model for resource allocation, transportation scheduling, and minimizing the impacts of resource shortages under simultaneous primary and secondary disaster events. In addition to reducing transportation time and cost, the proposed model aims to minimize unmet demand and ensure a fair distribution of resources among affected areas.
Methods: To achieve these goals, a three-objective model was developed to minimize transportation time, transportation cost, and unmet demand. Using the weighting method, the model was transformed into an equivalent single-objective formulation and solved under diverse uncertainty scenarios related to demand and the likelihood of secondary disasters. To evaluate model robustness, sensitivity analyses were conducted on key parameters, including resource demand and scenario occurrence probabilities. The model’s performance in larger-scale settings was also assessed by increasing the number of disaster points, storage centers, and scenarios. Additionally, separate analyses were performed to examine the effects of variations in secondary-disaster demand and transportation costs, allowing for a comprehensive assessment of the model’s capability in different crisis conditions.
Results: Initial results under equal weighting of the three objectives indicated that optimal transportation time and cost remained within acceptable ranges, while unmet demand was minimized, demonstrating the model’s effectiveness in balancing conflicting goals. Sensitivity analysis showed that a 20% increase in demand leads to a 5.3% rise in transportation time and a 7.1% increase in unmet demand, whereas costs rise by only 3.8%, indicating the model’s robustness. Similarly, a 10% increase in the probability of secondary-disaster scenarios increases transportation time by 4.6% and unmet demand by 3.2%. Large-scale experiments revealed that when the number of disaster points increases to 50 and scenarios to 100, applying the two-stage method reduces the solution time from 145 to 48 minutes, while the resource coverage rate declines by only 2.9%, confirming the model’s scalability. Evaluation of objective weights indicated that the cost function is the most sensitive to weight variations, whereas transportation time and unmet demand exhibit relatively stable behavior. Comparing resource allocation between scenarios with and without secondary disasters showed that including secondary crises increases the average resource coverage in non-priority areas from 8% to 60%, reflecting a more equitable distribution of resources. Analysis of the secondary disaster demonstrated that a 20% increase in storm-related demand raises total cost by 13% and unmet demand by 20%. Furthermore, a 20% increase in transportation cost in the secondary stage increases total cost by 10% while slightly improving transportation time. The final unmet-demand sensitivity analysis confirmed the model’s stability against variations in key parameters.
Conclusion: Overall, the proposed model exhibits robustness and flexibility under uncertainty and can effectively and equitably improve resource allocation in complex situations involving simultaneous disasters. The distinct sensitivity of the objectives and the significant role of secondary disasters suggest that effective humanitarian logistics planning requires an appropriate combination of objective weighting and careful consideration of secondary crisis dynamics.