A robust optimization model for allocation-routing problems under uncertain conditions

Abstract

Post-earthquake emergency logistics faces significant challenges such as limited resources, uncertain casualty numbers, and time constraints. Developing a scientific and efficient rescue plan is crucial. One of the key issues is integrating facility location and casualty allocation in emergency medical services, an area rarely explored in existing research. This study proposes a robust optimization model to optimize the location of medical facilities and the transfer of casualties within a three-level rescue chain consisting of disaster areas, temporary hospitals, and general hospitals. The model accounts for limited medical resources, casualty classification, and uncertainty in casualty numbers. The Trauma Index Score (TIS) method is used to classify casualties into two groups, and the dynamic changes in their injuries after treatment at temporary hospitals are considered. The objective is to minimize the total TIS of all casualties. A robust optimization approach is applied to derive the corresponding robust model, and its validity is verified through case studies based on the Lushan earthquake. The findings show that data variability and the uncertainty budget play a critical role in determining hospital locations and casualty transportation plans. Temporary hospital capacity significantly influences the objective function more than general hospitals. As the problem size increases, the robust optimization model performs better than the deterministic model. Furthermore, uncertainty in casualty numbers has a more significant impact on serious casualties than moderate casualties. To enhance the model's applicability, it is extended into a two-stage dynamic location-allocation model to better address the complexity of post-disaster scenarios.

Fig 1. Structure of the proposed emergency logistics network

Fig 2. The change in casualty deterioration rate over time.

Fig 3. Decision scheme of the deterministic model based on nominal data.

Fig 4. Changes in TIS with respect to uncertainty budget under different data variability.

Fig 5. Changes in TIS (a) and TIS difference (b) of different types of casualties with respect to uncertain parameters

Fig 6. Changes in objective value for increasing hospital capacity.