A bi-objective robust optimization model for location-transportation under uncertainty with psychological costs

After an earthquake, it is often difficult to obtain accurate information on the number of casualties in the disaster area, which brings significant uncertainty to emergency rescue logistics. In addition to physical injuries, victims often suffer from severe psychological trauma, further hindering the effectiveness of rescue efforts. As such, incorporating the psychological condition of casualties is essential to developing an effective rescue strategy under uncertainty in casualty numbers. Building on this, this paper proposes a bi-objective robust optimization model to determine the optimal locations of medical facilities and the transportation plans for the casualties within a three-tier rescue chain comprising disaster areas, temporary hospitals, and comprehensive hospitals. The Injury Severity Score (ISS) is employed to classify casualties into three categories and to give the dynamic evolution of the deterioration rate of casualties over time. The model also considers factors such as limited medical resources, casualty classification, uncertainty in casualty numbers, and psychological conditions. The objective is to minimize the total ISS and psychological cost. We use the robust optimization method to derive the robust counterpart model of the proposed stochastic model. The bi-objective model is solved using the ε − constraint method. Extensive computational experiments and sensitivity analyses based on the Yushu earthquake were conducted, and the main findings are as follows. The greater the uncertainty in casualty numbers, the more significant its impact on the total ISS. While greater attention to the psychological condition of casualties can improve humanitarian care, it may reduce rescue efficiency, and decision-makers need to make a trade-off based on actual preferences. The treatment needs of serious casualties deserve greater attention than those of moderate or mild ones. Moreover, expanding the capacity of temporary hospitals is more effective in improving rescue efficiency than comprehensive hospitals. Finally, the robust optimization model performs better than the deterministic model when expanding the problem size.