Multi-commodity rebalancing plays a critical role before and during the attack of large-scale disasters. In practice, some relief centers can be out of reach from the ground for vehicles due to the road disruption. Accordingly, alternative transportation systems are essential to maximize fairness and minimize the total transportation time, simultaneously. However, little study has reported on this issue for humanitarian logistics. To address it, a bi-objective stochastic optimization model is proposed to rebalance and transport commodities with the multi-modal transportation system. This work first linearizes the model and then applies an adaptive augmented $\mathcal{E}$-constraint method to obtain a number of Pareto-optimal solutions. Furthermore, a case study of an emergency event is carried out, of which the computational results indicate its decision making effectiveness. Lastly, sensitivity analysis on critical parameters is conducted and the trade-off between the objectives is also analyzed to provide valuable managerial insights.

在大规模灾难袭击发生之前和之中，多商品重新平衡起着至关重要的作用。在实践中，由于道路中断，一些救灾中心可能无法从地面到达车辆。因此，替代性运输系统对于最大化公平性和最小化总运输时间至关重要。但是，关于人道主义后勤问题的研究很少。为了解决这个问题，提出了一种双目标随机优化模型，利用多式联运系统来重新平衡和运输商品。这项工作首先线性化模型，然后应用自适应增强$\mathcal{Ë}$-constraint方法获得许多帕累托最优解。此外，还对一个紧急事件进行了案例研究，其计算结果表明了其决策的有效性。最后，对关键参数进行敏感性分析，并分析目标之间的权衡，以提供有价值的管理见解。