Disaster relief logistics (DRL) provides adequate relief supplies to victims of natural disasters (e.g., earthquakes and volcanic eruptions). This study explicitly considers supplier selection and inventory pre-positioning corresponding to static preparedness decisions, and post-disaster procurement and delivery associated with dynamic response decisions in actual DRL operations. To tackle issues triggered by shortage and surplus of multi-class relief resources, a flexible option contract is adopted to purchase relief items from suppliers. To measure the risk of demand ambiguity, a worst-case mean-quantile-deviation criterion is introduced to reflect the decision-maker’s risk-averse attitude. To handle the ambiguity in the probability distribution of demand, a novel two-stage distributionally robust optimization (DRO) model is developed for the addressed DRL problem. The proposed DRO model can be transformed into equivalent mixed-integer linear programs when the ambiguity sets incorporate all distributions within $L_1$-norm and joint $L_1$- and $L_{\infty }$-norms from a nominal (reference) distribution. A computational study of earthquakes in Iran is conducted to illustrate the applicability of the proposed DRO model to real-world problems. The experimental results demonstrate that our proposed DRO model has superior out-of-sample performance and can mitigate the effect of Optimization Bias compared to the traditional stochastic programming model. Some managerial insights regarding the proposed approach are provided based on numerical results.

救灾物流 (DRL) 为自然灾害（例如地震和火山爆发）的受害者提供充足的救灾物资。本研究明确考虑了与静态准备决策相对应的供应商选择和库存预先定位，以及与实际 DRL 操作中的动态响应决策相关的灾后采购和交付。针对多类救灾资源短缺和过剩引发的问题，采用灵活的期权合同向供应商采购救灾物资。为了衡量需求模糊的风险，引入了最坏情况的平均分位数偏差准则来反映决策者的风险规避态度。为了处理需求概率分布的歧义，针对所解决的 DRL 问题开发了一种新颖的两阶段分布稳健优化 (DRO) 模型。当歧义集包含所有分布时，所提出的 DRO 模型可以转化为等效的混合整数线性规划${\mathrm{大号}}_{\mathrm{1个}}$-规范和联合${\mathrm{大号}}_{\mathrm{1个}}$- 和${\mathrm{大号}}_{\infty }$-来自名义（参考）分布的规范。对伊朗地震进行了计算研究，以说明所提出的 DRO 模型对现实世界问题的适用性。实验结果表明，与传统的随机规划模型相比，我们提出的 DRO 模型具有优越的样本外性能，并且可以减轻优化偏差的影响。基于数值结果提供了有关所提出方法的一些管理见解。