Humanitarian relief food distribution problem is the pickup of the food supply from different donors and the distribution to individuals in need. The problem now becomes a meaningful work to alleviate people’s bad situations. Motivated by this prevalent steam of significant topic, we focus on the humanitarian relief problem. In this paper, we examine the equitable and effective food distribution to poor people who need food in the general poverty scenario. In the modeling process, we make a classification of the demand nodes. Then, we introduce an innovative robust goal programming model with priority factors and optimize the distribution decisions under uncertain supply and capacity characterized by an uncertainty set. Under robust optimization techniques, the solving process of our proposed robust model is discussed and depends on a parametric cone program which can be efficiently solved by the commercial software. Finally, we conduct a number of numerical experiments about the Food Bank of Central and Eastern North Carolina in America to illustrate the application of our new model. The computational results show that our model can realize the trade-off between equity and effectiveness under uncertainty for humanitarian relief problem.

人道主义救济粮食分配问题是从不同捐助者那里获取粮食供应，并分配给有需要的个人。现在，该问题已成为减轻人们的恶劣情况的有意义的工作。受到这一重要话题的热烈推动，我们将重点放在人道主义救济问题上。在本文中，我们研究了在一般贫困情景下向需要食物的穷人公平有效分配食物的情况。在建模过程中，我们对需求节点进行分类。然后，我们引入具有优先权因素的创新鲁棒目标规划模型，并在不确定供应和以不确定集为特征的产能下优化分配决策。在强大的优化技术下，讨论了我们提出的鲁棒模型的求解过程，该过程取决于可通过商业软件有效求解的参数锥程序。最后，我们对美国中北部和北卡罗来纳州的食物银行进行了许多数值实验，以说明我们新模型的应用。计算结果表明，该模型可以在人道主义救济问题不确定的情况下实现公平与有效性的权衡。