In humanitarian supply chains, there is a need to consider how to distribute the limited relief supplies that have not been prepared sufficiently to each shelter. Different from commercial supply chains that prioritize cost reduction, in humanitarian supply chains, it is important to consider not only reducing the distribution cost but also how to deliver goods quickly to satisfy the demands of shelters. Three metrics have been proposed for humanitarian supply chains: efficiency, equity, and efficacy. The objective of this paper is to define the metric of efficacy to minimize distribution time to each shelter considering the relief goods arrival. Under the situation after the disaster, to supply relief goods agilely and fairly, it is necessary to take account the weight of each metric adequately. We formulate a multi-objective mathematical model by the multiple metrics and carry out the optimization by using the model. The results show that the proposed multi-objective model is very promising in dealing with complicated humanitarian supply chains. Additionally, we show the deviation between the result of each metric and the multi-objective evaluation.