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On March 11, 2011, the Great East Japan Earthquake (GEJE) attacked the NorthEastern Parts of Japan and the scale of the earthquake was the largest in recorded history in Japan. Despite Japan's great efforts in this disaster relief operation, relief goods did not reach the affected area. Managing disaster relief operations in the disaster situation like the GEJE is complex. Therefore, it became clear that the logistics system in the situation of a disaster had a lot of problems. In disaster situation like the GEJE, organizing the relief supply operations to afflicted people can be efficiently conducted. There are many disaster relief operations issues that need to be considered and resolved through logistics. Especially, it is very important that the distribution to the many victims is conducted equally. In this study, from the point of flow of distribution relief goods to the victims, we focus on the relationship between the shelter and the secondary collection point. The purpose of this study is to propose a logistics model that achieves the fair distribution for the many victims from the view point of the difference of the arrival time. In the earthquake, there were many routes that were unavailable and there was a limit to the number of cars that was available because of shortage of fuel. While considering these phenomena, we propose the logistics model that minimizes the range of the delivery time that the victims received relief goods from the transportation vehicles. Finally, in order to confirm the effectiveness of the proposed model, we perform the numerical experiments using the data of the Great East Japan Earthquake and the efficiency of the model is confirmed.