Abstarct: Natural disasters, such as earthquakes, tsunamis and hurricanes, cause tremendous harm each year. In order to reduce casualties and economic losses during the response phase, rescue units must be allocated and scheduled efficiently. As this problem is one of the key issues in emergency response and has been addressed only rarely in literature, this paper develops a corresponding decision support model that minimizes the sum of completion times of incidents weighted by their severity. The presented problem is a generalization of the parallel-machine scheduling problem with unrelated machines, Since we deal with uncertain data baxsed, robust optimization model is also provided. Then Epsilon constraint method is used to solve the bi objective model and finally the most optimal allocation pattern of rescue teams to the incidents (TBS) by any objective function is identified.