Abstract: The frequent occurrence of earthquakes has brought great threats to people and seriously affected economic development and social stability. To reduce the loss caused by disasters and response quickly, it is urgent to realize scientific optimization of emergency facilities location and relief material distribution with the constraints of time, space and resource. However, inadequate information and the destructiveness of emergency disasters often lead to the uncertain emergency demand. And the disasters often damage the roads and make facilities failure, which bring great risks to the distribution of the emergency relief. Therefore, it is necessary to consider the relief uncertainty and the risk of facility failure after emergency. In this paper, demand uncertainty is described by a specified interval. A robust optimization model is proposed to combine the emergency location and the routing problem using helicopters, whose objective is to minimize total transportation time and the total system costs. The risk of facility failure is solved by the robust deviation optimization and the model is solved by genetic algorithm. Finally, numerical examples from Wang's LRP problem verified the validity of the model and algorithm Comparisons of three cases indicate that the total system cost increases as the growth of the budget of uncertainty and the data variability. The results further show that the relative robust optimization method can deal with the uncertain demand effectively, and the robust deviation optimization method can avoid the risk of emergency logistics system. It provides an effective method to help post-disaster managers to determine the emergency location and delivery the relief safely, timely.

Key words: location-routing, uncertain demand, facility failure, robust optimization