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In order to character a two-level emergency repair facility location problem, this paper proposed a 0-1 integer linear programming model which could guarantee the service quality of whole emergency repair system. And it designed two kernel search algorithms to solve the model. Based on linear programming relaxation and Lagrangian relaxation of the original model respectively, these two algorithms identified kernel problem and sub-problem, which significantly reduced the scale of the original problem. Appling these two algorithms to the solution of 56 numerical instances, the results show that the kernel search algorithm based on Lagrangian relaxation of the original problem can find better solution in reasonable computational time than MOSEK solver. It confirms the optimized solution of Lagrangian relaxation dual problem can be very helpful to solving original problem. [ABSTRACT FROM AUTHOR]