Open pit mine production scheduling is to specify the sequence of blocks extraction from the mine so as to obtain the highest NPV satisfying a variety of physical and economical constraints． According to production characteristics in practice，the evaluation of regularity is taken into consideration，and then an integer programming model is established． Lagrangian Ｒelaxation ( LＲ) method is proposed to solve the problem．Valid inequalities are established based on the knapsack structure of priority constraints to accelerate the algorithm without hurting the optimal solution; and then fast feasible solution strategy is constructed based on Directed Acyclic Graph structure; variable reductions are carried out to reduce the problem scale through strategies of earliest start time and latest start time． Computational results indicate that the proposed approach outperforms standard solver CPLEX in computational time． The proposed model and solution can realize the goal of regularity maintaining and profit maximizing while satisfying all production constraints