Abstract: The methods of the present disclosure can solve mine production scheduling problems modeled with multi capacities, grade blending, grade uncertainty, stockpiles, variable pit slopes, multi destinations and truck hours. In some embodiments, the methods disclosed can provide an optimal integer solution to the open pit mine production scheduling problem with capacity constraints together with lower and upper bound blending constraints. The difference between the integer feasible solution and the optimal linear solution of the same problem is called an “optimality gap”. In one example, the strength of the integer solution algorithm developed is highlighted by the ability of solving problems that have more than 7 million variables as an integer problem with an optimality gap as small as 0.01% within 5 hours 30 minutes.