New integer solution algorithm to solve open-pit mine production scheduling problems, A

Abstract

The strategic open pit mine production scheduling problem is usually formulated as a large-scale integer programming problem that is very difficult to solve. The life of mine production scheduling problem is currently modeled on a block by block basis in order to decide which blocks should be extracted, when they should be extracted, and what to do with the blocks once they are extracted. Due to the nature of the problem, the decisions on whether or not to mine an individual block should be addressed in a binary context. However, the large size of some real instances (3–10 million blocks, 15–20 time periods) has made these models impossible to solve with currently available optimization solvers. To overcome this challenge, many attempts have been made to solve the problem with numerous heuristic and aggregation methods which cannot be proven to converge to the true optimal solution. On the other hand, linear programming relaxation of the real sized mine planning problems can be solved to a proven optimality by applying the existing exact decomposition algorithms. However, the solution obtained from the LP relaxation problems may result in fractional blocks being mined which cannot be implemented practically. A novel integer solution algorithm is developed in this thesis which can solve the mine production scheduling problems modeled with multi capacities, grade blending, grade uncertainty, stockpiles, variable pit slopes, multi destinations and truck hours. It should be emphasized that the blocks will not have any pre-determined destinations based on grades, cycle times, material type or some other criteria since the best destination selection per block will be done automatically during the optimization process to maximize the NPV, in other words the dynamic cutoff concept is employed. Presently there is no known algorithm, either commercially available or presented in the literature, that 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. Therefore, the solution algorithm that can generate an optimal integer solution to a mine production scheduling problem that has never been solved will be a milestone in operations research. Moreover, a new cone pattern generation scheme is developed in order to integrate the variable pit slope angles based on complex geotechnical zones and multiple azimuths with any size block dimensions to the new integer solution algorithm.