A Constraint Programming approach to solve the clustering problem in open-pit mine planning

Since the open-pit precedence-constrained production scheduling problem is an NP-hard problem, solving it is always a challenging task, especially from a long-term perspective because a mineral deposit containing millions of blocks would require several million precedence arcs as constraints, making the solution time grow exponentially and making a direct approach unfeasible. Therefore, different strategies have been employed since the 1960s to reduce the size of this problem, such as determining the ultimate pit limit, subdividing it into phases, segmenting the production scheduling problem into long-, mid-, and short-term plans, as well as aggregating blocks into clusters, thus significantly reducing the number of precedence arcs. Different modeling and clustering strategies have already been employed in an attempt to reduce the size of the mine sequencing problem, such as layer modeling, re-blocking, bench-phase clustering, or polygon (mining cut) clustering based on a similarity function. The mining cut clustering problem has been solved lately by machine learning and heuristics techniques, and this approach can also introduce operational constraints to the mine sequencing problem, such as equipment size, minimum pit width, and preferential mining direction. In this study, we propose a mining cut clustering model based on Mixed Integer Linear Programming (MILP). Then we solve it by an exact approach and by Constraint Programming (CP), analyzing the strengths and weaknesses of the Constraint Optimization Problem (COP) and Constraint Satisfaction Problem (CSP) techniques. Numerical experiments were carried out on the Bench 15 of the Newmanl dataset, demonstrating the superiority of the COP approach.