# Analyzing solutions of the openpit block sequencing problem obtained via Lagrangian techniques

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Mining Engineering
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, 2013, Vol. 65, No. 2, pp. 39-45

Lambert, W.B.; Newman, A.M.

ABSTRACT:

A common decision in openpit mining is to determine the extraction sequence of notional three-dimensional production blocks so as to maximize the net present value of the extracted orebody, while adhering to precedence and operational resource constraints. This openpit block sequencing (OPBS) problem is commonly formulated as an integer program, with binary variables representing if and when each block is extracted. In practical applications, the number of blocks can be large and the time horizon can be long; therefore, instances of this problem can be difficult to solve using the exact approach of optimization. The problem is even more challenging to solve when it includes explicit minimum operational resource constraints. Our maximum value feasible pit (*MVFP*) algorithm generates an initial integer feasible solution for OPBS problems, in which minimum operational resource constraints are strictly enforced. As an exact approach, we present a Tailored Lagrangian Relaxation (TLR), in which the selection of constraints to dualize is guided by information provided by the *MVFP* algorithm. We present results and graphics to demonstrate the utility of our techniques for instances containing up to 25,000 blocks and 10 time periods.