A sliding time window heuristic for open pit mine block sequencing

Abstract

Abstract. The open pit mine block sequencing problem (OPBS) seeks a discrete-time production schedule that maximizes the net present value of the orebody extracted from an open-pit mine. This integer program (IP) discretizes the mine's volume into blocks, imposes precedence constraints between blocks, and limits resource consumption in each time period. We develop a "sliding time window heuristic" to solve this IP approximately. The heuristic recursively defines, solves and partially fixes an approximating model having: (i) fixed variables in early time periods, (ii) an exact submodel defined over a "window" of middle time periods, and (iii) a relaxed submodel in later time periods. The heuristic produces near-optimal solutions (typically within 2% of optimality) for model instances that standard optimization software fails to solve. Furthermore, it produces these solutions quickly, even though our OPBS model enforces standard upper-bounding constraints on resource consumption along with less standard, but important, lower-bounding constraints.

Logistic Principles Application for Managing the Extraction and Transportation of Solid Minerals

“…Logistic approach application to management of material and accompanying information, financial and service flow has been successfully implemented in various of economy sectors [1][2], including in the area of solid minerals mining [3][4][5][6].…”

A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines

“…They first use the method in [22] to generate a feasible solution, followed by an improvement integer programming-based heuristic, which is an enhanced version of that in [1]. Cullenbine et al [12] also solve a series of mixed-integer programs that have fixed variables. The authors consider, however, a variant of the MPSP incorporating lower bounds on mining and processing, which is, as noted by the authors, harder to solve than the variant where the lower bounds are omitted (i.e., the variant described in the beginning of this section and considered by Chicoisne et al [11]).…”

“…The authors consider, however, a variant of the MPSP incorporating lower bounds on mining and processing, which is, as noted by the authors, harder to solve than the variant where the lower bounds are omitted (i.e., the variant described in the beginning of this section and considered by Chicoisne et al [11]). The drawback of the recent hybrid algorithms [11,12] is that they rely on time consuming integer programming algorithms. The method in [11] can solve instances with up to five million blocks and 15 years but might require 8 h to improve the solution and cannot handle lower bound constraints.…”

“…The method in [11] can solve instances with up to five million blocks and 15 years but might require 8 h to improve the solution and cannot handle lower bound constraints. On the other hand, the method in [12] can handle lower bound constraints but has been able to tackle only instances with up to 25,000 blocks and 15 periods.…”

A maximum flow formulation of a multi-period open-pit mining problem

“…This is the process of deciding how and when to mine the blocks so as to maximize profit (typically the net present value), while obeying the wall slope and precedence constraints, as well as various mining capacity restrictions. Contributions within open-pit mine scheduling, from the view of mathematical optimization, have been given by Gershon (1983), Dagdelen and Johnson (1986), Caccetta and Hill (2003), Ramazan (2007), Rafiee and Asghari (2008), Bley et al (2010), and Cullenbine et al (2011), among others.…”