TY - JOUR
T1 - A recursive time aggregation-disaggregation heuristic for the multidimensional and multiperiod precedence-constrained knapsack problem
T2 - An application to the open-pit mine block sequencing problem
AU - Nancel-Penard, Pierre
AU - Morales, Nelson
AU - Cornillier, Fabien
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/12/16
Y1 - 2022/12/16
N2 - A recursive time aggregation-disaggregation (RAD) heuristic is proposed to solve large-scale multidimensional and multiperiod precedence-constrained knapsack problems (MMPKP) in which a profit is maximized by filling the knapsack in multiple periods while satisfying minimum and maximum resource consumption constraints per period as well as precedence constraints between items. An important strategic planning application of the MMPKP in the mining industry is the well-known open-pit mine block sequencing problem (BSP). In the BSP, a mine is modeled as a three-dimensional grid of blocks to determine a block extraction sequence that maximizes the net present value while satisfying constraints on the shape of the mine and resource consumption over time. Large real-life instances of this problem are difficult to solve, particularly with lower bounds on resource consumption. The advantage of the time aggregation-disaggregation heuristic over a rolling-horizon-based time decomposition is twofold: first, the entire horizon is considered for the resource consumption from the first aggregation; and second, only two-period subproblems have to be solved. This method is applied to a well-known integer programming model and a variant thereof in which blocks can be extracted in parts over multiple periods. Tests on benchmark instances show that near-optimal solutions for both of the models can be obtained for extremely large instances with up to 2,340,142 blocks and 10 periods.
AB - A recursive time aggregation-disaggregation (RAD) heuristic is proposed to solve large-scale multidimensional and multiperiod precedence-constrained knapsack problems (MMPKP) in which a profit is maximized by filling the knapsack in multiple periods while satisfying minimum and maximum resource consumption constraints per period as well as precedence constraints between items. An important strategic planning application of the MMPKP in the mining industry is the well-known open-pit mine block sequencing problem (BSP). In the BSP, a mine is modeled as a three-dimensional grid of blocks to determine a block extraction sequence that maximizes the net present value while satisfying constraints on the shape of the mine and resource consumption over time. Large real-life instances of this problem are difficult to solve, particularly with lower bounds on resource consumption. The advantage of the time aggregation-disaggregation heuristic over a rolling-horizon-based time decomposition is twofold: first, the entire horizon is considered for the resource consumption from the first aggregation; and second, only two-period subproblems have to be solved. This method is applied to a well-known integer programming model and a variant thereof in which blocks can be extracted in parts over multiple periods. Tests on benchmark instances show that near-optimal solutions for both of the models can be obtained for extremely large instances with up to 2,340,142 blocks and 10 periods.
KW - Heuristics
KW - Integer programming
KW - Multidimensional and multiperiod precedence-constrained knapsack problem
KW - Open pit mine scheduling
KW - Time decomposition
UR - http://www.scopus.com/inward/record.url?scp=85132668946&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2022.04.005
DO - 10.1016/j.ejor.2022.04.005
M3 - Article
AN - SCOPUS:85132668946
SN - 0377-2217
VL - 303
SP - 1088
EP - 1099
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 3
ER -