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

• Published in: Operational research Vol. 14; no. 1; pp. 1 - 10
• Main Authors: Amankwah, Henry, Larsson, Torbjörn, Textorius, Björn
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014; Springer Nature B.V
• Subjects: Anniversaries; Business and Management; Computational Intelligence; Graphs; Integer programming; Management Science; MATEMATIK; Mathematical models; MATHEMATICS; Mines; Mining; Operational research; Operations Research; Operations Research/Decision Theory; Optimization; Original Paper; Precedence constraints; Scheduling; Studies; Temporal logic; Integer programming; Maximal closure; 90C10; 90C35; Lagrangean relaxation; 90C90; Scheduling; Open-pit mining; Maximum flow
• ISSN: 1109-2858; 1866-1505; 1866-1505
• DOI: 10.1007/s12351-013-0140-7

We consider the problem of finding an optimal mining sequence for an open pit during a number of time periods subject to only spatial and temporal precedence constraints. This problem is of interest because such constraints are generic to any open-pit scheduling problem and, in particular, because it arises as a Lagrangean relaxation of an open-pit scheduling problem. We show that this multi-period open-pit mining problem can be solved as a maximum flow problem in a time-expanded mine graph. Further, the minimum cut in this graph will define an optimal sequence of pits. This result extends a well-known result of J.-C. Picard from 1976 for the open-pit mine design problem, that is, the single-period case, to the case of multiple time periods.