Evaluating the Effect of Block Aggregation Approach on Ultimate Pit Limit Characteristics Using the Linear Programming Model

نوع مقاله : مقاله پژوهشی

نویسندگان

1 Dept. of Mining Engineering, Sahand University of Technology, Tabriz, Iran

2 Dept. of Mining, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

چکیده

An open-pit mine production planning begins with determining the ultimate pit limit of an open-pit mine. The ultimate pit limit solver selects blocks whose total economic value is maximum while meeting the slope constraints. In other words, a group of blocks that maximize a selected parameter, such as profit, metal content, or net present value, is considered in determining the ultimate pit limit. Also, the ultimate pit limit is designed to select the waste dump location, surface facilities, extractable reserves, and the amount of waste removal. The production planning problem in large-scale open-pit mines is referred to as an NP-hard problem because it cannot be solved in a reasonable computational time. To solve this, various methods, including aggregation methods, have been proposed to reduce the size of the issue. In this paper, to evaluate the efficiency of the block aggregation technique based on the pit values and computational times, at first, the heuristic Tabesh-AskariNasab aggregation algorithm was applied to the block models with 2400 and 11400 blocks. Then the ultimate pit limit based on the original block model and reconstructed block models were determined using the linear programming model. Comparing the results in both block models indicates that the block aggregation approach considerably decreased computational time while generating near-optimal pit values. These results are more critical in large-scale production planning problems, exactly in open pit mine scheduling. Furthermore, the slope of pit walls was decreased by increasing the size of clusters, and the stripping ratio increased in both block models.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Evaluating the Effect of Block Aggregation Approach on Ultimate Pit Limit Characteristics Using the Linear Programming Model

نویسندگان [English]

  • Nooshin Azadi 1
  • Hossein Mirzaei Nasirabad 1
  • Amin Mousavi 2
1 Dept. of Mining Engineering, Sahand University of Technology, Tabriz, Iran
2 Dept. of Mining, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
چکیده [English]

An open-pit mine production planning begins with determining the ultimate pit limit of an open-pit mine. The ultimate pit limit solver selects blocks whose total economic value is maximum while meeting the slope constraints. In other words, a group of blocks that maximize a selected parameter, such as profit, metal content, or net present value, is considered in determining the ultimate pit limit. Also, the ultimate pit limit is designed to select the waste dump location, surface facilities, extractable reserves, and the amount of waste removal. The production planning problem in large-scale open-pit mines is referred to as an NP-hard problem because it cannot be solved in a reasonable computational time. To solve this, various methods, including aggregation methods, have been proposed to reduce the size of the issue. In this paper, to evaluate the efficiency of the block aggregation technique based on the pit values and computational times, at first, the heuristic Tabesh-AskariNasab aggregation algorithm was applied to the block models with 2400 and 11400 blocks. Then the ultimate pit limit based on the original block model and reconstructed block models were determined using the linear programming model. Comparing the results in both block models indicates that the block aggregation approach considerably decreased computational time while generating near-optimal pit values. These results are more critical in large-scale production planning problems, exactly in open pit mine scheduling. Furthermore, the slope of pit walls was decreased by increasing the size of clusters, and the stripping ratio increased in both block models.

کلیدواژه‌ها [English]

  • Open-Pit Mine Production Planning
  • Ultimate Pit Limit
  • Block Aggregation
  • Linear Programming Model
  • Block Model
[1]          Mwangi, A., et al.,(2020). Ultimate Pit Limit Optimization Methods in Open Pit Mines: A Review. Journal of Mining Science. 56(4): p. 588-602.
[2]          Osanloo, M., J. Gholamnejad, and B. Karimi,(2008). Long-term open pit mine production planning: a review of models and algorithms. International Journal of Mining, Reclamation and Environment. 22(1): p. 3-35.
[3]          Lerchs, H.,(1965). Optimum design of open-pit mines. Trans CIM. 68: p. 17-24.
[4]          Frimpong, S. and P.K. Achireko,(2007). The MCS/MFNN algorithm for open pit optimization. International Journal of Surface Mining, Reclamation and Environment. 11(1): p. 45-52.
[5]          Askari-Nasab, H. and K. Awuah-Offei,(2009). Open pit optimisation using discounted economic block values. Mining Technology. 118(1): p. 1-12.
[6]          Sayadi, A.R., N. Fathianpour, and A.A. Mousavi,(2011). Open pit optimization in 3D using a new artificial neural network. Archives of Mining Sciences. 56(3): p. 389-403.
[7]          Khodayari, A.A.,(2013). A New Algorithm for Determining Ultimate Pit Limits Based on Network Optimization. International Journal of Mining and Geo-Engineering. 47(2): p. 129-137.
[8]          Esmaeil, R., et al.,( 2018). Optimized algorithm in mine production planning, mined material destination, and ultimate pit limit. Journal of Central South University. 25(6): p. 1475-1488.
[9]          Gershon, M.E., (1983). Optimal mine production scheduling: evaluation of large scale mathematical programming approaches. International journal of mining engineering. 1(4): p. 315-329.
[10]        Ramazan, S., (2001). Open pit mine scheduling based on fundamental tree algorithm. PhD thesis.
[11]        Ramazan, S.,(2007). The new Fundamental Tree Algorithm for production scheduling of open pit mines. European Journal of Operational Research. 177(2): p. 1153-1166.
[12]        Ramazan, S., K. Dagdelen, and T. Johnson,(2005). Fundamental tree algorithm in optimising production scheduling for open pit mine design. Mining Technology. 114(1): p. 45-54.
[13]        Askari-Nasab, H., K. Awuah-Offei, and H. Eivazy,(2010). Large-scale open pit production scheduling using mixed integer linear programming. International Journal of Mining and Mineral Engineering. 2(3): p. 185-214.
[14]        Tabesh, M. and H. Askari-Nasab, (2011). Two-stage clustering algorithm for block aggregation in open pit mines. Mining Technology. 120(3): p. 158-169.
[15]        Ren, H. and E. Topal,(2014). Using Clustering Methods for Open Pit Mine Production Planning. Mining Education Australia. 3: p. 45-49.
[16]        Jélvez, E., et al.,(2016). Aggregation heuristic for the open-pit block scheduling problem. European Journal of Operational Research. 249(3): p. 1169-1177.
[17]        Mai, N.L., E. Topalt, and O. Ertent,(2018). A new open-pit mine planning optimization method using block aggregation and integer programming. Journal of the Southern African Institute of Mining and Metallurgy. 118(7).
[18]        Lotfian, R., J. Gholamnejad, and Y. Mirzaeian Lardkeyvan, (2020). Effective solution of the long-term open pit production planning problem using block clustering. Engineering Optimization, p. 1-16.
[19]        Tabesh, M., (2015). Aggregation and Mathematical Programming for Long-Term Open Pit Production Planning. University of Alberta.
[20]        Hochbaum, D.S. and A. Chen, (2000). Performance analysis and best implementations of old and new algorithms for the open-pit mining problem. Operations Research. 48(6): p. 894-914.
[21]        Espinoza, D., et al.,(2013). MineLib: a library of open pit mining problems. Annals of Operations Research. 206(1): p. 93-114.
[22]        Marcos Dósea a, L.S.a., Maria A. Silva b, Sócrates C.H. (2008). Cavalcanti Adaptive Mean-Linkage with Penalty: A new algorithm for cluster analysis. Chemometrics and Intelligent Laboratory Systems. 94: p. 8.