Skip to main content
SpringerLink
Log in

Exact algorithms for production planning in mining considering the use of stockpiles and sequencing of power shovels in open-pit mines

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

Chile is the world’s leading producer of copper, with a market share of 26.8% and accounting for approximately 10% of the gross domestic product. Given the importance of this industrial sector in the country, mine planning is a fundamental tool for achieving strategic, tactical and operational goals. This paper proposes methods to solve the problem of scheduling production in mining, considering the storage and sequencing of power shovels in open-pit mines. The first problem is tactical and operational and seeks to determine the extraction period and destination of each block. The second problem is of an operational nature and consists of defining the optimal sequence of block extraction, considering the mining power shovels. To solve both problems, two mixed integer linear programming models have been proposed and tested in real and random structured instances. The objective function of the proposed models is to maximize the net present value (NPV) of scheduling and maximize the work efficiency of the power shovels in the extraction. The proposed models have been implemented in AMPL and have been solved through the IBM CPLEX and Gurobi solvers. The results show the efficiency of the proposed models, demonstrating that including the storage option in the production schedule increases the operational NPV.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Source Adapted from Saavedra-Rosas et al. (2016)

Fig. 2

Source Owner

Fig. 3

Source Owner

Fig. 4

Source Owner

Fig. 5

Source Owner

Fig. 6

Source Owner

Fig. 7

Source Owner

Fig. 8

Source Owner

Fig. 9

Source Owner

Fig. 10

Source Owner

Fig. 11

Source Owner

Similar content being viewed by others

References

  • Asad MWA (2005) Cutoff grade optimization algorithm with stockpiling option for open pit mining operations of two economic minerals. Int J Surf Min Reclam Environ 19(3):176–187. https://doi.org/10.1080/13895260500258661

    Article  Google Scholar 

  • Asad MWA, Dimitrakopoulos R (2013) Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand. J Oper Res Soc 64(2):185–197. https://doi.org/10.1057/jors.2012.26

    Article  Google Scholar 

  • Bakhtavar E, Mahmoudi H (2020) Development of a scenario-based robust model for the optimal truck-shovel allocation in open-pit mining. Comput Oper Res 115(104539):1–10

    Google Scholar 

  • Bernal J, Escobar JW, Paz JC, Linfati R, Gatica G (2018) A probabilistic granular tabu search for the distance constrained capacitated vehicle routing problem. Int J Ind Syst Eng 29(4):453–477

    Google Scholar 

  • Bley A, Boland N, Froyland G, Zuckerberg M (2012). Solving mixed integer nonlinear programming for mine production planning with stockpiling. From Optimization Online: http://www.optimization-online.org/DB_HTML/2012/11/3674.html

  • Caccetta L, Hill SP (2003) An application of branch and cut to open pit mine scheduling. J Global Optim 27(2–3):349–365. https://doi.org/10.1023/A:1024835022186

    Article  Google Scholar 

  • Chatterjee S, Sethi MR, Asad MWA (2016) Production phase and ultimate pit limit design under commodity price uncertainty. Eur J Oper Res 248(2):658–667. https://doi.org/10.1016/j.ejor.2015.07.012

    Article  Google Scholar 

  • Chicoisne R, Espinoza D, Goycoolea M, Moreno E, Rubio E (2012) A new algorithm for the open-pit mine production scheduling problem. Oper Res 60(3):517–528. https://doi.org/10.1287/opre.1120.1050

    Article  Google Scholar 

  • Epstein R, Goic M, Weintraub A, Catalán J, Santibáñez P, Urrutia R, Caro F (2012) Optimizing long-term production plans in underground and open-pit copper mines. Oper Res 60(1):4–17. https://doi.org/10.1287/opre.1110.1003

    Article  Google Scholar 

  • Escobar JW, Linfati R, Toth P (2013) A two-phase hybrid heuristic algorithm for the capacitated location-routing problem. Comput Oper Res 40(1):70–79

    Article  Google Scholar 

  • Escobar JW, Linfati R, Toth P, Baldoquin MG (2014a) A hybrid granular tabu search algorithm for the multi-depot vehicle routing problem. J Heuristics 20(5):483–509

    Article  Google Scholar 

  • Escobar JW, Linfati R, Baldoquin MG, Toth P (2014b) A granular variable Tabu neighborhood search for the capacitated location-routing problem. Transp Res Part B Methodol 67:344–356

    Article  Google Scholar 

  • Espinoza D, Goycoolea M, Moreno E, Newman A (2013) Minelib: a library of open pit mining problems. Ann Oper Res 206(1):93–114. https://doi.org/10.1007/s10479-012-1258-3

    Article  Google Scholar 

  • Gholamnejad, J., Bafghi, A. Y. (2008). A practical short-term production scheduling model for open pit mines. 8th International Scientific Conference-SGEM2008, 333–338

  • Gy P (1999) Optimizing the operational strategy of a mine-metallurgy or quarry-cement works complex. Can Metall Q 38(3):157–163. https://doi.org/10.1179/cmq.1999.38.3.157

    Article  Google Scholar 

  • Jélvez E, Morales N, Nancel-Penard P, Peypouquet J, Reyes P (2016) Aggregation heuristic for the open-pit block scheduling problem. Eur J Oper Res 249(3):1169–1177. https://doi.org/10.1016/j.ejor.2015.10.044

    Article  Google Scholar 

  • Johnson TB (1968) Optimum open pit mine production scheduling (No. ORC-68–11). California Univ Berkeley Operations Research Center, California

    Book  Google Scholar 

  • Kumral M (2006) Bed blending design incorporating multiple regression modelling and genetic algorithms. J South Afr Inst Min Metall 106(3):229–236

    Google Scholar 

  • Lane KF (1988) The economic definition of ore: cut-off grades in theory and practice. Mining Journal Books, London

    Google Scholar 

  • Laurich R, Kennedy B (1990) Planning and design of surface mines. Surf Min 5:465–469

    Google Scholar 

  • Lerchs H, Grossman F (1965) Optimum design of open-pit mines. Trans CIM 58:47–54

    Google Scholar 

  • Liu SQ, Kozan E (2016) New graph-based algorithms to efficiently solve large scale open pit mining optimisation problems. Expert Syst Appl 43:59–65. https://doi.org/10.1016/j.eswa.2015.08.044

    Article  Google Scholar 

  • Miller CE, Tucker AW, Zemin RA (1960) Integer programming formulation of traveling salesman problems. J Assoc Comput Mach 7(4):326–329

    Article  Google Scholar 

  • Moreno E, Rezakhah M, Newman A, Ferreira F (2017) Linear models for stockpiling in open-pit mine production scheduling problems. Eur J Oper Res 260(1):212–221. https://doi.org/10.1016/j.ejor.2016.12.014

    Article  Google Scholar 

  • Mousavi A, Kozan E, Liu SQ (2016) Open-pit block sequencing optimization: a mathematical model and solution technique. Eng Opt 40(3):1932–1950. https://doi.org/10.1080/0305215X.2016.1142080

    Article  Google Scholar 

  • Newman AM, Rubio E, Caro R, Weintraub A, Eurek K (2010) A review of operations research in mine planning. Interfaces 40(3):222–245. https://doi.org/10.1287/inte.1090.0492

    Article  Google Scholar 

  • Paz J, Orozco J, Salinas J, Buriticá N, Escobar J (2015) Redesign of a supply network by considering stochastic demand. Int J Ind Eng Comput 6(4):521–528

    Google Scholar 

  • Polo A, Peña N, Muñoz D, Cañón A, Escobar JW (2019) Robust design of a closed-loop supply chain under uncertainty conditions integrating financial criteria. Omega 88:110–132

    Article  Google Scholar 

  • Rezakhah M (2017). Open mit mine planing with stockpiling. Doctoral Dissertation, Colorado School of Mines

  • Robinson GK (2004) How much would a blending stockpile reduce variation? Chemom Intell Lab Syst 74(1):121–133

    Article  Google Scholar 

  • Rodado D, Escobar J, García-Cáceres R, Atencio F (2017) A mathematical model for the product mixing and lot-sizing problem by considering stochastic demand. Int J Ind Eng Comput 8(2):237–250

    Google Scholar 

  • Saavedra-Rosas J, Jéivez E, Amaya J, Morales N (2016) Optimizing open-pit block scheduling with exposed ore reserve. J South Afr Inst Min Metall 116(7):655–662

    Article  Google Scholar 

  • Upadhyay SP, Askari-Nasab H (2019) Dynamic shovel allocation approach to short-term production planning in open-pit mines. Int J Min Reclam Environ 33(1):1–20

    Article  Google Scholar 

Download references

Acknowledgements

This work has been partially supported by project CONICYT FONDEF IT16M10019, the research project 2060222 IF/R from Universidad del Bio-Bio, the supercomputing infrastructure of the NLHPC (ECM-02) and Universidad del Valle, Colombia. This support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. School of Industrial Engineering, Universidad del Bío-Bío, 4030000, Concepción, Chile

    César Flores-Fonseca

  2. Department of Industrial Engineering, Universidad del Bío-Bío, 4030000, Concepción, Chile

    Rodrigo Linfati

  3. Department of Accounting and Finance, Universidad del Valle, 760001, Cali, Colombia

    John Willmer Escobar

Authors
  1. César Flores-Fonseca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rodrigo Linfati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Willmer Escobar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John Willmer Escobar.

Ethics declarations

Conflict of interest

Authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Flores-Fonseca, C., Linfati, R. & Escobar, J.W. Exact algorithms for production planning in mining considering the use of stockpiles and sequencing of power shovels in open-pit mines. Oper Res Int J 22, 2529–2553 (2022). https://doi.org/10.1007/s12351-020-00618-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-020-00618-x

Keywords

Search

Navigation