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Short- and medium-term optimization of underground mine planning using constraint programming

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Abstract

In the past few years, the mining industry has seen a lot of operational changes. Digitalization and automation of many processes have paved the way for an increase in its general productivity. In keeping with this trend, this article presents a novel approach for optimizing underground mine scheduling for the short- and medium-term. This problem is similar to the Resource-Constrained Project Scheduling Problem, with the difference that all task completions are optional. The model uses Constraint Programming principles to maximize the Net Present Value of a mining project. It plans work shifts for up to a year in advance, considering specialized equipment, rock support and operational constraints. This is the first published paper using optional variables to model optional tasks in a real-life application. Results from its applications to datasets based on a Canadian gold mine demonstrate its ability to find optimal solutions in a reasonable time. A comparison with an equivalent Mixed Integer Programing model proves that the Constraint Programming approach offers clear gains in terms of computability and readability of the constraints.

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References

  1. Artigues, C. (2017). On the strength of time-indexed formulations for the resource-constrained project scheduling problem. Operations Research Letters, 45(2), 154–159.

    Article  MathSciNet  MATH  Google Scholar 

  2. Astrand, M., Johansson, M., & Zanarini, A. (2018). Fleet scheduling in underground mines using constraint programming. In International conference on the integration of constraint programming, artificial intelligence, and operations research (Vol. 10848 pp. 605–613). https://doi.org/10.1007/978-3-319-93031-2

  3. Bienstock, D., & Zuckerberg, M. (2010). Solving LP relaxations of large-scale precedence constrained problems, pp. 1–14, Springer.

  4. Bjørndal, T., Herrero, I., Newman, A., Romero, C., & Weintraub, A. (2012). Operations research in the natural resource industry. International Transactions in Operational Research, 19(1-2), 39–62. https://doi.org/10.1111/j.1475-3995.2011.00800.x

    Article  MathSciNet  Google Scholar 

  5. Bley, A., & Terblanche, S.F. (2015). An improved formulation of the underground mine scheduling optimization problem when considering selective mining. Optimization Online, 31(1), 1–16. https://doi.org/10.5784/31-1-422

    Article  Google Scholar 

  6. Campeau, L.P., Gamache, M., & Martinelli, R. (2022). Integrated optimisation of short-and medium-term planning in underground mines. International Journal of Mining, Reclamation and Environment, 36(4), 235–253.

    Article  Google Scholar 

  7. Campeau, L.P., & Michel, G. (2020). Short-term planning optimization model for underground mines. Computer & Operations Research, 115, 104642.

    Article  MathSciNet  MATH  Google Scholar 

  8. Carpentier, S., Gamache, M., & Dimitrakopoulos, R. (2016). Underground long-term mine production scheduling with integrated geological risk management. Mining Technology, 125 (2), 93–102. https://doi.org/10.1179/1743286315Y.0000000026

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Schutt, A., Chu, G., Stuckey, P. J., & Wallace, M. G. (2012). Maximising the net present value for resource-constrained project scheduling. International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming, pp. 362–378. Springer.

  11. Hartmann, S., & Briskorn, D. (2010). A survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research, 207(1), 1–14. https://doi.org/10.1016/j.ejor.2009.11.005

    Article  MathSciNet  MATH  Google Scholar 

  12. Martinelli, R., Collard, J., & Gamache, M. (2020). Strategic planning of an underground mine with variable cut-off grades. Optimization and Engineering, 21(3), 803–849. Springer.

    Article  Google Scholar 

  13. Kreter, S., Schutt, A., & Stuckey, P.J. (2017). Using constraint programming for solving RCPSP/max-cal. Constraints, 22(3), 432–462. https://doi.org/10.1007/s10601-016-9266-6

    Article  MathSciNet  MATH  Google Scholar 

  14. Laborie, P., Rogerie, J., Shaw, P., & Vilím, P. (2018). IBM ILOG CP optimizer for scheduling: 20+ years of scheduling with constraints at IBM/ILOG. Constraints, 23(2), 210–250. https://doi.org/10.1007/s10601-018-9281-x

    Article  MathSciNet  MATH  Google Scholar 

  15. Little, J., Knights, P., & Topal, E. (2013). Integrated optimization of underground mine design and scheduling. Journal of the Southern African Institute of Mining and Metallurgy, 113(10), 775–785.

    Google Scholar 

  16. Lustig, I.J., & Puget, J.F. (2001). Program does not equal program: Constraint programming and its relationship to mathematical programming. Interfaces, 31(6), 29–53.

    Article  Google Scholar 

  17. Martinelli, R., Collard, J., & Gamache, M. (2020). Strategic planning of an underground mine with variable cut-off grades. Optimization and Engineering 21(3), pp. 803–849. Springer.

  18. Martinez, M.A., & Newman, A.M. (2011). A solution approach for optimizing long- and short-term production scheduling at LKAB’s Kiruna mine. European Journal of Operational Research, 211(1), 184–197. https://doi.org/10.1016/j.ejor.2010.12.008

    Article  MATH  Google Scholar 

  19. Montiel, L., Dimitrakopoulos, R., & Kawahata, K. (2016). Globally optimising open-pit and underground mining operations under geological uncertainty. Mining Technology, 125(1), 2–14. https://doi.org/10.1179/1743286315Y.0000000027

    Article  Google Scholar 

  20. Muñoz, G., Espinoza, D., Goycoolea, M., Moreno, E., Queyranne, M., & Letelier, O.R. (2018). A study of the Bienstock–Zuckerberg algorithm: applications in mining and resource constrained project scheduling Vol. 69. Springer. https://doi.org/10.1007/s10589-017-9946-1

    MATH  Google Scholar 

  21. Musingwini, C. (2016). Presidential address: Optimization in underground mine planning-developments and opportunities. Journal of the Southern African Institute of Mining and Metallurgy. https://doi.org/10.17159/2411-9717/2016/v116n9a1

  22. Nehring, M., Topal, E., Kizil, M., & Knights, P. (2012). Integrated short- and medium-term underground mine production scheduling. Journal of the Southern African Institute of Mining and Metallurgy, 112(5), 365–378.

    Google Scholar 

  23. Newman, A.M., 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 

  24. O’Sullivan, D., & Newman, A. (2015). Optimization-based heuristics for underground mine scheduling. European Journal of Operational Research, 241(1), 248–259. https://doi.org/10.1016/j.ejor.2014.08.020

    Article  MathSciNet  MATH  Google Scholar 

  25. O’Sullivan, D., Brickey, A., & Newman, A. (2015). Is open pit production scheduling ’easier’ than its underground counterpart? Mining Engineering, 67(4), 68–73.

    Google Scholar 

  26. Torres, V.F.N., Nader, B., Ortiz, C.E.A., Souza, F.R., Burgarelli, H.R., Soares chaves, L., Carvalho, L.A., Renata Câmara, T., Zanetti, E., & Galery, R. (2018). Classical and stochastic mine planning techniques, state of the art and trends. Mining, 71(2), 289–297.

    Google Scholar 

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Authors and Affiliations

  1. GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Québec, H3C 3A7, Canada

    Louis-Pierre Campeau & Michel Gamache

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  1. Louis-Pierre Campeau
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  2. Michel Gamache
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Correspondence to Louis-Pierre Campeau.

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This research was funded with the Discovery Grant no. RGPIN-06402-2016 from The Natural Sciences and Engineering Research Council of Canada (NSERC)

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Campeau, LP., Gamache, M. Short- and medium-term optimization of underground mine planning using constraint programming. Constraints 27, 414–431 (2022). https://doi.org/10.1007/s10601-022-09337-w

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