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.
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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
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
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
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
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
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
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
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
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
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
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
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
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.19184.108.40.206
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
Johnson TB (1968) Optimum open pit mine production scheduling (No. ORC-68–11). California Univ Berkeley Operations Research Center, California
Kumral M (2006) Bed blending design incorporating multiple regression modelling and genetic algorithms. J South Afr Inst Min Metall 106(3):229–236
Lane KF (1988) The economic definition of ore: cut-off grades in theory and practice. Mining Journal Books, London
Laurich R, Kennedy B (1990) Planning and design of surface mines. Surf Min 5:465–469
Lerchs H, Grossman F (1965) Optimum design of open-pit mines. Trans CIM 58:47–54
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
Miller CE, Tucker AW, Zemin RA (1960) Integer programming formulation of traveling salesman problems. J Assoc Comput Mach 7(4):326–329
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
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
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
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
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
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
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
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
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
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.
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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 (2021). https://doi.org/10.1007/s12351-020-00618-x
- Mine planning
- Production scheduling
- Power shovel sequencing
- Mixed integer linear programming
- Net present value (NPV)