Modeling Long-Term Production Scheduling Problem and Its Solution Using a Bat Meta-heuristic Method

  • Ehsan MoosaviEmail author
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


The long-term production scheduling problem, in which a schedule must obey physical constraints and operational constraints between pairs of activities, is one of the most studied scheduling problems. An important variation of this problem is to find a schedule which maximizes the net present value. Since production scheduling problems are NP-hard, there is a need of improving scheduling methodologies to get good solutions. At present, the research on scheduling theory has been paid an overwhelming attention, and has made great progress. However, it is still not mature enough. Among them, the research on complexity of the scheduling problem has become a branch of applied mathematics with a strong engineering background. The mathematical model of production scheduling problem is established, and a novel improved bat algorithm (BA) is proposed. For the purpose of expressing the relationship effectively between the process and the bat population, a new method of encoding strategy based on dual flexibility degree is proposed. For the purpose of overcoming the shortcomings of the fixed parameters in the bat algorithm, the value of the inertia weight was adjusted, and a linear decreasing inertia weight strategy was proposed. This shows that the proposed algorithm is more excellent in solving the production scheduling problem, and it is an efficient scheduling algorithm.


Long-term production scheduling Expected economic loss Open pit mine Bat algorithm 


  1. 1.
    Denby, B., Schofield, D.: Open-pit design and scheduling by use of genetic algorithms. Trans. Inst. Min. Metall. Section A: Min. Technol. 103, A21–A26 (1994)Google Scholar
  2. 2.
    Denby, B., Schofield, D.: Genetic algorithms for open pit scheduling-extension into 3-dimensions. In: Proceedings of the Mine Planning and Equipment Selection Conference, MPES 1996, pp. 177–185, Sao Paulo, Brazil (1996)Google Scholar
  3. 3.
    Denby, B., Schofield, D., Surme, T.: Genetic algorithms for flexible scheduling of open pit operations. In: Proceedings of the 27th Application of Computers and Operations Research in the Mineral Industry (APCOM) 1998, London, UK, pp. 473–483 (1998)Google Scholar
  4. 4.
    Zhang, M.: Combination Genetic algorithms and topological sort to optimize open-pit mine plans. In: Proceedings of 15th Conference on Mine Planning and Equipment Selection, Torino, Italy (2006)Google Scholar
  5. 5.
    Sattarvand, J., Niemann-Delius, C.: Long-term open-pit planning by ant colony optimization. Institut für Bergbaukunde III, RWTH Aachen University (2009)Google Scholar
  6. 6.
    Sattarvand, J., Niemann-Delius, C.: A new metaheuristic algorithm for long-term open-pit production planning. Arch. Min. Sci. 58(1), 107–118 (2013)Google Scholar
  7. 7.
    Khan, A.: Long-term production scheduling of open pit mines using particle swarm and bat algorithms under grade uncertainty. J. South Afr. Inst. Min. Metall. 118, 361–368 (2018)CrossRefGoogle Scholar
  8. 8.
    Boucher, A., Dimitrakopoulos, R.: Multivariate block-support simulation of the yandi iron ore deposit. Math. Geosci. 44(4), 449–468 (2012)CrossRefGoogle Scholar
  9. 9.
    Kumral, M., Dowd, P.A.: Short-term mine production scheduling for industrial minerals using multi-objective simulated annealing. In: Proceedings of the 30th Application of Computers and Operations Research in the Mineral Industry (APCOM) 2002, Fairbanks, Alaska, USA, pp. 731–742 (2002)Google Scholar
  10. 10.
    Kumral, M., Dowd, P.A: A simulated annealing approach to mine production scheduling. J. Oper. Res. Soc. 56(8), 922–930 (2005)CrossRefGoogle Scholar
  11. 11.
    Roman, R.J.: The role of time value of money in determining an open pit mining sequence and pit limits. In: Proceedings of 12th Symposium on Application of Computers and Operations Research in the Mineral Industry (APCOM) (1974)Google Scholar
  12. 12.
    Dowd, P.A., Onur, A.H.: Optimizing open pit design and sequencing. In: Proceedings of 23rd Symposium on Application of Computers and Operations Research in the Mineral Industry (APCOM) (1992)Google Scholar
  13. 13.
    Tolwinski, B., Underwood, R.: A scheduling algorithm for open pit mines. IMA J. Math. Appl. Bus. Ind. 7(3), 247–270 (1996)Google Scholar
  14. 14.
    Tolwinski, B.: Scheduling production for open pit mines. In: Proceedings of 27th International Symposium on Application of Computers and Operations Research in the Mineral Industry (APCOM), pp. 651–662 (1998)Google Scholar
  15. 15.
    Wang, Q., Gu, X., Chu, D.: A dynamic optimization method for determining cut-off grades in underground mines. Mineral Resources Management (2008)Google Scholar
  16. 16.
    Tolwinski, B., Underwood, R.: An algorithm to estimate the optimal evolution of an open pit mine. In: Proceedings of 23rd Symposium of Application of Computers and Operations Research in the Mineral Industry (APCOM), pp. 399–409 (1992)Google Scholar
  17. 17.
    Elevli, B.: Open pit mine design and extraction sequencing by use of OR and AI concept. Int. J. Surf. Min. Reclam. Environ. 9(4), 149–453 (1995)CrossRefGoogle Scholar
  18. 18.
    Ibrahimov, M., Mohais, A., Schellenberg, S., Michalewicz, Z.: Scheduling in iron ore open-pit mining. Int. J. Adv. Manufac. Technol. 72, 1021–1037 (2014)CrossRefGoogle Scholar
  19. 19.
    Talbi, E.: Metaheuristics: From Design to Implementation. Wiley, Chichester (2009)CrossRefGoogle Scholar
  20. 20.
    Yang, X.S: A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization, vol. 284, pp. 65–74 (2010)CrossRefGoogle Scholar
  21. 21.
    Yang, X.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, London (2010)Google Scholar
  22. 22.
    Richmond, A.J.: Maximum profitability with minimum risk and effort. Application of Computers and Operations Research in the Mineral Industry, pp. 45–50 (2001)Google Scholar
  23. 23.
    Moosavi, E., Gholamnejad, J.: Optimal extraction sequence modeling for open pit mining operation considering the dynamic cutoff grade. J. Min. Sci. 52(5), 956–964 (2016)CrossRefGoogle Scholar
  24. 24.
    Ramazan, S., Dimitrakopoulos, R.: Stochastic optimization of long-term production scheduling for open pit mines with a new integer programming formulation. In: Proceedings of Orebody Modelling and Strategic Mine Planning: Uncertainty and Risk Management Models. Australasian Institute of Mining and Metallurgy, Melbourne, pp. 385–392 (2004)Google Scholar
  25. 25.
    Afrabandpey, H., Ghaffari, M., Mirzaei, A., Safayani, M.: A novel bat algorithm based on chaos for optimization tasks. In Proceedings of the Iranian Conference on Intelligent Systems (ICIS 2014), pp. 1–6. IEEE, Bam, Iran (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Petroleum and Mining Engineering, South Tehran BranchIslamic Azad UniversityTehranIran

Personalised recommendations