Scheduling with Fixed Maintenance, Shared Resources and Nonlinear Feedrate Constraints: A Mine Planning Case Study

  • Christina N. Burt
  • Nir Lipovetzky
  • Adrian R. Pearce
  • Peter J. Stuckey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9075)

Abstract

Given a short term mining plan, the task for an operational mine planner is to determine how the equipment in the mine should be used each day. That is, how crushers, loaders and trucks should be used to realise the short term plan. It is important to achieve both grade targets (by blending) and maximise the utilisation (i.e., throughput) of the mine. The resulting problem is a non-linear scheduling problem with maintenance constraints, blending and shared resources. In this paper, we decompose this problem into two parts: the blending, and the utilisation problems. We then focus our attention on the utilisation problem. We examine how to model and solve it using alternative approaches: specifically, constraint programming, MIQP and MINLP. We provide a repair heuristic based on an outer-approximation, and empirically demonstrate its effectiveness for solving the real-world instances of operational mine planning obtained from our industry partner.

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References

  1. 1.
    Aggoune, R.: Minimizing the makespan for the flow shop scheduling problem with availability constraints. European Journal of Operational Research 153(3), 534–543 (2004)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Bley, A., Boland, N., Froyland, G., Zuckerberg, M.: Solving mixed integer nonlinear programming problems for mine production planning with stockpiling. Tech. rep., University of New South Wales (2012). http://web.maths.unsw.edu.au/ froyland/bbfz.pdf
  3. 3.
    Burt, C.N., Lipovetzky, N., Pearce, A.R., Stuckey, P.J.: Approximate uni-directional Benders decomposition. In: Proceedings of PlanSOpt-15 Workshop on Planning, Search and Optimization AAAI-15 (2015)Google Scholar
  4. 4.
    Coal Shovel Clip Art: Accessed: 17/11/2014 (2014). gofreedownload.net/
  5. 5.
    Fox, M., Long, D.: PDDL2. 1: An extension to PDDL for expressing temporal planning domains. Journal of Artificial Intelligence Research 20, 61–124 (2003)MATHGoogle Scholar
  6. 6.
    Gecode Team: Gecode: Generic constraint development environment (2006). http://www.gecode.org
  7. 7.
    HSL: a collection of Fortran codes for large scale scientific computation (2013). http://www.hsl.rl.ac.uk
  8. 8.
    Immersive Technologies: Accessed: 17/11/2014 (2014). http://www.immersivetechnologies.com/
  9. 9.
    Jamshidi, R., Esfahani, M.M.S.: Reliability-based maintenance and job scheduling for identical parallel machines. International Journal of Production Research 53(4), 1216–1227 (2015)CrossRefGoogle Scholar
  10. 10.
    Khayat, G.E., Langevin, A., Riopel, D.: Integrated production and material handling scheduling using mathematical programming and constraint programming. In: Proceedings CPAIOR (2003)Google Scholar
  11. 11.
    Kubzin, M.A., Strusevich, V.A.: Planning machine maintenance in two-machine shop scheduling. Operations Research 54(4), 789–800 (2006)CrossRefMATHGoogle Scholar
  12. 12.
    Lipovetzky, N., Burt, C.N., Pearce, A.R., Stuckey, P.J.: Planning for mining operations with time and resource constraints. In: Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling, ICAPS 2014 (2014)Google Scholar
  13. 13.
    Moradi, E., Ghoma, S.F., Zandieh, M.: Bi-objective optimization research on integrated fixed time interval preventive maintenance and production for scheduling flexible job-shop problem. Expert Systems with Applications 38(6), 7169–7178 (2011)CrossRefGoogle Scholar
  14. 14.
    Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.R.: MiniZinc: towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  15. 15.
    Sbihi, M., Varnier, C.: Single-machine scheduling with periodic and flexible periodic maintenance to minimize maximum tardiness. Computers & Industrial Engineering 55, 830–840 (2008)CrossRefGoogle Scholar
  16. 16.
    Ta, C., Kresta, J., Forbes, J., Marquez, H.: A stochastic optimization approach to mine truck allocation. International Journal of Surface Mining 19, 162–175 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Christina N. Burt
    • 1
  • Nir Lipovetzky
    • 1
  • Adrian R. Pearce
    • 1
  • Peter J. Stuckey
    • 1
  1. 1.Department of Computing and Information SystemsThe University of MelbourneParkvilleAustralia

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