IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v274y2019i1p227-239.html
   My bibliography  Save this article

Optimizing a mineral value chain with market uncertainty using benders decomposition

Author

Listed:
  • Zhang, Jian
  • Nault, Barrie R.
  • Dimitrakopoulos, Roussos G.

Abstract

A Benders decomposition-based method is developed to simultaneously optimize upstream and downstream operations of a mineral value chain. In each iteration of the proposed method, the mineral value chain optimization model is decomposed to a master problem that only includes the variables that determine the upstream mine production schedule, and a subproblem that includes all other variables that define the downstream material flow and processing plan. In order to reduce the master problem in each iteration, mining blocks representing mineral deposits are dynamically aggregated based on the dual solution of the subproblem. The production schedule obtained based on the aggregated scheduling units is then improved through a moving-window amelioration method. By observing the results of a series of numerical tests, we show that the proposed method efficiently optimizes a mineral value chain by synchronizing the upstream mine production scheduling as well as the downstream material flow and process planning. The numerical tests also show that ignoring market uncertainty results in profits being underestimated because of the underestimated value of low-grade material. To adapt to market uncertainty, the stochastic optimizer suggests greater investment to increase capacity in the processing plant and a different long-term mine production schedule.

Suggested Citation

  • Zhang, Jian & Nault, Barrie R. & Dimitrakopoulos, Roussos G., 2019. "Optimizing a mineral value chain with market uncertainty using benders decomposition," European Journal of Operational Research, Elsevier, vol. 274(1), pages 227-239.
    • Handle: RePEc:eee:ejores:v:274:y:2019:i:1:p:227-239
    DOI: 10.1016/j.ejor.2018.09.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718308294
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.09.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michelle L. Blom & Adrian R. Pearce & Peter J. Stuckey, 2016. "A Decomposition-Based Algorithm for the Scheduling of Open-Pit Networks Over Multiple Time Periods," Management Science, INFORMS, vol. 62(10), pages 3059-3084, October.
    2. Rafael Epstein & Marcel Goic & Andrés Weintraub & Jaime Catalán & Pablo Santibáñez & Rodolfo Urrutia & Raúl Cancino & Sergio Gaete & Augusto Aguayo & Felipe Caro, 2012. "Optimizing Long-Term Production Plans in Underground and Open-Pit Copper Mines," Operations Research, INFORMS, vol. 60(1), pages 4-17, February.
    3. Mariel, Katharina & Minner, Stefan, 2017. "Benders decomposition for a strategic network design problem under NAFTA local content requirements," Omega, Elsevier, vol. 68(C), pages 62-75.
    4. Keyvanshokooh, Esmaeil & Ryan, Sarah M. & Kabir, Elnaz, 2016. "Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition," European Journal of Operational Research, Elsevier, vol. 249(1), pages 76-92.
    5. Montiel, Luis & Dimitrakopoulos, Roussos, 2015. "Optimizing mining complexes with multiple processing and transportation alternatives: An uncertainty-based approach," European Journal of Operational Research, Elsevier, vol. 247(1), pages 166-178.
    6. Kergosien, Y. & Gendreau, M. & Billaut, J.-C., 2017. "A Benders decomposition-based heuristic for a production and outbound distribution scheduling problem with strict delivery constraints," European Journal of Operational Research, Elsevier, vol. 262(1), pages 287-298.
    7. Renaud Chicoisne & Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Enrique Rubio, 2012. "A New Algorithm for the Open-Pit Mine Production Scheduling Problem," Operations Research, INFORMS, vol. 60(3), pages 517-528, June.
    8. Lamghari, Amina & Dimitrakopoulos, Roussos, 2016. "Network-flow based algorithms for scheduling production in multi-processor open-pit mines accounting for metal uncertainty," European Journal of Operational Research, Elsevier, vol. 250(1), pages 273-290.
    9. Keles, Dogan & Genoese, Massimo & Möst, Dominik & Fichtner, Wolf, 2012. "Comparison of extended mean-reversion and time series models for electricity spot price simulation considering negative prices," Energy Economics, Elsevier, vol. 34(4), pages 1012-1032.
    10. Jélvez, Enrique & Morales, Nelson & Nancel-Penard, Pierre & Peypouquet, Juan & Reyes, Patricio, 2016. "Aggregation heuristic for the open-pit block scheduling problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1169-1177.
    11. Alexandra M. Newman & Enrique Rubio & Rodrigo Caro & Andrés Weintraub & Kelly Eurek, 2010. "A Review of Operations Research in Mine Planning," Interfaces, INFORMS, vol. 40(3), pages 222-245, June.
    12. Ramazan, Salih, 2007. "The new Fundamental Tree Algorithm for production scheduling of open pit mines," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1153-1166, March.
    13. Newman, Alexandra M. & Kuchta, Mark, 2007. "Using aggregation to optimize long-term production planning at an underground mine," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1205-1218, January.
    14. Dorit S. Hochbaum & Anna Chen, 2000. "Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem," Operations Research, INFORMS, vol. 48(6), pages 894-914, December.
    15. Michelle L. Blom & Christina N. Burt & Adrian R. Pearce & Peter J. Stuckey, 2014. "A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 658-676, November.
    16. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    17. Lamghari, Amina & Dimitrakopoulos, Roussos, 2012. "A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty," European Journal of Operational Research, Elsevier, vol. 222(3), pages 642-652.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zeng, Lanyan & Liu, Shi Qiang & Kozan, Erhan & Corry, Paul & Masoud, Mahmoud, 2021. "A comprehensive interdisciplinary review of mine supply chain management," Resources Policy, Elsevier, vol. 74(C).
    2. Arabi, Mahsa & Gholamian, Mohammad Reza, 2023. "Resilient closed-loop supply chain network design considering quality uncertainty: A case study of stone quarries," Resources Policy, Elsevier, vol. 80(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zeng, Lanyan & Liu, Shi Qiang & Kozan, Erhan & Corry, Paul & Masoud, Mahmoud, 2021. "A comprehensive interdisciplinary review of mine supply chain management," Resources Policy, Elsevier, vol. 74(C).
    2. Cinna Seifi & Marco Schulze & Jürgen Zimmermann, 2021. "Solution procedures for block selection and sequencing in flat-bedded potash underground mines," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 409-440, June.
    3. Samavati, Mehran & Essam, Daryl & Nehring, Micah & Sarker, Ruhul, 2017. "A methodology for the large-scale multi-period precedence-constrained knapsack problem: an application in the mining industry," International Journal of Production Economics, Elsevier, vol. 193(C), pages 12-20.
    4. Moreno, Eduardo & Rezakhah, Mojtaba & Newman, Alexandra & Ferreira, Felipe, 2017. "Linear models for stockpiling in open-pit mine production scheduling problems," European Journal of Operational Research, Elsevier, vol. 260(1), pages 212-221.
    5. Zhang, Jian & Dimitrakopoulos, Roussos G., 2017. "A dynamic-material-value-based decomposition method for optimizing a mineral value chain with uncertainty," European Journal of Operational Research, Elsevier, vol. 258(2), pages 617-625.
    6. Michelle L. Blom & Adrian R. Pearce & Peter J. Stuckey, 2016. "A Decomposition-Based Algorithm for the Scheduling of Open-Pit Networks Over Multiple Time Periods," Management Science, INFORMS, vol. 62(10), pages 3059-3084, October.
    7. Paithankar, Amol & Chatterjee, Snehamoy & Goodfellow, Ryan, 2021. "Open-pit mining complex optimization under uncertainty with integrated cut-off grade based destination policies," Resources Policy, Elsevier, vol. 70(C).
    8. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    9. Nancel-Penard, Pierre & Morales, Nelson & Cornillier, Fabien, 2022. "A recursive time aggregation-disaggregation heuristic for the multidimensional and multiperiod precedence-constrained knapsack problem: An application to the open-pit mine block sequencing problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1088-1099.
    10. W. Lambert & A. Newman, 2014. "Tailored Lagrangian Relaxation for the open pit block sequencing problem," Annals of Operations Research, Springer, vol. 222(1), pages 419-438, November.
    11. Lamghari, Amina & Dimitrakopoulos, Roussos, 2016. "Network-flow based algorithms for scheduling production in multi-processor open-pit mines accounting for metal uncertainty," European Journal of Operational Research, Elsevier, vol. 250(1), pages 273-290.
    12. Paithankar, Amol & Chatterjee, Snehamoy & Goodfellow, Ryan & Asad, Mohammad Waqar Ali, 2020. "Simultaneous stochastic optimization of production sequence and dynamic cut-off grades in an open pit mining operation," Resources Policy, Elsevier, vol. 66(C).
    13. César Flores-Fonseca & Rodrigo Linfati & John Willmer Escobar, 2022. "Exact algorithms for production planning in mining considering the use of stockpiles and sequencing of power shovels in open-pit mines," Operational Research, Springer, vol. 22(3), pages 2529-2553, July.
    14. Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Alexandra Newman, 2013. "MineLib: a library of open pit mining problems," Annals of Operations Research, Springer, vol. 206(1), pages 93-114, July.
    15. Thomas W. M. Vossen & R. Kevin Wood & Alexandra M. Newman, 2016. "Hierarchical Benders Decomposition for Open-Pit Mine Block Sequencing," Operations Research, INFORMS, vol. 64(4), pages 771-793, August.
    16. Chung, Joyce & Asad, Mohammad Waqar Ali & Topal, Erkan, 2022. "Timing of transition from open-pit to underground mining: A simultaneous optimisation model for open-pit and underground mine production schedules," Resources Policy, Elsevier, vol. 77(C).
    17. Rafael Epstein & Marcel Goic & Andrés Weintraub & Jaime Catalán & Pablo Santibáñez & Rodolfo Urrutia & Raúl Cancino & Sergio Gaete & Augusto Aguayo & Felipe Caro, 2012. "Optimizing Long-Term Production Plans in Underground and Open-Pit Copper Mines," Operations Research, INFORMS, vol. 60(1), pages 4-17, February.
    18. Chatterjee, Snehamoy & Sethi, Manas Ranjan & Asad, Mohammad Waqar Ali, 2016. "Production phase and ultimate pit limit design under commodity price uncertainty," European Journal of Operational Research, Elsevier, vol. 248(2), pages 658-667.
    19. King, Barry & Goycoolea, Marcos & Newman, A., 2017. "Optimizing the open pit-to-underground mining transition," European Journal of Operational Research, Elsevier, vol. 257(1), pages 297-309.
    20. Hassan Zohali & Bahman Naderi & Vahid Roshanaei, 2022. "Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 315-332, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:274:y:2019:i:1:p:227-239. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.