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A methodology for the large-scale multi-period precedence-constrained knapsack problem: an application in the mining industry

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  • Samavati, Mehran
  • Essam, Daryl
  • Nehring, Micah
  • Sarker, Ruhul

Abstract

This paper considers a generalization of the precedence-constrained knapsack problem known as multi-period precedence-constrained knapsack, in which the decision maker faces a horizon of several periods. Associated with each period is a capacity limit that cannot be exceeded by items chosen in that specific period. The motivation for studying this problem comes from a recognized problem in the mining industry, known as open pit mine production scheduling. An old, yet fast sequencing heuristic has been used in the literature to tackle similar combinatorial problems with precedence constraints. In this study, we first strengthen the LP relaxation formulation of the problem by adding inequalities derived from both precedence and knapsack constraints, and then use the LP solutions to generate efficient weights for the sequencing heuristic. Generating the heuristic's weights in this way significantly improves its output. Using this methodology, extremely large instances can be solved to near-optimum levels in minutes. The performance of this methodology is tested on a set of benchmark instances in the mining industry, where this problem is a major application.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:193:y:2017:i:c:p:12-20
    DOI: 10.1016/j.ijpe.2017.06.025
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    8. Samavati, Mehran & Essam, Daryl & Nehring, Micah & Sarker, Ruhul, 2017. "A local branching heuristic for the open pit mine production scheduling problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 261-271.
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    13. 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.
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    1. Jélvez, Enrique & Morales, Nelson & Nancel-Penard, Pierre & Cornillier, Fabien, 2020. "A new hybrid heuristic algorithm for the Precedence Constrained Production Scheduling Problem: A mining application," Omega, Elsevier, vol. 94(C).
    2. Haonan, Zhou & Samavati, Mehran & Hill, Andrew J., 2021. "Heuristics for integrated blending optimisation in a mining supply chain," Omega, Elsevier, vol. 102(C).
    3. 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).
    4. Mauricio Diéguez & Jaime Bustos & Carlos Cares, 0. "Mapping the variations for implementing information security controls to their operational research solutions," Information Systems and e-Business Management, Springer, vol. 0, pages 1-30.
    5. Mauricio Diéguez & Jaime Bustos & Carlos Cares, 2020. "Mapping the variations for implementing information security controls to their operational research solutions," Information Systems and e-Business Management, Springer, vol. 18(2), pages 157-186, June.
    6. Alipour, Aref & Khodaiari, Ali Asghar & Jafari, Ahmad & Tavakkoli-Moghaddam, Reza, 2022. "An integrated approach to open-pit mines production scheduling," Resources Policy, Elsevier, vol. 75(C).
    7. Tabesh, Mohammad & Moradi Afrapoli, Ali & Askari-Nasab, Hooman, 2023. "A two-stage simultaneous optimization of NPV and throughput in production planning of open pit mines," Resources Policy, Elsevier, vol. 80(C).
    8. 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.
    9. 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).

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