Publication Cover
Mining Technology
Transactions of the Institutions of Mining and Metallurgy
Volume 130, 2021 - Issue 1
196
Views
1
CrossRef citations to date
0
Altmetric
Articles

An efficient algorithm for the precedence constraint knapsack problem with reference to large-scale open-pit mining pushback design

, &
Pages 8-21 | Received 02 Sep 2020, Accepted 15 Dec 2020, Published online: 14 Jan 2021

References

  • Bienstock D, Zuckerberg M. 2010. Solving LP relaxations of large-scale precedence constrained problems. In: Eisenbrand F, Shepherd FB, editor. Integer programming and combinatorial optimization, June 9–11. Lausanne, Switzerland: Springer; p. 1–14.
  • Boland N, Bley A, Fricke C, Froyland G, Sotirov R. 2012. Clique-based facets for the precedence constrained knapsack problem. Math Program. 133(1–2):481–511.
  • Boyd EA. 1993. Polyhedral results for the precedence-constrained knapsack problem. Discrete Appl Math. 41(3):185–201.
  • Byun J, Dimitrakopoulos R. 2013. An efficient algorithm for the LP relaxation of the maximal closure problem with a capacity constrain. Cahiers du GERAD, G-2013-60.
  • Caccetta L, Hill SP. 2003. An application of branch and cut to open pit mine scheduling. J Glob Optim. 27(2–3):349–365.
  • Chandran BG, Hochbaum DS. 2009. A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem. Oper Res. 57(2):358–376.
  • 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.
  • Dagdelen K. 1985. Optimum multi-period open pit mine production scheduling by Lagrangian parameterization [unpublished PhD thesis]. Colorado School of Mines, Golden, Colorado, p. 1–325.
  • Elkington T, Durham R. 2011. Integrated open pit pushback selection and production capacity optimization. J Min Sci. 47(2):177–190.
  • Espinoza D, Goycoolea M, Moreno E, Newman A. 2013. MineLib: a library of open pit mining problems. Ann Oper Res. 206 (1): 93–114.
  • Gallo G, Grigoriadis MD, Tarjan RE. 1989. A fast parametric maximum flow algorithm and applications. SIAM J Comput. 18(1):30–55.
  • Hiriart-Urruty JB, Lemaréchal C. 1993. Convex analysis and minimization algorithms, Vols. 1 and 2. Berlin: Springer Verlag.
  • Hochbaum DS, Chen A. 2000. Performance analysis and best implementations of old and new algorithms for the open-pit mining problem. Oper Res. 48(6):894–914.
  • Lerchs H, Grossman I. 1965. Optimum design of open-pit mines. CIM Bull. 12:47–54.
  • Meagher C, Dimitrakopoulos R, Avis D. 2014. Optimized open pit mine design, pushbacks and the gap problem – a review. J Min Sci. 50(3):508–526.
  • Meagher C, Sabour SA, Dimitrakopoulos R. 2009. Pushback design of open pit mines under geological and market uncertainties. In Orebody modelling and strategic mine planning. p. 297–304.
  • Osanloo M, Gholamnejad J, Karimi B. 2008. Long-term open pit mine production planning: a review of models and algorithms. Int J Min Reclam Environ. 22(1):3–35.
  • Park K, Park S. 1997. Lifting cover inequalities for the precedence-constrained knapsack problem. Discrete Appl Math. 72(3):219–241.
  • Picard JC. 1976. Maximal closure of a graph and applications to combinatorial problems. Manage Sci. 22(11):1268–1272.
  • Tachefine B, Soumis F. 1997. Maximal closure on a graph with resource constraints. Comput Oper Res. 24(10):981–990.
  • Tolwinski B. 1998. Scheduling production for open pit mines. International Symposium Computer Applications in the Minerals Industries; UK. p. 651–662.
  • Zhao X, Luh P. 2002. New bundle methods for solving Lagrangian relaxation dual problems. J Optim Theory Appl. 113(2):373–397.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.