Hierarchical Benders Decomposition for Open-Pit Mine Block Sequencing

References

• Ahuja R, Magnanti T, Orlin J (1993) Network Flows (Prentice Hall, Englewood Cliffs, NJ).Google Scholar
• Ahuja RK, Hochbaum DS, Orlin JB (2003) Solving the convex cost integer dual network flow problem. Management Sci. 49(7):950–964.Link, Google Scholar
• Akaike A, Dagdelen K (1999) A strategic production scheduling method for an open pit mine. Dardano C, Francisco M, Proud J, eds. Proc. 28th Internat. Sympos. Comput. Appl. Minerals Industries, APCOM ’99 (Colorado School of Mines, Golden, CO), 729–738.Google Scholar
• Appleget JA, Wood RK (2000) Explicit-constraint branching for solving mixed-integer programs. Laguna M, González-Velarde JL, eds. Computing Tools for Modeling, Optimization and Simulation (Kluwer Academic Publishers, Boston), 245–261.Crossref, Google Scholar
• Barnhart C, Johnson E, Nemhauser G, Savelsbergh M, Vance P (1998) Branch-and-price: Column generation for solving huge integer programs. Oper. Res. 46(3):316–329.Link, Google Scholar
• Beale EML, Tomlin JA (1970) Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. Lawrence J, ed. Proc. 5th IFORS Conf. (Tavistock, London), 447–454.Google Scholar
• Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(3):238–252.Crossref, Google Scholar
• Bienstock D, Zuckerberg D (2010) Solving LP relaxations of large-scale precedence constrained problems. Eisenbrand F, Shepherd FB, eds. Proc. 14th Internat. Conf. Integer Programming Combinatorial Optimization, IPCO ’10, Lecture Notes Comput. Sci., Vol. 6080 (Springer, Berlin), 1–14.Crossref, Google Scholar
• Birge JR (1997) State-of-the-art survey—stochastic programming: Computation and applications. INFORMS J. Computing 9(2):111–133.Link, Google Scholar
• Birge JR, Louveaux FV (1988) A multicut algorithm for two-stage stochastic linear programs. Eur. J. Oper. Res. 34(3):384–392.Crossref, Google Scholar
• Boland N, Dumitrescu I, Froyland G (2008) A multistage stochastic programming approach to open pit mine production scheduling with uncertain geology. http://www.optimization-online.org/DB_HTML/2008/10/2123.html.Google Scholar
• Boland N, Dumitrescu I, Froyland G, Gleixner A (2009) LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity. Comput. Oper. Res. 36(4):1064–1089.Crossref, Google Scholar
• Brown G, Keegan J, Vigus B, Wood K (2001) The Kellogg Company optimizes production, inventory and distribution. Interfaces 31(6):1–15.Link, Google Scholar
• Caccetta L, Hill S (2003) An application of branch and cut to open pit mine scheduling. J. Global Optim. 27(2–3):349–365.Crossref, Google Scholar
• Cai W (2001) Design of open-pit phases with consideration of schedule constraints. Xie H, Wang Y, Jiang Y, eds. Proc. 29th Internat. Sympos. Comput. Appl. Minerals Industries, APCOM ’01 (A.A. Balkema, Lisse, Netherlands), 217–221.Google Scholar
• Chicoisne R, Espinoza D, Goycoolea M, Moreno E, Rubio E (2012) A new algorithm for the open-pit mine scheduling problem. Oper. Res. 60(3):517–528.Link, Google Scholar
• Cullenbine C, Wood K, Newman A (2011) A sliding time window heuristic for open pit mine block sequencing. Optim. Lett. 88(3):365–377.Crossref, Google Scholar
• Dagdelen K, Johnson T (1986) Optimum open pit mine production scheduling by Lagrangian parameterization. Proc. 19th Internat. Sympos. Comput. Appl. Minerals Industries APCOM ’86 (SME, Littleton, CO), 127–141.Google Scholar
• Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper. Res. 8(1):101–111.Link, Google Scholar
• Denby B, Schofield D (1994) Open-pit design and scheduling by use of genetic algorithms. Trans. Institution Mining Metallurgy Section A. Mining Indust. 103:A21–A26.Google Scholar
• Eivazy H, Askari-Nasab H (2012) A mixed integer linear programming model for short-term open pit mine production scheduling. Mining Tech. 121(2):97–108.Crossref, Google Scholar
• Elhedhli S, Goffin J-L (2004) The integration of an interior-point cutting plane method within a branch-and-price algorithm. Math. Programming 100(2):267–294.Crossref, Google Scholar
• Entriken R (1989) The parallel decomposition of linear programming. Doctoral dissertation, Stanford University, Stanford, CA.Crossref, Google Scholar
• Entriken R (1996) Parallel decomposition: Results for staircase linear programs. SIAM J. Optim. 6(4):961–977.Crossref, Google Scholar
• Epstein R, Goic M, Weintraub A, Catalán J, Santibáñez P, Urrutia R, Cancino R, Gaete S, Aguayo A, Caro F (2012) Optimizing long-term production plans in underground and open-pit copper mines. Oper. Res. 60(1):4–17.Link, Google Scholar
• Espinoza D, Goycoolea M, Moreno E, Newman A (2012) MineLib: A library of open pit mining problems. Ann. Oper. Res. 206(1):1–22.Google Scholar
• Gabbay H (1979) Multi-stage production planning. Management Sci. 25(11):1138–1148.Link, Google Scholar
• Gassman H (1990) MSLiP: A computer code for the multistage stochastic linear programming problem. Math. Programming 47(1–3):407–423.Crossref, Google Scholar
• Geoffrion AM, Graves GW (1974) Multicommodity distribution system design by Benders decomposition. Management Sci. 20(5):822–844.Link, Google Scholar
• Gershon M (1983) Optimal mine production scheduling: Evaluation of large scale mathematical programming approaches. Internat. J. Mining Engrg. 1(4):315–329.Crossref, Google Scholar
• Gershon M (1987) Heuristic approaches for mine planning and production scheduling. Internat. J. Mining Geological Engrg. 5(1):1–13.Crossref, Google Scholar
• Gholamnejad J, Moosavi E (2012) A new mathematical programming model for long-term production scheduling considering geological uncertainty. J. Southern African Inst. Mining Metallurgy 112(2):77–81.Google Scholar
• Glassey CR (1971) Dynamic linear programs for production scheduling. Oper. Res. 19(1):45–56.Link, Google Scholar
• Glassey CR (1973) Nested decomposition and multi-stage linear programs. Management Sci. 20(3):282–292.Link, Google Scholar
• Gleixner A (2008) Solving large-scale open pit mining production scheduling problems by integer programming. Master’s thesis, Technische Universität Berlin, Berlin, Germany.Google Scholar
• Gondzio J, Sarkissian R, Vial J-P (1997) Using an interior point method for the master problem in a decomposition approach. Eur. J. Oper. Res. 101(3):577–587.Crossref, Google Scholar
• Ho J, Manne A (1974) Nested decomposition for dynamic models. Math. Programming 6(1):121–140.Crossref, Google Scholar
• Hochbaum D, 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.Link, Google Scholar
• Hummeltenberg W (1984) Implementations of special ordered sets in MP software. Eur. J. Oper. Res. 17(1):1–15.Crossref, Google Scholar
• IBM Corp. (2013) IBM ILOG CPLEX Optimization Studio CPLEX User’s Manual, Version 12 Release 5. http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r5/topic/ilog.odms.studio.help/pdf/usrcplex.pdf.Google Scholar
• IBM Corp. (2014) IBM ILOG CPLEX Optimization Studio CPLEX User’s Manual, Version 12 Release 6. http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r6/topic/ilog.odms.studio.help/pdf/usrcplex.pdf.Google Scholar
• Infanger G (1994) Planning Under Uncertainty: Solving Large-Scale Stochastic Linear Programs (Boyd & Fraser, Danvers, MA).Google Scholar
• Johnson T (1968) Optimum open pit mine production scheduling. Doctoral dissertation, University of California, Berkeley, Berkeley.Crossref, Google Scholar
• Kallio MJ, Porteus EL (1977) Decomposition of arborescent linear programs. Math. Programming 33(1):348–356.Crossref, Google Scholar
• Karlsson J, Rönnqvist M, Bergström J (2003) Short-term harvest planning including scheduling of harvest crews. Internat. Trans. Oper. Res. 10(5):413–431.Crossref, Google Scholar
• Kawahata K (2007) A new algorithm to solve large scale mine production scheduling problems by using the Lagrangian relaxation method. Doctoral dissertation, Colorado School of Mines, Golden, CO.Google Scholar
• Krige D (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J. Chemical Metallurgical Mining Soc. South Africa 52(6):119–139.Google Scholar
• Lambert WB, Newman AM (2014) Tailored Lagrangian relaxation for the open pit block sequencing problem. Ann. Oper. Res. 222(1):419–438.Crossref, Google Scholar
• Lambert WB, Brickey A, Newman AM, Eurek K (2014) Open-pit block-sequencing formulations: A tutorial. Interfaces 44(2):127–142.Link, Google Scholar
• Lerchs H, Grossmann I (1965) Optimum design of open-pit mines. Canadian Mining Metallurgical Bull. 68:17–24.Google Scholar
• Linderoth JT, Savelsbergh MWP (1999) A computational study of search strategies for mixed integer programming. INFORMS J. Comput. 11(2):173–187.Link, Google Scholar
• Morton DP (1996) An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling. Ann. Oper. Res. 64(1):211–235.Crossref, Google Scholar
• Pochet Y, Wolsey L (2006) Production Planning by Mixed Integer Programming (Springer, New York).Google Scholar
• Ramazan S (2007) The new fundamental tree algorithm for production scheduling of open pit mines. Eur. J. Oper. Res. 177(2):1153–1166.Crossref, Google Scholar
• Ramazan S, Dimitrakopoulos R (2007) Stochastic optimisation of long-term production scheduling for open pit mines with a new integer programming formulation. Orebody Modelling and Strategic Mine Planning (Australasian Institute of Mining and Metallurgy, Melbourne, Australia), 385–391.Google Scholar
• Rojas CR, Goodwin GC, Seron MM, Zhang MM (2007) Open-cut mine planning via closed-loop receding-horizon optimal control. Sánchez Peña RS, Casín JQ, Cayuela VP, eds. Identification and Control (Springer, London), 43–62.Crossref, Google Scholar
• Rousseau L-M, Gendreau M, Feillet D (2007) Interior point stabilization for column generation. Oper. Res. Lett. 35(5):660–668.Crossref, Google Scholar
• Ruszczyński A (1986) A regularized decomposition method for minimizing a sum of polyhedral functions. Math. Programming 35(3):309–333.Crossref, Google Scholar
• Ryan DM, Foster BA (1981) An integer programming approach to scheduling. Wren A, ed. Comput. Scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling (North-Holland, Amsterdam, Netherlands), 269–280.Google Scholar
• Singh KJ, Philpott AB, Wood RK (2009) Dantzig-Wolfe decomposition for solving multistage stochastic capacity-planning problems. Oper. Res. 57(5):1271–1286.Link, Google Scholar
• Stolarczyk L (1992) Definition imaging of an orebody with the radio imaging method. IEEE Trans. Indust. Appl. 28(5):1141–1147.Crossref, Google Scholar
• Van Den Heever SA, Grossmann IE (2000) An iterative aggregation/disaggregation approach for the solution of a mixed-integer nonlinear oilfield infrastructure planning model. Indust. Engrg. Chemistry Res. 39(6):1955–1971.Crossref, Google Scholar
• Whittle J (1998) Four-X™ Strategic Planning Software for Open Pit Mines, Reference Manual (Whittle Programming Pty Ltd., Melbourne, Australia).Google Scholar
• Wittrock RJ (1985) Dual nested decomposition of staircase linear programs. Math. Programming Study 24:65–86.Crossref, Google Scholar
• Wollmer RD (1980) Two stage linear programming under uncertainty with 0–1 integer first stage variables. Math. Programming 19(1):279–288.Crossref, Google Scholar