A variable neighbourhood descent algorithm for the open-pit mine production scheduling problem with metal uncertainty

Uncertainty is an inherent aspect of the open-pit mine production scheduling problem (MPSP); however, little is reported in the literature about solution methods for the stochastic versions of the problem. In this paper, two variants of a variable neighbourhood descent algorithm are proposed for solving the MPSP with metal uncertainty. The proposed methods are tested and compared on actual large-scale instances, and very good solutions, with an average deviation of less than 3% from optimality, are obtained within a few minutes up to a few hours.

[1]  J. Dupacová,et al.  Scenario reduction in stochastic programming: An approach using probability metrics , 2000 .

[2]  Roussos Dimitrakopoulos,et al.  Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design , 2002 .

[3]  Amina Lamghari,et al.  A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty , 2012, Eur. J. Oper. Res..

[4]  Roussos Dimitrakopoulos,et al.  Algorithmic approach to pushback design based on stochastic programming: method, application and comparisons , 2010 .

[5]  Mark Gershon Heuristic approaches for mine planning and production scheduling , 1987 .

[6]  J. Picard Maximal Closure of a Graph and Applications to Combinatorial Problems , 1976 .

[7]  Ambros M. Gleixner,et al.  LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity , 2009, Comput. Oper. Res..

[8]  Timothy C. Coburn,et al.  Geostatistics for Natural Resources Evaluation , 2000, Technometrics.

[9]  Hasan Sevim,et al.  The Problem Of Production Planning In Open Pit Mines , 1998 .

[10]  Gourab Sen Gupta,et al.  Autonomous Robots and Agents , 2007 .

[11]  Alexandra M. Newman,et al.  A Review of Operations Research in Mine Planning , 2010, Interfaces.

[12]  Salih Ramazan,et al.  The new Fundamental Tree Algorithm for production scheduling of open pit mines , 2007, Eur. J. Oper. Res..

[13]  Salih Ramazan,et al.  Production scheduling with uncertain supply: a new solution to the open pit mining problem , 2013 .

[14]  Alexandre Boucher,et al.  Multivariate Block-Support Simulation of the Yandi Iron Ore Deposit, Western Australia , 2012, Mathematical Geosciences.

[15]  John M. Wilson,et al.  Introduction to Stochastic Programming , 1998, J. Oper. Res. Soc..

[16]  Natashia Boland,et al.  A strengthened formulation and cutting planes for the open pit mine production scheduling problem , 2010, Comput. Oper. Res..

[17]  Taylor Francis Online Transactions of the Institution of Mining and Metallurgy. Section A, Mining technology , 2000 .

[18]  Robert Underwood,et al.  A scheduling algorithm for open pit mines , 1996 .

[19]  Jacques A. Ferland,et al.  Application of a Particle Swarm Algorithm to the Capacitated Open Pit Mining Problem , 2007 .

[20]  Jef Caers,et al.  Representing Spatial Uncertainty Using Distances and Kernels , 2009 .

[21]  Lou Caccetta,et al.  An Application of Branch and Cut to Open Pit Mine Scheduling , 2003, J. Glob. Optim..

[22]  Eduardo Moreno,et al.  Large-scale multi-period precedence constrained knapsack problem: A mining application , 2010, Electron. Notes Discret. Math..

[23]  Daniel Bienstock,et al.  Solving LP Relaxations of Large-Scale Precedence Constrained Problems , 2010, IPCO.

[24]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[25]  Thys B Johnson,et al.  OPTIMUM OPEN PIT MINE PRODUCTION SCHEDULING , 1968 .

[26]  R. Dimitrakopoulos,et al.  Managing risk and waste mining in long-term production scheduling of open-pit mines , 2004 .

[27]  Jitka Dupacová,et al.  Scenario reduction in stochastic programming , 2003, Math. Program..

[28]  R. Dimitrakopoulos,et al.  Stochastic mine design optimisation based on simulated annealing: pit limits, production schedules, multiple orebody scenarios and sensitivity analysis , 2009 .

[29]  Mohammad Waqar Ali Asad,et al.  Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand , 2013, J. Oper. Res. Soc..

[30]  I. Dumitrescu,et al.  A Multistage Stochastic Programming Approach to Open Pit Mine Production Scheduling with Uncertain Geology , 2008 .