CSA Global Principal Consultant-Corporate, Alexey Tsoy will present at the upcoming MiningMath Creating Value in Mining; Strategy Optimisation through Data Science Conference on November 6 2018 at the Museum of Mines and Metals in Belo Horizonte, Brazil.
Alexey will present on Strategic Schedule Optimisation.
INTRODUCTION
This abstract describes long term mining schedule optimization approach that may be suitable for complex marginal projects and is based on modern scheduling techniques.
INDUSTRY STANDARD PRACTICES
The techniques are an attempt to solve limitations of the Lerch Grossmann (LG) algorithm that became an industry standard. The algorithm (designed in 1964-1965) is used to define economic viability of a pit by outlining the ultimate pit using economic and mining parameters.
The mine scheduling is done based on nested shells approach where the same LG algorithm is used to define the nested pits with different revenue factors. Somewhere in the process a cut-off grade (or series of cut off grades) is calculated to define what material should go to the plant.
A deficiency of Lerch Grossman and fixed cut-off grade(s) is the lack of the concept of time hence no concept of constraints related to the time or throughput capacity per unit of time.
THE THEORY OF CONSTRAINTS IN MINE SCHEDULING
But mining is a constrained system as any industrial system is. Thus, the theory of constraints (Goldratt, Cox, 2004) should apply. And as suggested by Goldratt:
1. IDENTIFY the system’s constraint
2. Decide how to EXPLOIT the system’s constraint
3. SUBORDINATE everything else to the above decisions
4. ELEVATE the system’s constraint
5. If in the previous steps a constraint has been broken Go back to step 1, but do not allow inertia to cause a system constraint.
A flexible cut-off grade taking into account opportunity costs (Uopp (x) = −i t NPVi , Rendu, 2014) and other variables could partially solve the problem and would allow to EXPLOIT and SUBORDINATE other parts of mining enterprise to the constraint/bottle neck. But it means introducing complexity into scheduling process. For example, each iteration of cut-off grade optimization will require another scheduling iteration to produce a long term plan with new cut-off followed by recalculation of NPV. And the process should be repeated until the highest NPV has been reached. More complex ore bodies sometimes require introduction of several processing streams that in turn increases number of required cut-off calculations dramatically as cut-off grade considers processes in pairs i.e. each cut-off grade expresses an economic threshold between sending ore to one process or another. In the most basic case it’s a threshold between ore being sent to processing plant and to waste dump.
There has been a number of attempts to define an approach that will work around these complexities. The concept of using linear programming in mine scheduling was initially described by Thys Jonson in 1968. Newman et al. (2010) summarised modern approaches to maximise NPV of a project in scheduling for both open pit and underground. Several academic sources quoted there use various approaches such as dynamic programming with a variable cone algorithm, linear integer programming, linear integer programming with relaxation, dynamic programming, multiperiod mixed-integer programming. To simplify optimisation task many approaches described in the article use fixed cut-off grade (Halactchev (2005), Amaya et al. (2009), Bley et al. (2010)) and sometimes predefined ultimate pits and benches (Halactchev (2005).
OPTIMISATION OF ECONOMIC SYSTEM
The next phase of development of mine scheduling was signified by the work on Stochastic integer programming methodology (Dimitrakopoulos, Ramazan, 2008, 2012). The authors attempt to introduce natural uncertainty of resource estimation into mine scheduling process by considering several possible scenarios and averaging resulting NPV.
Whittle Consulting (Whittle, 2010) uses a concept of Enterprise Optimisation to describe a holistic optimisation to mining enterprise using Lane’s theory, Theory of constraints, and Activity based costing.
The approach that is described in this paper is based on directly assigning economic values to each block according to its geological, geotechnical, mining and processing properties followed by application of constraints to physical throughput units in the system, as well as other variables such as resource reliability.
The constraints can be defined in different units and applied in parallel. For example, total mining capacity can be expressed in tonnes, while total crushing or milling capacity in energy (with respective BWi properties for each circuit and assigned to each block), oxide ore capacity (in tonnes), total deleterious elements content (in tonnes) in a period and other parameters can be defined simultaneously.
Thus, it allows to avoid using the proxy of economic value of cut-off grade. It also allows to manage uncertainty with either stochastic approach i.e. by having equiprobable scenarios and respective economic values assigned to a single block or by assigning probability values based mineral resource classification and reliability and limiting total risk in a period. The combined economic model is then run through a mixed integer linear programming algorithm to optimise the schedule trying to achieve maximum NPV.
Limitations of the approach are the consequences of its advantages – the resulting schedule is strategic in nature and will require further analysis and design work, and sometimes what is the most economic solution in long term is not always what a company may require right now. An example of the latter may be a cash strapped miner that would prefer to sacrifice long term NPV to this year’s cashflow.
REFERENCES
- Lerchs H. Grossmann I.F. Optimum Design of Open Pit Mines. The Canadian Mining and Metallurgical Bulletin for January, 1965, Montreal)
- E.M. Goldratt, J. Cox. The Goal. A process of Ongoing Improvement. Third Revised Edition. 2004. North River Press
- J.-M. Rendu. An introduction to cut-off grade estimation. Second edition. 2014. Society for Mining, Metallurgy & Exploration Inc.
- A.M. Newman, E. Rubio, et al. A Review of Operations Research in Mine Planning. Interfaces 40(3), pp. 222–245, ©2010 INFORMS
- R. Dimitrakopoulos, S. Ramazan, Stochastic integer programming for optimising long term production schedules of open pit mines: methods, application and value of stochastic solutions. Mining Technology 2008 VOL 117 NO 4. Institute of Materials, Minerals and Mining
- T.B. Johnson. Optimum Open Pit Mine Production Schedule. May 1968. Operations Research Centre. University of California – Berkeley.
ABOUT OUR PRESENTER
Alexey Tsoy
Principal Consultant-Corporate
Alexey is a Principal Consultant of Corporate and Business Development and possesses more than 15 years’ commercial experience in contract negotiations, sales, marketing and business development. He led several complex resource and reserve estimation projects as Project Manager. He is also a contributor to major Russian mining and geology magazines on international reporting standards for reporting on resources and reserves, on the impact mining has on the general economy and the required changes to maximize it.
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