Open Pit(s) Mine Planning - "PITSTRAT"
The mining of mineral deposits in such a manner that at depletion, the maximum possible profit is realised, has been an unsolved problem since man's discovery of the usable elements buried beneath the earth's surface.
Since World War Two, the depletion of the most accessible of the world's high grade reserves took place, forcing the mining industry into working with declining grade material. As a result, the sequence of extraction has now become more important; and, in many cases, has become a problem, the solution of which is vital to the existence of a profitable operation.
During the past six decades, mathematicians, geostatisticians and mining engineers have been actively applying their minds to finding elegant and comprehensive mathematical models that would not only solve the open pit mining problem, but also provide optimal answers in terms of maximum profitability over the life of open pit projects. The technique that immediately comes to mind in seeking for an optimal answer, is mathematical programming, specifically LP and MIP.
As far back as May 1964, Helmut Lerchs and Ingo Grossmann realised this and reported that "a mathematical model taking into account all possible alternatives simultaneously would provide optimal answers in terms of maximum profitability, however, it would be of formidable size and its formulation/solution would be beyond the means of present know-how".
Since the 1960's meteoric developments took place in the Computing Sciences and today, mathematical models, constituting tens of thousands of variables and/or integer variables in hundreds of thousands of constraints, are successfully solved within a finite time period (couple of hours) on desktop computers and workstations.
The PITSTRAT optimisation software allows the planner to determine the optimal "utility" (*) plan of the total system: "mining via plant to markets".
• which blocks from
• which pits are to be
• blended in which proportions in
• which time periods and routed to
• which plants in order to meet multiple mineral specifications
so as to optimise "utility" (*).
(*) Optimisation can mean maximisation or minimisation. Utility can be defined as cash flow (in today’s money), N.P.V. (net present value being the discounted difference between escalated revenue and escalated costs) or costs. Generally, optimisation of utility can mean maximisation of “profits” or minimisation of “costs”.
Where-as the Lerchs Grossmann algorithm, as solved by the Mintec/Whittle software, generates the mined out final pit shells as it will be at the end of the life of mine, PITSTRAT generates the "how to get to the optimal pit over time” scenario. From year to year, as time goes by, product specifications and sales volumes, exchange rates, selling prices and technology can change and PITSTRAT is used to optimally plan for the exploitation of the mentioned changes. The Mintec/Whittle software and PITSTRAT are complementary systems.
The objective function of PITSTRAT is the maximisation of accounting contribution before tax. Contribution is defined as the difference between revenue ex mineral units sold (e.g. Fe units) and the variable cost of producing those units - mining costs, waste removal costs, haulage costs, handling costs, plant costs, loading and road/rail transport costs up to the point of sale. By incorporating fixed costs (a user function), the objective function can be changed to maximise cash flow before tax. In both cases, by entering the required factors, the objective can be changed to maximise the N.P.V. of the above functions.
The PITSTRAT constraints constitute the following:
• the open pit mining geometry
• hauling capacity between pits and plants
• plant capacity
• tons mined per pit capacity
• tons waste generated per pit capacity
• upper and lower limits on strip ratios
• sales volumes
• selling prices (with or without exchange rate)
• chemical specifications
The model will only “mine” while the contribution (utility) of the total system remains positive. Each block is techno-economically evaluated in the full context of ALL CONSTRAINTS in the model, including an element of cross-subsidy, e.g. a given layer/bench of blocks may be unprofitable to mine, however, a block or layer/bench below it may be of sufficiently high grade to economically warrant the mining of the unprofitable layer/bench or block in order to reach and extract the high grade layer/bench or block. It should be clear that the model does not use conventional cut-off grade policies to decide whether to mine a block or not. It is far more complex than that, e.g. if mining costs increase with depth, the model will e.g. cease mining at that layer where the contribution of the TOTAL system becomes zero or negative. (This in itself can be an indication to initiate underground mining).
PITSTRAT output consists of a life of mine plan, split up into time periods to indicate to the planner when to progress which pit(s) by how much. (Remember, PITSTRAT will identify the most economical). In the case of the planner force feeding the model with unrealistic constraints, e.g. specifying a chemical analysis or a strip ratio which is impossible to achieve, the model will indicate so by generating an infeasible output report. If a plan is optimal, it means that there is mathematically no better contribution (cash flow) plan possible than the optimal plan, i.e. under the given constraints. Should one want to direct the planning into different areas than what was indicated by the model in the optimal plan, e.g. due to limited infrastructure or difficult terrain, then the involved blocks can be excluded from the input data, and a second optimisation will then indicate the next best plan under the new set of constraints. The difference in objective value tells the planner the worth of the first plan above the second plan and thus whether it is economically justifiable to inject capital to procure sufficient infrastructure and/or upgrade the terrain - depending the case in question.
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