MODEL - Lerchs-Grossman Optimization
MODEL - Lerchs-Grossman Optimization
MODEL - Lerchs-Grossman Optimization
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Raw Cell Value ($) = [Assay (unit/t) x Tonnes (t) x Recovery (%) x Ore Price
($/unit) x Ore Proportion (%)] Modifiers ($/T)
Equation 2: Calculation of raw cell value
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Cell Value ($) = Raw Cell Value ($) - Cell Processing Value ($)
Equation 4: Calculation of cell value
Final Cell ($) = Cell Value ($) [Tonnes (t) x Ore Mining Cost ($/t)]
Equation 5: Calculation of final cell value
If
then
(i.e.
a model cell cannot cost more to mine than the basic cost of mining).
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definition
(<Model><Block
Model
7. If the waste dollar value is constant with depth then it can be assigned to the model using the
<Model><Block Model Operations><Adjust Cells With a Constant...> menu item.
8. If the waste dollar value varies by depth then use the <Model><Update...> menu item to
create a range of values for the background waste (according to bench depth). This option
uses a value assigned to a polygon that encompasses the model area and injects that value into
all cells for a bench. The value may change for each bench.
9. Import the database data (<Model><Import/ Export Cells><Import...>).
NOTE: Every cell in the model has a valid dollar value. Failure to assign dollar values to cells will
result in miscalculation of the optimum pit.
Economic Data
Economic data should be prepared before running the Lerch-Grossman module (probably by way of
an external program). This data must have for every bench/block in the model the net profit that
would be obtained from mining that block once it has been exposed. It is not necessary to provide a
cost for the uncovering of each block since this is one of the factors automatically taken into account
by the program. Waste blocks should be assigned negative economic values.
Laminar Models
Optimization of laminar models can be performed indirectly by exporting the model to a block model
(<Model><Laminar Model Operations><Export to Block Model...>). A resultant quality of this
conversion is the RD of LG Ore Percent assay (see LAMINAR MODEL OPERATIONS) which is
used by the Lerch-Grossman module.
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1. Enter the area of the model defined by the minimum and maximum rows and columns and the
number of benches.
2. Enter the number of cells to be bulked together to form a larger cell size. If you do not wish to
bulk cells together then enter 1 for each direction. See the notes below for more information.
3. Enter the average relative density of ore. This value is only used if relative density is not
modelled already or if the modelled relative density is too low (< 0.1).
4. Press next to go to the next page in the wizard.
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This will have the effect of reducing the number of cells (albeit large ones) that need to be processed,
and hence make it possible for all the optimisation data to fit in RAM. Bulking starts from the
minimum row / column and from the deepest bench. If the bulked cells break out beyond the limits of
the model, as a result of the bulking parameters not being even multiples of the number of rows,
columns and benches, then that portion of the breakout is considered to be air. This is acceptable
because the crest of the pit will always be computed to be inside the row and column limits.
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1. Enter the cut-off profit value. This will usually be 0.0 since higher values will high-grade the
deposit.
2. Select an assay from the assay list to focus on that assay.
3. Enter the price for that assay in dollars per unit (the unit depends on the quality: e.g. gold
would be $/gram). A blank value is converted to 0.0. The price can be fixed or variable as
follows:
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Variable recoveries are useful if qualities had been modelled (i.e. weathered, transitional, fresh rock)
that affect ore recovery. Note, however, if variable recoveries are used then the cut off grades will not
be reported in the report file.
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If variable processing costs are used then the cut off grades will not be reported in the report file.
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PI
C00000035
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If the default modifier is 0 and there no entries in the modifiers list then focus assay does not use ore
modification.
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PIC00000023 There are three methods of entering mining costs (Figure 12):
1. Enter an ore cost and waste cost for each bench.
2. Select the <Global Values...> button to enter global costs to a nominated bench and all
benches below it (Figure 13).
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3. Select the <Import...> button to select a text file containing the required costs (Figure 14).
The text file must be a comma separated file with the format:
ore cost,waste cost,field 3,field 4,
Only the first two fields are required. If the model benches are required for reference then use
field 3. No header lines should be included in the file.
These methods can be used in conjunction if required. For example, you can import a file to fill all the
bench cost values and then modify a few benches.
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The dollar value of every cell is compared against the cut-off value. If the dollar value is less than the
cut-off then the cell is assigned a waste cost.
Only one dollar quality can be used for optimisation. You can, however, have a number of dollar
values in the model to examine discounted cash flow.
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5. Repeat steps 1 through 3 for each additional bench group (PIC0000002D Figure 17).
The slope angles start from the floor of the bench level. The slope gradient should be the overall angle
of the pit wall including catch berms and one or more passes of the haul road with a batter included
for each horizontal plane.
Bearing angles start from North, with East being 90 o, South 180o and West 270o. These define the
area where the corresponding wall slope is generated. The program interpolates the slope angles
between supplied bearings.
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1. Enter the name of a model that will contain the optimized pit or leave the name blank if the
model is not required.
The model produced consists of a single stratigraphic unit. The cell elevations in this model
depict the economic depth of that part of the model according to the costing parameters
specified. The model can be contoured in the PLAN VIEW PUBLISHER.
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Economic Values
SYMBOLIC: ECON
CONTENTS: Economic values of every block in the model
PREP. BY:
FORMAT:
B.2
FORMAT : Direct access, unformatted 12-byte records made up of one 4-byte integer (next vertex
on the path from this vertex to the root vertex) and one 8-byte double precision float
(the weight supported by the vertex).
Record number X contains the next vertex on the path from the vertex X to the root
vertex and the weight supported by vertex X.
B.3
Results
Lerch-Grossman module
FORMAT : Sequential access, unformatted 6-byte records. The three fields in the record contain
the x, y and z coordinates respectively of a block in the optimum pit. (The coordinates
are given with respect to IMS model coordinate system).
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The value of the variable NEVER should be checked. It should be, compared to the
economic values assigned to the blocks in the model, a very large negative double
precision floating point number. If the value appears to be satisfactory or if it cannot be
increased any further, try scaling the economic values assigned to the blocks.
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