A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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every ore block and searches for any cone
with positive value. Korobov (1974)
attempted to improve the Pana’s moving
cone method (Kim, 1979).
Lerchs and Grossman (1965) used the
concept of dynamic programming and they
introduced their well-known twodimensional
algorithm in order to find an
optimum pit limit (Lerchs and Grossman,
1965). Later, Johnson and Sharp (1971) used
this idea in order to design a 3Dimensional
pit. Koenigsberg (1982) used dynamic
programming to find a 3Dimensional
optimum pit limit. It was also Lerchs and
Grossman (1965) who introduced the use of
graph theory in optimum pit design (LG
algorithm). They converted the block model
of the mine into a graph and determine the
ultimate pit limits by solving for the
maximum closure of the graph. Zhao and
Kim (1992) used this idea with some
modifications and they claim that their
method is simpler and faster than the LG
algorithm. Tolwinski and Underwood (1998)
used the concept of graph theory and
mathematical programming and solve the
dual form of the ultimate pit limit problem.
The concept of linear programming in pit
limit design problem was first used by Meyer
(1969). He made so many hypotheses in his
work which results in a non-optimal solution.
Huttagosol and Cameron (1992) dealt with
pit design as a transportation problem.
Pit parameterization is another method
introduced by Matheron (1976). In this
method instead of directly searching for the
pit limit, a parameterization function is
determined
combine the pit limit determination and
production planning using genetic algorithm.
Network flow and maximum flow
algorithms are other methods for solving the
ultimate pit limits. Johnson (1969), Picard
(1976), Giannini (1991), Yegulalp et al
(1992) and Hochbaum and Chen (2000) used
the algorithms of maximum flow to
determine the pit limit. Hochbaum and Chen
(2002) have extended the recent
improvements in network flow algorithms
into the LG algorithm (Muir, 2004).
Newman et al. (2010) provided a thorough
review of pit design algorithms.
The traditional open pit optimization
algorithms are affected by the uncertainty in
key input parameters, leading to suboptimal
solutions and deviations from production
plans. Whittle and Bozorgebrahimi (2004)
developed the concept of hybrid pits to
determine the ultimate pit limit in the
presence of grade uncertainty. In this
approach, conditional simulation and LG
algorithm are combined, and using set
theory, it leads to the creation of pit outlines
with quantifiable degree of risk. The hybrid
pits can be used as design guides to avoid the
higher uncertainty in early stages of a mine
development. Meagher et al. (2009)
combined conditional simulation and
maximum flow theory to determine the
ultimate pit limit and push back design in the
presence of grade and price uncertainty.
Osanloo et al. (2009) take the advantage of
real option to determine the ultimate pit
design, in the presence of price uncertainty.
The algorithms, developed in the presence
of uncertainty are beyond the scope of this
paper. In all the algorithms developed to
determine the ultimate pit limit, it is assumed
that, BEVs are calculated correctly. It should
be noted that, the BEVs of the blocks
blended to be marketable are the same.
However, pit optimization techniques do not
deal with the blending issues.
3 BLEND OPTIMIZATION
Different objective functions can be defined
and used for blend optimization, such as, (1)
the total tonnage of blended ore is
maximized, while satisfying grade
constraints, and (2) the cost of producing a
unit of blended product is minimized by
determining the ratios in which ore-types
should be used, given a unit cost for each
ore-type, and satisfying grade constraints of
final product.
The mathematical model to maximize the
total tonnage of single blended product is
presented in equations 2-5. In this model it is
assumed that there is just one final blended
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