405
calculated for each block. In fact, transforming the ore geological model into an economic
block model paves the way to use mathematical optimization methods for mine designing and
scheduling. An example of a block model is shown in Fig. 2.
The number of each block along the X, Y, and Z axes indicate the number of columns,
rows, and layers or benches and are shown by i, j, and k, respectively.
2.2 Determine of the ultimate pit limit
At this stage, the possible most valuable (optimum) pit is obtained using the Lerch-Grossman
3-D method or the network flow taking into account the safe slope angle in different parts of
the mine. This can determine the amount of minable ore reserves.
2.3 Pushbacks design
After designing the ultimate pit limit, extraction of blocks to the ultimate pit limit can be
planned using mathematical algorithms. Since the implementation of mathematical models
on the whole ultimate pit limit is difficult and impossible in some cases, computerized techniques have been used for extraction from mineral resources in the past two decades, which
geometrically resembles to the removal of onion shell from its bulb. Therefore, the blocks in
this limit are divided into smaller volumes, which are called pushback. In fact, a pushback
refers to the intermediate pits whose successive extraction leads to the extraction of the final
pit; in other words, the pushback shows the growth stages of an open pit mine over time.
In this method, after determining the ultimate pit limit using the break-even cutoff grade,
that limit is converted into a series of smaller pits or pushbacks based on NPV. The initial
or central pit, like the core of onion, which has a higher quality than outer shells, has the
highest NPV, while NPV is reduced by moving toward the next pushbacks or pits. Depending on the mine size, even 10 pushbacks can be designed for a pit, and the distance between
pushbacks or the pushbacks’ thickness may vary between 30 to 90 m based on the minable
reserve size and the machinery. Each sequence of pushbacks results in a different annual cash
flow stream that gives different NPV for a project. Because, a series of pits with different sizes
are obtained by generating an economic model at different price for the commodity, cut-off
grade, or mining and processing costs (Osanloo 2005, Dagdelen 2000).
2.4 Production scheduling using mathematical algorithms
At this stage, the mathematical model of production scheduling is implemented in the limit
of each pushback. Mathematical models not only can determine the pattern of block extraction with maximum profit, but also can guarantee production and geometric constraints.
3 TYPES OF PRODUCTION SCHEDULING AT OPEN PIT MINES
Depending on the time horizon and the intended objectives, production scheduling in mines
can be long-term, mid-term, and short-term.
3.1 Long-term production scheduling
Long-term Scheduling is provided to extract and process minerals for a period of 10 to 20
years. The main goal in long-term production scheduling (LTPS) is to prepare the annual
(multi-year) plans for all blocks in the ultimate pit limit, but, as already mentioned, since
the number of these blocks is very high, all of them cannot be considered for a good annual
Scheduling. To solve this problem, the progress should be designed after designing the ultimate pit limit.
The long-term production Scheduling goals are (Steffen 1997):
calculated for each block. In fact, transforming the ore geological model into an economic
block model paves the way to use mathematical optimization methods for mine designing and
scheduling. An example of a block model is shown in Fig. 2.
The number of each block along the X, Y, and Z axes indicate the number of columns,
rows, and layers or benches and are shown by i, j, and k, respectively.
2.2 Determine of the ultimate pit limit
At this stage, the possible most valuable (optimum) pit is obtained using the Lerch-Grossman
3-D method or the network flow taking into account the safe slope angle in different parts of
the mine. This can determine the amount of minable ore reserves.
2.3 Pushbacks design
After designing the ultimate pit limit, extraction of blocks to the ultimate pit limit can be
planned using mathematical algorithms. Since the implementation of mathematical models
on the whole ultimate pit limit is difficult and impossible in some cases, computerized techniques have been used for extraction from mineral resources in the past two decades, which
geometrically resembles to the removal of onion shell from its bulb. Therefore, the blocks in
this limit are divided into smaller volumes, which are called pushback. In fact, a pushback
refers to the intermediate pits whose successive extraction leads to the extraction of the final
pit; in other words, the pushback shows the growth stages of an open pit mine over time.
In this method, after determining the ultimate pit limit using the break-even cutoff grade,
that limit is converted into a series of smaller pits or pushbacks based on NPV. The initial
or central pit, like the core of onion, which has a higher quality than outer shells, has the
highest NPV, while NPV is reduced by moving toward the next pushbacks or pits. Depending on the mine size, even 10 pushbacks can be designed for a pit, and the distance between
pushbacks or the pushbacks’ thickness may vary between 30 to 90 m based on the minable
reserve size and the machinery. Each sequence of pushbacks results in a different annual cash
flow stream that gives different NPV for a project. Because, a series of pits with different sizes
are obtained by generating an economic model at different price for the commodity, cut-off
grade, or mining and processing costs (Osanloo 2005, Dagdelen 2000).
2.4 Production scheduling using mathematical algorithms
At this stage, the mathematical model of production scheduling is implemented in the limit
of each pushback. Mathematical models not only can determine the pattern of block extraction with maximum profit, but also can guarantee production and geometric constraints.
3 TYPES OF PRODUCTION SCHEDULING AT OPEN PIT MINES
Depending on the time horizon and the intended objectives, production scheduling in mines
can be long-term, mid-term, and short-term.
3.1 Long-term production scheduling
Long-term Scheduling is provided to extract and process minerals for a period of 10 to 20
years. The main goal in long-term production scheduling (LTPS) is to prepare the annual
(multi-year) plans for all blocks in the ultimate pit limit, but, as already mentioned, since
the number of these blocks is very high, all of them cannot be considered for a good annual
Scheduling. To solve this problem, the progress should be designed after designing the ultimate pit limit.
The long-term production Scheduling goals are (Steffen 1997):