approach. For a block ∀ ∊ and an annual period ∀ ∊ , an integer variable , ∊ {0,1} equals 1 if the block is completely extracted in the period , or 0 otherwise. Therefore, for a discount rate = 0.1 and for one type of block values as mentioned in the different scenarios, an economic return , can be obtained from the excavation (and processing) of a block during time period , resulting in the objective function modelled as Equation (4): (4) ∑∑( , ⋅ , ) − =1 =1 Since equals a set of time periods ∊ and is the list of blocks ′ that precede a block ∊ , considering a slope angle of 45º degrees, hard constraints related to slope angle, precedence, and reserve have been modelled as Equations (5) and (6), respectively: ∑( , ) ≤ ≤ ∑( ′, ) ≤ ∑( , ) =1 , ∀ ∊ , ∀ ′ ∊ , ∀ ∊ (5) (6) ≤ 1, ∀ ∊ The soft constraints described as in Equation (4) are related to equipment and processing capacity, as shown in Equations (7) and (8), respectively: 1 = ∑ (0, − ) =1 | = ∑( , ⋅ ) =1 , ∀ ∊ (7) (8) 2 = ∑ (0, − ) =1 | = ∑( , ⋅ ) =1 , ∀ ∊
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