, = ∑( , , ) ∈ + ∑( , , ) ∈ + ∑( , , ∗ , ) ∈ ∀ ∈ ℂ, ∈ ℙ (3) , =∑( , , ∗ , + , , ∗ , ) ∈ + ∑( , , ∗ , + , , ∈ ∗ , ) ∀ ∈ ℂ, ∈ ℙ (4) Gross revenue function for each period is given by Equation 2, where , , represents the recovered metal and is the price evaluated for the product at the moment of sale. In Equation 3, the operational costs are computed based on , , (trucks’ operating costs), , , (shovels’ operating cost), , , (tonnage delivered for processing) and , (processing cost). In the case of total penalties, Equation 4 displays the disaggregation of penalties from production variations ( , , as material surplus, , , as material slack, , and , for the cost of variation above and below the production target, respectively) and penalties from grade variations ( , , as difference of grade over target, , , for grade under target, , and , for the cost of grade variation above and below target grade, respectively). The model evaluates ancillary variables to store and simplify the values of mining production (PROD), weighted grade (GRAD), and recovered metal (RM) for each destination and period. These variables are given by: , , =∑∑∑∑( , , , , , ∗ , ∗ , , , ) ∈ ∈ ∈ ∈ ∀ ∈ ℂ, ∈ ℙ, ∈ (5) , , =∑∑∑∑( , , , , , ∗ , ∗ , , , ∗ , , +ℯ ) ∈ ∈ ∈ ∈ ∀ ∈ ℂ, ∈ ℙ, ∈ (6) , , = , , ∗ , , ∗ , ∀ ∈ ℂ, ∈ ℙ, ∈ (7) From Equations 5 and 6 above, , , , , represents the allocation of a truck to a shovel to perform a material transportation at a given moment during the period of analysis, , is the effective heaped capacity of the truck, , , represents the shovel allocation to a given muck pile, is the weighted grade of each muckpile, and ℯ represents a small enough number to prevent division by zero in case the production associated with a given destination is none, therefore ℯ≈
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