2078 2.2.3 Scenario 3: incorporating specific energy into the block value For this scenario, Equation (1) was adapted for different processing costs as a function of the total specific energy (kWh/t) obtained from Mazzinghy et al. (2025). For blocks with any metal content, it was verified that the mean, minimum, and maximum values of energy consumption were 11.7, 7.3, and 15.4 kWh/t, respectively. Therefore, given that an average processing cost of f3 = 4.0 $/h was adopted by Minelib (2025), this cost was associated with the average specific energy ̅ <c̅̅̅ = 7.3 k1ℎ/? from Mazzinghy et al. (2025), and then a proportional processing cost value <c, associated with the energy consumption of each block was calculated. Equation (2) presents the function used in scenario 3: %/,, = %/ ⋅ <c, / <c̅̅̅, ∀_ ∊ b (2) where %/ → %/,, ∀_ ∊ b. 2.2.4 Scenario 4: incorporating both variable recovery and specific energy into the block value Finally, for this scenario, Equation (1) was adapted for both different recovery and specific energy ∀_ ∊ b, as shown in Equation (3), incorporating all the changes proposed in the previous scenarios: * (3) N, = OP QRS → U, ⋅ ∑ (Y,,) ⋅ R,,) ⋅ (Z) − [))) − U, ⋅ (%.) − U, ⋅ (%/,,) ù=1 Q?ℎSR^O[S → −U, ⋅ (%.) 2.3 Mine sequencing model and simulated annealing metaheuristic 2.3.1 A mine sequencing model The mine sequencing problem was modelled as a direct block scheduling (DBS) approach. For a block ∀_ ∊ b and an annual period ∀? ∊ !, an integer variable l,,4 ∊ {0,1} equals 1 if the block _ is completely extracted in the period ?, or 0 otherwise. Therefore, for a discount rate oR = 0.1 and for one type of block values as mentioned in the different scenarios, an economic return SR,,4 can be obtained from the excavation (and processing) of a block _ during time period ?, resulting in the objective function modelled as Equation (4): 5 6 (4) UplOAOqS ∑ ∑(l,,4 ⋅ SR,,4) − ZSrps?OS[ †=1 °=1 Since t equals a set of time periods ? ∊ ! and b, is the list of blocks _′ that precede a block _ ∊ b, 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: ∑(D/,5) ≤ ∑(D/′,5) , ∀2 ∊ ~, ∀2′ ∊ ~/, ∀% ∊ > ¢ ≤ ° ¢ ≤ ° (5) § (6) ∑(l,,4) ≤ 1, ∀_ ∊ b °=1
RkJQdWJsaXNoZXIy MTM0Mzk2