Table 7 Fundamental equations of five subsystems.
Category | Equations |
|---|---|
Geological reserve subsystem | \({Q_a}=INTEG(0 - {Q_d},{Q_{{m_I}}}+{Q_{{m_{II}}}}+{Q_{{m_{III}}}})\) |
\({Q_{{a_i}}}=INTEG(0 - {Q_{{d_i}}},{Q_{{m_i}}}){\text{ }}i{\text{=}}I,II,III\) | |
\({Q_{{d_i}}}={Q_{{t_i}}} \times {(1 - {\mu _i})^{ - 1}}\) | |
\({Q_{{m_{_{i}}}}}={Q_i} \times (1 - {\mu _i}) \times {(1 - {\rho _i})^{ - 1}}\) | |
Mining subsystem | \({g_{{e_i}}}={g_{{k_i}}} \times (1-{\rho _i})\) |
\({T_i}=INTEGER{({Q_{{m_i}}} \times {Q_{{t_i}}})^{ - 1}}\) | |
Ore processing and smelting subsystem | \({Q_{{r_i}}}=IF{\text{ }}THEN{\text{ }}ELSE(Time \leqslant {T_i},{Q_{{t_i}}},0){\text{ }}\) |
\({g_h}=({Q_{{t_{_{I}}}}} \times {g_{{e_I}}}+{Q_{{t_{II}}}} \times {g_{{{\text{e}}_{II}}}}+{Q_{{t_{III}}}} \times {g_{{e_{III}}}}) \times {({Q_{{t_{_{I}}}}}+{Q_{{t_{II}}}}+{Q_{{t_{III}}}})^{ - 1}}\) | |
\({M_c}={Q_r} \times {10^4} \times {g_h} \times {\gamma _h} \times {g_m}^{{ - 1}}\) | |
\({M_t}={Q_r} - {M_c}\) | |
\(M={M_c} \times {g_m} \times 0.001 \times {\gamma _s} \times {\gamma _c}\) | |
Financial subsystem | \(P=INTEG(R+{P_u}+\sum\nolimits_{{i=1}}^{I} \pi (\Delta {e_i}) - C,0)\) |
\(R={P_g} \times M \times 0.1\) | |
\(C=K+{C_p}\) | |
\({P_u}={P_u}^{o} \times {M_t} \times {10^4}\) | |
\({C_f}=C \times {Q_r}^{{ - 1}}\) | |
\({C_g}=C \times 10 \times {M^{ - 1}}\) | |
\({S_t}=R \times 0.06\) | |
\(\begin{gathered} {C_p}={C_u}+{C_d}+({C_o}+{C_s}+{C_h}) \times {Q_r}+{C_{{m_I}}} \times {Q_{{r_I}}}+{C_{{m_{II}}}} \times {Q_{{r_{II}}}}+{C_{{m_{III}}}} \times {Q_{{r_{III}}}} \hfill \\ +w \times (W({Q_{{r_I}}},{J_I})+W({Q_{{r_{II}}}},{J_{II}})+W({Q_{{r_{III}}}},{J_{III}}))+{J_I}+{J_{II}}+{J_{III}}+{S_t} \hfill \\ \end{gathered} \) | |
\({C_d}={C_d}^{o} \times {M_t} \times {10^{ - 4}}\) | |
\({C_u}={C_u}^{o} \times {M_t} \times {10^{ - 4}}\) | |
Carbon reduction subsystem | \(W({Q_{{r_i}}},{J_i})=3{Q_{{r_i}}}^{2}{(8067+{J_i})^{ - 1}}\) |
\(\sum\nolimits_{{i=1}}^{I} \pi (\Delta {e_i})=\beta \times \sum\nolimits_{{i=1}}^{I} {\Delta {e_i}} \) | |
\(w=\left\{ \begin{gathered} {L_w},\sum\nolimits_{{i=1}}^{I} {W({Q_{{r_i}}},{J_i})} \in (0,{\chi _1}) \hfill \\ \frac{{({L_w} - {U_w})}}{{{{({\chi _1} - {\chi _2})}^2}}}{(\sum\nolimits_{{i=1}}^{I} {W({Q_{{r_i}}},{J_i})} - {\chi _2})^2}+{U_w},\sum\nolimits_{{i=1}}^{I} {W({Q_{{r_i}}},{J_i})} \in \left[ {{\chi _1},{\chi _2}} \right] \hfill \\ {U_w},\sum\nolimits_{{i=1}}^{I} {W({Q_{{r_i}}},{J_i})} \in ({\chi _2},+\infty ) \hfill \\ \end{gathered} \right.\) |
