$$ \begin{aligned}
& {\text{Min}}G = \frac{{\sum_{u = 1}^I {\sum_{z =
1}^I {\left| {\frac{1}{{{S_u}}}(\pi _{u,t}^0 + \sum_{r \in
{I_t}} {\pi _{u,t}^r{\text{AW}}_r} ) - \frac{1}{{{S_z}}}(\pi
_{z,t}^0 + \sum_{r \in {I_t}} {\pi _{z,t}^r{\text{AW}}_r} )}
\right|} } }}{{2I\sum_{i = 1}^I {\frac{1}{{{S_i}}}} (\pi
_{i,t}^0 + \sum_{r \in {I_t}} {\pi _{i,t}^r{\text{AW}}_r} )}}
\\ & {\text{s.t.}}\ \left\{\begin{array}{l}\sum\limits_{t =
1}^T {\sum\limits_{i = 1}^I {\pi _{i,t}^0} } + \left(
{\sum\limits_{i = 1}^I {\sum\limits_{r \in {I_t}} {\pi _{i,t}^r - 1}
} } \right){\text{AW}}_r \leqslant 0 \\ D_i^{{\rm min}} - \left(
{\pi _{i,t}^0 + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^r{\text{AW}}_r} } \right) \leqslant 0 \\
{(d_i^{{\text{Ind}}})_{{\rm min}}} - \left( {\pi _{i,t}^{0,{\text{Ind}}}
+ \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Ind}}}{\text{AW}}_r} } \right) \leqslant 0
\\ \left( {\pi _{i,t}^{0,{\text{Ind}}} + \sum\limits_{r \in {I_t}}
{\pi _{i,t}^{r,{\text{Ind}}}{\text{AW}}_r} } \right) -
c_i^{{\text{Ind}}} \leqslant 0 \\
{(d_i^{{\text{Agr}}})_{{\rm min}}} - \left( {\pi _{i,t}^{0,{\text{Agr}}}
+ \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Agr}}}{\text{AW}}_r} } \right) \leqslant 0
\\ \left( {\pi _{i,t}^{0,{\text{Agr}}} + \sum\limits_{r \in {I_t}}
{\pi _{i,t}^{r,{\text{Agr}}}{\text{AW}}_r} } \right) -
c_i^{{\text{Agr}}} \leqslant 0 \\ c_i^{{\text{Dom}}} -
\left( {\pi _{i,t}^{0,{\text{Dom}}} + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Dom}}}{\text{AW}}_r} } \right) \leqslant 0
\\ {(d_i^{{\text{Dom}}})_{{\rm min}}} - \left( {\pi
_{i,t}^{0,{\text{Dom}}} + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Dom}}}{\text{AW}}_r} } \right) \leqslant 0
\\ {(d_i^{{\text{Eco}}})_{{\rm min}}} - \left( {\pi
_{i,t}^{0,{\text{Eco}}} + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Eco}}}{\text{AW}}_r} } \right) \leqslant 0
\\ s_i^{2 + } - s_i^{2 - } + s_i^{3 + } - s_i^{3 - } + s_i^{4 + } +
s_i^{4 + + } + s_i^{5 + } - s_i^{5 - } \\ \quad +
(p_i^{{\text{Ind}}} + p_i^{{\text{Dom}}} + p_i^{{\text{Agr}}}) = 0
\\ s_i^{2 + }\left( {\pi _{i,t}^{0,{\text{Ind}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Ind}}}{\text{AW}}_r}
- {{(d_i^{{\text{Ind}}})}_{{\rm min}}}} \right) - s_i^{2 -
}(c_i^{{\text{Ind}}} - (\pi _{i,t}^{0,{\text{Ind}}} + \sum\limits_{r
\in {I_t}} {\pi _{i,t}^{r,{\text{Ind}}}{\text{AW}}_r} )) \\
\quad + s_i^{3 + }\left( {\pi _{i,t}^{0,{\text{Agr}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Agr}}}{\text{AW}}_r}
- {{(d_i^{{\text{Agr}}})}_{{\rm min}}}} \right) - s_i^{3 - }\left(
{c_i^{{\text{Agr}}} - \left( {\pi _{i,t}^{0,{\text{Agr}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Agr}}}{\text{AW}}_r}
} \right)} \right) \\ \quad + s_i^{4 + }\left( {\pi
_{i,t}^{0,{\text{Dom}}} + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Dom}}}{\text{AW}}_r} - c_i^{{\text{Dom}}}} \right)
+ s_i^{4 + + }\left( {\pi _{i,t}^{0,{\text{Dom}}} + \sum\limits_{r
\in {I_t}} {\pi _{i,t}^{r,{\text{Dom}}}{\text{AW}}_r} -
{{(d_i^{{\text{Dom}}})}_{{\rm min}}}} \right) \\ \quad + s_i^{5
+ }\left( {\pi _{i,t}^{0,{\text{Eco}}} + \sum\limits_{r \in {I_t}}
{\pi _{i,t}^{r,{\text{Eco}}}{\text{AW}}_r} -
{{(d_i^{{\text{Eco}}})}_{{\rm min}}}} \right) - s_i^{5 - }\left(
{{{(d_i^{{\text{Eco}}})}_{{\rm max}}} - \left( {\pi
_{i,t}^{0,{\text{Eco}}} + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Eco}}}{\text{AW}}_r} } \right)} \right. = 0
\\ s_i^6\left( {\left( {\pi _{i,t}^{0,{\text{Ind}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Ind}}}{\text{AW}}_r}
} \right) + \left( {\pi _{i,t}^{0,{\text{Agr}}} + \sum\limits_{r \in
{I_t}} {\pi _{i,t}^{r,{\text{Agr}}}{\text{AW}}_r} } \right)} \right.
\\ \quad \left. { + \left( {\pi _{i,t}^{0,{\text{Dom}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Dom}}}{\text{AW}}_r}
} \right) + \left( {\pi _{i,t}^{0,{\text{Eco}}} + \sum\limits_{r \in
{I_t}} {\pi _{i,t}^{r,{\text{Eco}}}{\text{AW}}_r} } \right)} \right)
= 0 \\ \pi _{i,t}^0 + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^r{\text{AW}}_r} \geqslant 0,\pi _{i,t}^{0,{\text{Ind}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Ind}}}{\text{AW}}_r
\geqslant 0} \\ \pi _{i,t}^{0,{\text{Agr}}} +
\sum\limits_{r \in {I_t}} {\pi _{i,t}^{r,{\text{Agr}}}{\text{AW}}_r
\geqslant 0,\pi _{i,t}^{0,{\text{Dom}}} + \sum\limits_{r \in {I_t}}
{\pi _{i,t}^{r,{\text{Dom}}}{\text{AW}}_r \geqslant 0} } \\
\pi _{i,t}^{0,{\text{Eco}}} + \sum\limits_{r \in {I_t}} {\pi
_{i,t}^{r,{\text{Eco}}}{\text{AW}}_r \geqslant 0,s_i^{j \pm }
\geqslant 0,j = 1 \ldots 5,s_i^6 \geqslant 0}\end{array} \right.
\end{aligned} $$
(20)
$$ \begin{aligned}
& {\text{Min}}G = \frac{{\sum_{u = 1}^I {\sum_{z = 1}^I {\left| {\left( {\frac{{\pi _{u,t}^0}}{{{S_u}}} - \frac{{\pi _{z,t}^0}}{{{S_z}}}} \right) + \left( {\sum_{t = 1}^T {\gamma _1^u} {\text{AW}}^{*} - \sum_{t = 1}^T {\gamma _1^z} {\text{AW}}^{*}} \right) + \theta \left( {\sum_{t = 1}^T {\rho _1^u{\text{AW}}^{*}} + \sum_{t = 1}^T {\rho _1^z{\text{AW}}^{*}} } \right)} \right|} } }}{{2I\sum\limits_{i = 1}^I {\left( {\frac{{\pi _{i,t}^0}}{{{S_i}}} + \sum\nolimits_{t = 1}^T {\gamma _1^i} {\text{AW}}^{*} + \theta \sum\nolimits_{t = 1}^T {\rho _1^i{\text{AW}}^{*}} } \right)} }} \cr
& {\text{s.t.}}\ \left\{ \begin{array}{l}
D_i^{{\rm min}} - \left( {\pi _{i,t}^0 + \sum\limits_{t = 1}^T {{\gamma _1}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _1}{\text{AW}}^{*}} } \right) \leqslant 0 \\
\sum\limits_{i = 1}^I {\pi _{i,t}^0} + \sum\limits_{t = 1}^T {{\gamma _2}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _2}{\text{AW}}^{*}} \leqslant 0 \\
{(d_i^{{\text{Ind}}})_{{\rm min}}} - \left( {\pi _{i,t}^{0,{\text{Ind}}} + \sum\limits_{t = 1}^T {{\gamma _3}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _3}{\text{AW}}^{*}} } \right) \leqslant 0 \\
\left( {\pi _{i,t}^{0,{\text{Ind}}} + \sum\limits_{t = 1}^T {{\gamma _3}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _3}{\text{AW}}^{*}} } \right) - c_i^{{\text{Ind}}} \leqslant 0 \\
{(d_i^{{\text{Agr}}})_{{\rm min}}} - \left( {\pi _{i,t}^{0,{\text{Agr}}} + \sum\limits_{t = 1}^T {{\gamma _4}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _4}{\text{AW}}^{*}} } \right) \leqslant 0 \\
\left( {\pi _{i,t}^{0,{\text{Agr}}} + \sum\limits_{t = 1}^T {{\gamma _4}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _4}{\text{AW}}^{*}} } \right) - c_{\text{i}}^{{\text{Agr}}} \leqslant 0 \\
c_i^{{\text{Dom}}} - \left( {\pi _{i,t}^{0,{\text{Dom}}} + \sum\limits_{t = 1}^T {{\gamma _5}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _5}{\text{AW}}^{*}} } \right) \leqslant 0 \\
{(d_i^{{\text{Dom}}})_{{\rm min}}} - \left( {\pi _{i,t}^{0,{\text{Dom}}} + \sum\limits_{t = 1}^T {{\gamma _5}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _5}{\text{AW}}^{*}} } \right) \leqslant 0 \\
{(d_i^{{\text{Eco}}})_{{\rm min}}} - \left( {\pi _{i,t}^{0,{\text{Eco}}} + \sum\limits_{t = 1}^T {{\gamma _6}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _6}{\text{AW}}^{*}} } \right) \leqslant 0 \\
\left( {\pi _{i,t}^{0,{\text{Eco}}} + \sum\limits_{t = 1}^T {{\gamma _6}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _6}{\text{AW}}^{*}} } \right) - {(d_i^{{\text{Eco}}})_{{\rm max}}} \leqslant 0 \\
s_i^{2 + } - s_i^{2 - } + s_i^{3 + } - s_i^{3 - } + s_i^{4 + } + s_i^{4 + + } + s_i^{5 + } - s_i^{5 - } \\
\quad + (p_i^{{\text{Ind}}} + p_i^{{\text{Dom}}} + p_i^{{\text{Agr}}}) = 0 \\
(s_i^{2 + }\pi _{i,t}^{0,{\text{Ind}}} + s_i^{2 - }\pi _{i,t}^{0,{\text{Ind}}} + s_i^{3 + }\pi _{i,t}^{0,{\text{Agr}}} + s_i^{3 - }\pi _{i,t}^{0,{\text{Agr}}} + s_i^{4 + }\pi _{i,t}^{0,{\text{Dom}}} + s_i^{4 + + }\pi _{i,t}^{0,{\text{Dom}}} + s_i^{5 + }\pi _{i,t}^{0,{\text{Eco}}} + s_i^{5 - }\pi _{i,t}^{0,{\text{Eco}}}) \\
\quad + \left( {s_i^{2 + }\left( {\sum\limits_{t = 1}^T {{\gamma _3}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _3}{\text{AW}}^{*}} } \right) + s_i^{2 - }\left( {\sum\limits_{t = 1}^T {{\gamma _3}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _3}{\text{AW}}^{*}} } \right)} \right. \\
\quad + s_i^{3 + }\left( {\sum\limits_{t = 1}^T {{\gamma _4}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _4}{\text{AW}}^{*}} } \right) + s_i^{3 - }\left( {\sum\limits_{t = 1}^T {{\gamma _4}} {\text{AW}}^{*} - \theta \sum\limits_{t = 1}^T {{\rho _4}{\text{AW}}^{*}} } \right) \\
\quad + s_i^{4 + }\left( {\sum\limits_{t = 1}^T {{\gamma _5}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _5}{\text{AW}}^{*}} } \right) + s_i^{4 + + }\left( {\sum\limits_{t = 1}^T {{\gamma _5}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _5}{\text{AW}}^{*}} } \right) \\
\quad \left. { + s_i^{5 + }\left( {\sum\limits_{t = 1}^T {{\gamma _6}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _6}{\text{AW}}^{*}} } \right) + _i^{5 - }\left( {\sum\limits_{t = 1}^T {{\gamma _6}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _6}{\text{AW}}^{*}} } \right)} \right) \\
\quad - (s_i^{2 + }{(d_i^{{\text{Ind}}})_{{\rm min}}} + s_i^{2 - }c_i^{{\text{Ind}}} + s_i^{3 + }{(d_i^{{\text{Agr}}})_{{\rm min}}} + s_i^{3 - }c_i^{{\text{Agr}}} + s_i^{4 + }c_i^{{\text{Dom}}} + s_i^{4 + + }{(d_i^{{\text{Dom}}})_{{\rm min}}} + s_i^{5 + }{(d_i^{{\text{Eco}}})_{{\rm min}}} + s_i^{5 - }{(d_i^{{\text{Eco}}})_{{\rm max}}}) = 0 \\
s_i^6\pi _{i,t}^0 + \sum\limits_{t = 1}^T {{\gamma _7}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _7}A{W^*}} = 0 \\
\pi _{i,t}^0 + \sum\limits_{t = 1}^T {{\gamma _1}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _1}{\text{AW}}^{*}} \geqslant 0,\pi _{i,t}^{0,{\text{Ind}}} + \sum\limits_{t = 1}^T {{\gamma _3}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _3}{\text{AW}}^{*} \geqslant 0,} \\
\pi _{i,t}^{0,{\text{Agr}}} + \sum\limits_{t = 1}^T {{\gamma _4}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _4}{\text{AW}}^{*} \geqslant 0} ,\pi _{i,t}^{0,{\text{Dom}}} + \sum\limits_{t = 1}^T {{\gamma _5}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _5}{\text{AW}}^{*} \geqslant 0,} \\
\pi _{i,t}^{0,{\text{Eco}}} + \sum\limits_{t = 1}^T {{\gamma _6}} {\text{AW}}^{*} + \theta \sum\limits_{t = 1}^T {{\rho _6}{\text{AW}}^{*} \geqslant 0} ,s_i^{j \pm } \geqslant 0,j = 1 \ldots 5,s_i^6 \geqslant 0 \\
\end{array} \right.\end{aligned} $$
(21)
$$ \begin{aligned} \gamma_{1} & = \sum\limits_{i = 1}^{T} {\pi_{i,t}^{r} } , - \rho_{1} \le \gamma_{1} \le \rho_{1} \\ \gamma_{2} & = \sum\limits_{i = 1}^{I} {\sum\limits_{i = 1}^{T} {\pi_{i,t}^{r} } } - 1, - \rho_{2} \le \gamma_{2} \le \rho_{2} \\ \gamma_{3} & = \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Ind}}}} } , - \rho_{3} \le \gamma_{3} \le \rho_{3} \\ \gamma_{4} & = \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Agr}}}} } , - \rho_{4} \le \gamma_{4} \le \rho_{4} \\ \gamma_{5} & = \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Dom}}}} } , - \rho_{5} \le \gamma_{5} \le \rho_{5} \\ \gamma_{6} & = \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Eco}}}} } , - \rho_{6} \le \gamma_{6} \le \rho_{6} \\ \gamma_{7} & = s_{i}^{6} \left( {\sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Ind}}}} } + \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Agr}}}} } + \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Dom}}}} } + \sum\limits_{t = 1}^{T} {\pi_{i,t}^{{r,{\text{Eco}}}} } } \right), \\ &\quad - \rho_{7} \le \gamma_{7} \le \rho_{7} \\ \end{aligned} $$
(22)