# Two-Sided Matching Decision Method of Electricity Sales Package Based on Disappointment Theory
## 3 Matching Method between Power User Demand and Power-Selling Package of Power-Selling Company
### Multi-Objective Optimization Model  
Next, after obtaining the satisfaction matrix of power user set \(P\) and the satisfaction matrix of power sales package set \(Q\), a two-objective optimization model can be constructed, and the optimal stable matching of both parties can be obtained by solving the model.  
Set \(x_{ij}\) as a binary decision variable. When the user \(P_{i}\) matches the package \(Q_{j}\), \(x_{ij}=1\); otherwise, \(x_{ij}=0\).  
With the maximum satisfaction of electric power customers and electricity sales package as the optimization objective, a stable two-sided matching multi-objective optimization model can be established:  
\[\text{max}Z_{1}=\sum_{i=1}^{n}\sum_{j=1}^{m}\overline{u_{ij}^{p}}x_{ij} \tag{37}\]  
\[\text{max}Z_{2}=\sum_{j=1}^{m}\sum_{i=1}^{n}\overline{u_{ij}^{\Omega}}x_{ij} \tag{38}\]  
\[\sum_{j=1}^{m}x_{ij}\leq 1,\ i\in I \tag{39}\]  
\[\sum_{i=1}^{n}x_{ij}\leq 1,\ j\in J \tag{40}\]  
\[x_{ij}+\sum_{u_{ij}^{p}>u_{ij}^{p}}x_{ih}+\sum_{u_{ij}^{\Omega}>u_{ij}^{\Omega }}x_{ij}\geq 1,\ \forall(P_{i},Q_{j})\in\Omega \tag{41}\]  
\[x_{ij}\in\{0,1\}\ i\in I,\ j\in J \tag{42}\]  
In the above model, formulas (37) and (38) are objective functions, which describe the maximization of satisfaction between electric power customers and electricity sales packages. Equations (39) and (40) are inequality constraints, which respectively ensure that each object in user \(P\) can only match one package in package \(Q\) at most, and that one power-selling package in package set \(Q\) can only match one user in user set \(P\). Equation (41) is a stable two-sided matching constraint, including two situations: (1) power user \(P_{i}\) and electricity sales package \(Q_{j}\) match each other; (2) if power user \(P_{i}\) does not match the electricity sales package \(Q_{j}\), then power user \(P_{i}\) will match electricity sales package \(Q_{j}\) with a higher degree of preference or electricity sales package \(Q_{j}\) will match power user \(P_{i}\) with a higher degree of preference. In Equation (41), the meaning of \(\overline{u_{ih}^{p}}>\overline{u_{ij}^{p}}\) is that, in the electricity user set P, the preference of the \(i\)-th power user for the \(h\)-th electricity sales package is higher than that for the \(j\)-th electricity sales package. Similarly, the meaning of \(\overline{u_{ih}^{p}}>\overline{u_{ij}^{p}}\) is that, in the electricity sales package set \(Q\), the preference of the \(j\)-th electricity sales package for the \(k\)-th electricity user is higher than that for the \(i\)-th electricity user.  
In order to facilitate the solution, the weight coefficient \(\omega\) is introduced to transform the two-objective optimization model into a single-objective optimization model:  
\[\text{max}Z=\omega\sum_{i=1}^{n}\sum_{j=1}^{m}\overline{u_{ij}^{p}}x_{ij}+(1 -\omega)\sum_{j=1}^{m}\sum_{i=1}^{n}\overline{u_{ij}^{\Omega}}x_{ij} \tag{43}\]  
\[\sum_{j=1}^{m}x_{ij}\leq 1,\ i\in I \tag{44}\]  
\[\sum_{i=1}^{n}x_{ij}\leq 1,\ j\in J \tag{45}\]  
\[x_{ij}+\sum_{u_{ij}^{\Omega}>u_{ij}^{p}}x_{ih}+\sum_{u_{ij}^{\Omega}>u_{ij}^{ \Omega}}x_{ij}\geq 1,\ \forall(P_{i},Q_{j})\in\Omega \tag{46}\]\[x_{ij}\in\{0,1\},\;i\in I,\;j\in J \tag{47}\]  
In model (43), \(Z\) represents the total satisfaction of the matching parties, and \(\omega\) is a weight coefficient, where \(0<\omega<0.5\) indicates that the feeling of electric power customers is more important than the adaptation degree of the electricity sales package, \(0.5<\omega<1\) indicates that the adaptability of the electricity sales package is more important than the satisfaction of the electric power customers, and \(\omega=0.5\) indicating that both parties are equally important. In this paper, we take \(\omega=0.5\) for analysis.  
According to the two-sided matching theory, after adding the disappointment-elation perception effect of electric power customers and electricity sales packages, the stable two-sided matching process between electric power customers and electricity sales package is as shown in Figure 3.