## 2 Problem Formulation
### Problem Formulation with the Extended E-CARGO Model
The normalization method is as follows:  
\[q^{\prime}_{ij}~{}=~{}\frac{q_{ij}-\min(q_{j})}{\max(q_{j})-\min(q_{j})}. \tag{1}\]  
where \(q^{\prime}_{ij}\) represents the value after the normalization of \(q_{ij}\), \(\min(q_{j})\) represents the minimum value of the \(j\)th column, and \(\max(q_{j})\) represents the maximum value of the \(j\)th column. The maintenance time when the \(i\)th resource completes the \(j\)th maintenance task is denoted as \(t_{ij}\), and the maintenance time matrix is expressed as \(QT[i,j]~{}=~{}t_{ij}\). Both the platform and the user want the maintenance time to be as short as possible, so the maintenance time is inversely related to the evaluation value. Therefore, the time evaluation matrix is expressed as the reciprocal of the real maintenance time. The time matrix is normalized as \(Q_{t}[i,j]~{}=~{}qt_{ij}\). The maintenance cost when the \(i\)th resource completes the \(j\)th maintenance task is denoted as \(c_{ij}\), and the maintenance cost matrix is expressed as \(QC[i,j]~{}=~{}c_{ij}\). The platform wants the maintenance cost to be as low as possible, so the maintenance cost is inversely related to the evaluation value. Therefore, the cost evaluation matrix is expressed as the reciprocal of the real maintenance cost. The cost matrix is normalized as \(Q_{c}[i,j]~{}=~{}qc_{ij}\). The maintenance price when the \(i\)th resource completes the \(j\)th maintenance task is denoted as \(p_{ij}\), and the maintenance price matrix is expressed as \(QP[i,j]~{}=~{}p_{ij}\). The user wants the maintenance price to be as low as possible, so the maintenance price is inversely related to the evaluation value. Therefore, the price evaluation matrix is expressed as the reciprocal of the real maintenance price. The price matrix is normalized as \(Q_{p}[i,j]~{}=~{}qp_{ij}\). **Definition 5**. : _The role vector is denoted by \(L\), representing the number of resources required for each task. L[j] denotes the number of agents required to assume role j. In this article, each maintenance task may require multiple resource groups; for example, \(L\) = [1,2,1,4] means that the first task requires one resource group, the second task requires two resource groups, the third task requires one resource group, and the fourth task requires four resource groups. The value of each number in L[j] is in the range \(0\leq L[j]\leq m\), \(\sum\limits_{j\,=\,1}^{m}L[j]~{}=~{}L_{m}\leq m\) (where \(m\) is the total number of tasks and L[j] must be a natural number). With vector \(L\), we know how many resource groups must be assigned to each task._  
**Definition 6**. : _The effect produced by the maintenance group to maintain the equipment is defined as the effect value. Then, the maintenance effect values formed by the maintenance time, maintenance cost, and maintenance price are denoted as \(\sigma_{t}\), \(\sigma_{c}\), and \(\sigma_{p}\), respectively, and the solution formulas are as follows:_  
\[\sigma_{t}~{}=~{}\sum\limits_{i\,=\,1}^{m}\sum\limits_{j\,=\,1}^{n}Q_{t}[i,j] \times T[i,j], \tag{2}\]  
\[\sigma_{c}~{}=~{}\sum\limits_{i\,=\,1}^{m}\sum\limits_{j\,=\,1}^{n}Q_{c}[i,j] \times T[i,j], \tag{3}\]  
\[\sigma_{p}~{}=~{}\sum\limits_{i\,=\,1}^{m}\sum\limits_{j\,=\,1}^{n}Q_{p}[i,j] \times T[i,j]. \tag{4}\]  
_where \(\sigma_{c}\) is the cost benefit of the platform, \(\sigma_{p}\) is the price benefit of the user, and \(\sigma_{t}\) is the time benefit of both the platform and the user._