## 2 Task Description and Mathematical Model of Agricultural Machinery Rental
### QoS Evaluation Model  
To solve various optimal combination problems, QoS evaluation models are often used [19] and have a great effect. Therefore, the QoS evaluation model is used in the paper. Due to the universality of the calculation method, to establish a QoS evaluation model, this paper only uses urgency of time (\(UT\)), working conditions (\(WC\)), size (\(SE\)) and distance (\(DT\)) to achieve this goal. The evaluation will also involve terrain, planting characteristics, weather and other factors under special circumstances. This paper only considers several common factors that are suitable for standardized farmland without special circumstances, which is not much different from reality. * Urgency of time (\(UT\)): Urgency of time is mainly determined by the optimal harvest time. The rental task that is closer to the optimal harvest time will have a greater urgency of time. This task must be given priority to avoid delaying farming production;
* Working conditions (\(WC\)): Working conditions are mainly determined by soil conditions, traffic conditions and all kinds of farm crop conditions. The preliminary data are given by farmers;
* Size (\(SE\)): The size of farmland can represent the profit that can be obtained in the rental service. In a rental service, the larger the size of the farmland is, the higher the profit, which is also the ideal situation in the agricultural machinery rental service. \(SE\) data are given by farmers;
* Distance (\(DT\)): The cost loss in the scheduling process is represented by the \(DT\). The coordinate position is uploaded by farmers through the client;
* Dynamic Coefficient (\(P\)): A key indicator in the QoS evaluation model is urgency of time. Therefore, the purpose of setting the dynamic coefficient is to adjust the proportion of urgency of time in the QoS evaluation model. To avoid the emergence of discontinuities and fluctuations, fixed coefficients cannot be adopted to control the proportion of urgency of time. Therefore, to solve this problem, this paper proposes a dynamic coefficient. According to data analysis, there is a certain functional relationship between the dynamic coefficient and the urgency of time; that is, the higher the \(UT\) of a task is, the greater the proportion of the \(UT\) of the task in the QoS evaluation model. According to the  
Figure 1: Multitasking composition process. research of [PERSON] et al. [17] and the verification of this paper, the calculation method of the dynamic coefficient \(P\) is shown in Equation (1):  
\[P=\frac{UT^{2}}{100} \tag{1}\]  
Since the quantitative unit and range interval of each evaluation index are different, the same quantitative method is used for data processing to improve the accuracy of the evaluation model. The data can be divided into two categories: positive and negative attributes [20]. For positive attributes (\(q_{i}^{+}\)), including urgency of time, working conditions and size, Equation (2) is the calculation method. For the negative attribute (\(q_{i}^{-}\)), including distance, Equation (3) is the calculation method. \[q_{i}^{+}=\left\{ \begin{array}{ll}\frac{x_{i}-x_{min}}{x_{max}-x_{min}},& \text{if }x_{max}\
eq x_{min}\\ 1,&\text{if }x_{max}=x_{min}\end{array} \right. \tag{2}\]  
\[q_{i}^{-}=\left\{ \begin{array}{ll}\frac{x_{i}-x_{min}}{x_{min}-x_{max}},& \text{if }x_{max}\
eq x_{min}\\ 1,&\text{if }x_{max}=x_{min}\end{array} \right. \tag{3}\]  
Each agricultural machine executes many tasks consecutively, and the QoS evaluation model can be described as follows:  
\[QoS(s)= \begin{bmatrix}q_{ut}(S_{1})&q_{wc}(S_{1})&q_{se}(S_{1})&q_{dt}(S_{1}) \\ q_{ut}(S_{2})&q_{wc}(S_{2})&q_{se}(S_{2})&q_{dt}(S_{2})\\ \vdots&\vdots&\vdots&\vdots\\ q_{ut}(S_{m})&q_{wc}(S_{m})&q_{se}(S_{m})&q_{dt}(S_{m})\end{bmatrix}  \tag{4}\]  
The aggregation of the individual evaluation index is the QoS model combination evaluation index [21]. The aggregation method depends on the task structure of the model.