# A Multi-Customer Vehicle Scheduling Optimization Method for Coal Intelligent Loading System
## 3 Construction of Vehicle Scheduling Optimization Model for Coal Mine Enterprises
### Determination of Customer Order Priority
#### 3.1.2 Customer Prioritization Based on VIKOR Method  
VIKOR is a multi-criteria decision-making method based on ideal point compromise ordering. It is characterized by its ability to determine the ordering of finite decision options by considering both the maximization of group utility and the minimization of individual regret [31]. In this paper, the VIKOR method is employed to prioritize customer orders. The specific steps are outlined below:  
(1) Standardized Data Processing  
\(a_{u}\) denotes the \(u\) order. The term \(a_{uv}\) (where \(v=1,2,3,4,5\)) denotes the initial value of the \(v\) influencing factor associated with order \(u\). Through the process of normalized transformation, customer order data are normalized to fall within the range of [0, 1] using the following conversion formulas:  
\[x_{uv}=\frac{x_{uv}-min\ x_{uv}}{max\ x_{uv}-min\ x_{uv}} \tag{1}\]  
\[x_{uv}=\frac{max\ x_{uv}-x_{uv}}{max\ x_{uv}-min\ x_{uv}} \tag{2}\]  
where: \(x_{uv}\) represents the indicator value of the \(v\) influencing factor of the \(u\) order, and \(max\ x_{uv}\) and \(min\ x_{uv}\) represent the maximum and minimum values of the \(v\) influencing factor indicator of the order with priority to be determined, respectively. In addition, the benefit indicator is converted using Formula (1) and the cost indicator is converted using Formula (2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Influencing Factor** & **Indicators** & \begin{tabular}{c} **Indicators** \\ **Classification** \\ \end{tabular} & **Description** \\ \hline \begin{tabular}{c} Urgency of \\ delivery date \\ \end{tabular} & \(X_{1}\) & Cost indicator & \
\begin{tabular}{c} The more urgent the delivery date \\ of the order, the higher the level. \\ The higher the default cost of the \\ order, the higher the level. \\ The better the relationship \\ between the enterprise and the \\ customer, the higher the level. \\ The higher the profit of the \\ product \\ On-time \\ delivery rate \\ \end{tabular} & \(X_{2}\) & Cost indicator &
\begin{tabular}{c} The more urgent the delivery date \\ of the order, the higher the level. \\ The higher the default cost of the \\ order, the higher the level. \\ The better the relationship \\ between the enterprise and the \\ customer, the higher the level. \\ The higher the profit of the \\ product, the higher the level. \\ The more stringent the customer’s \\ demand for punctuality, the higher \\ the level. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of customer priority indicators. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Evaluation Level** & **Very Bad** & **Bad** & **Normal** & **Good** & **Very Good** \\ \hline Membership degree & 0.2 & 0.4 & 0.6 & 0.8 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Membership degree of evaluation level. 2. Determine the Positive and Negative Ideal Solutions for Each Order Positive ideal solution: \[f_{v}^{+}=\big{(}f_{1}^{+},f_{2}^{+},\cdots,f_{5}^{+}\big{)}\] (3) Negative Ideal Solutions: \[f_{v}^{-}=\big{(}f_{1}^{-},f_{2}^{-},\cdots,f_{5}^{-}\big{)}\] (4) where: \(f_{v}^{+}=max_{v}(f_{uv}),f_{v}^{-}=min_{v}(f_{uv})\). 3. Group Benefit Value \(S_{u}\), Individual Regret Value \(R_{u}\), and Benefit Ratio \(Q_{u}\) were calculated \[S_{u}=\sum_{u=1}^{5}\left[\frac{f_{v}^{+}-f_{uv}}{f_{v}^{+}-f_{v}^{-}}\right]\] (5) \[R_{u}=\max_{v}\left[\frac{f_{v}^{+}-f_{uv}}{f_{v}^{+}-f_{v}^{-}}\right]\] (6) \[Q_{u}=a\frac{S_{u}-S^{-}}{S^{+}-S^{-}}+(1-a)\frac{R_{u}-R^{-}}{R^{+}-R^{-}}\] (7) where: \(S^{+}=max_{u}(S_{u})\), \(S^{-}=min_{u}(S_{u})\), \(R^{+}=max_{u}(R_{u})\), \(R^{-}=min_{u}(R_{u})\), \(a\) represents the decision coefficient, and \(a\in[0,1]\) indicates that the decision preference of the order is maximum group benefit or minimum individual regret. Here, \(a=0.5\) is assumed. 4. Sort Each Order Orders are sorted by \(S_{u}\), \(R_{u}\), and \(Q_{u}\) values. The smaller the value, the better the order. The value of the priority penalty coefficient is determined based on its order.