A Multi-Customer Vehicle Scheduling Optimization Method for Coal Intelligent Loading System

Abstract

Intelligent loading systems are extensively employed in coal enterprises. Nevertheless, pre-loading customer vehicle scheduling predominantly depends on manual expertise. This frequently results in extended vehicle waiting periods, elevated carbon emissions, and reduced customer satisfaction, particularly in multi-customer scenarios. Therefore, this study introduces a multi-customer vehicle scheduling optimization approach for an intelligent coal loading system. Customer priorities are first identified to enhance satisfaction. Considering various customers and enterprise factors, the multi-customer vehicle scheduling model is established to minimize the total cost. The optimal vehicle scheduling scheme is obtained by using the enhanced sparrow search algorithm. The validity of the proposed approach is demonstrated through a case study of a coal mining enterprise. The results show that the total cost of the optimized plan was 79% lower than the traditional plan, which means a significant reduction in vehicle waiting time, and an improvement in customer satisfaction.

1. Introduction

Many countries have increasingly prioritized the advancement of intelligent coal mines in recent years [1], resulting in improvements in intelligence, carbon footprint, and efficiency levels in the coal mining industry. Coal loading has transcended traditional methods. Numerous researchers have delved into intelligent coal loading systems using sensing, navigation, and communication technologies [2]. Nevertheless, as an important part of coal intelligent loading systems, studies on pre-loading vehicle scheduling are necessary. Presently, the majority of coal enterprises rely heavily on manual determination of loading time and location (loading bunker serial number), which is a subjective process devoid of scientific guidance. Furthermore, the varying needs, loading capacities, and priorities of multiple customers, combined with manual scheduling practices, result in disorderly vehicle queues and excessive waiting times. As a consequence, numerous issues arise, including elevated carbon emissions, diminished loading efficiency, and decreased customer satisfaction [3]. Consequently, investigating optimization methods for multi-customer vehicle scheduling (MCVS) in coal intelligent loading systems has emerged as a critical issue.

Many scholars have conducted vehicle scheduling optimization research in diverse fields utilizing various methods. Bao et al. [4] devised a multi-objective intelligent scheduling model for unmanned vehicles in surface mines, aiming to ascertain the optimal number of vehicles for dispatch and the traffic flow scheduling scheme. Fang et al. [5] explored the optimization of multi-automated vehicle scheduling in surface mines, considering both temporal and spatial factors. Zhang et al. [6] took into account vehicle travel and speed, and proposed a real-time scheduling system for automated trucks in a stochastic dynamic mining environment. Yan et al. [7] suggested an intelligent distribution strategy for all mineral materials within an underground coal mine auxiliary transportation system. Chen et al. [8] introduced a global scheduling strategy utilizing the Baidu industrial solver for auxiliary vehicle scheduling of trackless rubber-wheeled vehicles in underground coal mines. Overall, vehicle scheduling has emerged as a significant research focus across multiple disciplines. In the coal industry, research primarily concentrates on vehicle scheduling within open-pit coal mines and underground auxiliary transportation; however, studies focusing on customer vehicle scheduling before coal intelligent loading remain relatively limited.

Customer priorities are essential in MCVS, as they directly impact both the vehicle scheduling scheme and customer satisfaction. Numerous scholars have conducted thorough research on customer priorities in scheduling issues. Kou et al. [9] developed a comprehensive evaluation model for an open-pit mine vehicle scheduling system utilizing grey relation analysis and the ideal similarity ranking preference technique and determined the final weighting combination for each factor based on game theory. Xiang et al. [10] applied a combination of grey relation analysis and the entropy weight method to address the multi-objective solving challenge in multi-automatic guided vehicle dispatching operations under a composite operation mode. Liu et al. [11] tackled the optimization problem in cold chain delivery routes by incorporating customer priority into the analysis through the utilization of a clustering algorithm. Ltaif et al. [12] addressed prolonged queuing times for hospital patients by optimizing with a focus on priority queue principles, leading to a considerable enhancement in patient satisfaction. Albert [13] introduced a prioritized list approach for decision-making in ambulance dispatch to various customer types, considering ambulance availability as a key factor. Currently, the research on customer priority has been extensively applied in various domains, including vehicle scheduling, multi-automated guided vehicle systems, cold chain distribution routes, and vehicle dispatch decision-making processes. Such studies indicate the customer priorities has the potential to significantly enhance customer satisfaction and exert a beneficial influence on decision-making processes of scheduling [14]. However, the application of customer priority research remains relatively underexplored within the context of vehicle scheduling in coal loading.

Vehicle scheduling is a complex optimization conundrum that frequently necessitates algorithmic solutions. Presently, vehicle scheduling dilemmas are commonly tackled through diverse methodologies, including genetic algorithms [15,16], ant colony algorithms [17,18], particle swarm algorithms [19,20], and simulated annealing algorithms [21,22]. Gou et al. [23] employed an optimized genetic algorithm to address baggage vehicle scheduling issue at airports. Jia et al. [24] presented an innovative and enhanced ant colony optimization algorithm for managing the production allocation scheduling issue, encompassing non-identical batch machines and multiple vehicles. Ma et al. [25] utilized a hybrid particle swarm algorithm to address a hazardous materials vehicle scheduling model involving multiple distribution centers. Yu et al. [26] proposed an adaptive neighborhood simulated annealing algorithm for tackling the heterogeneous fleet vehicle path problem with multiple cross-docking facilities. Li et al. [27] introduced a quantum adaptive sparrow search algorithm to tackle this large-scale intricate scheduling problem, considering factors like renewable energy and loads. Li et al. [28] developed an improved Sparrow Search Algorithm by integrating a coded transformation technique for operation sequencing and chaotic mapping. Vehicle scheduling problems can be addressed using a range of algorithms. The MCVS problem addressed in this study is characterized by its large scale and complexity. In comparison to the four aforementioned algorithms, the Sparrow search algorithm is noted for its simplicity and ease of implementation, making it particularly well-suited for addressing large-scale and complex scheduling problems [29]. However, the traditional Sparrow search algorithm exhibits limitations, including lower efficiency and a propensity to converge to local optima [30]. Enhancements to the Sparrow search algorithm with other optimization techniques could potentially enhance its performance and search efficacy.

This study introduces customer priority into vehicle scheduling and applies an algorithm to address this issue, aiming to improve overall scheduling efficiency and customer satisfaction within intelligent coal loading systems, thereby addressing a gap in existing research on vehicle scheduling before coal loading. This approach is expected to provide a robust theoretical and practical foundation for advancing intelligence and efficiency within the coal industry.

This paper mainly studies the MCVS of coal mine industries, which is divided into five chapters, and its specific structure is as follows: The Section 1 analyzes the coal loading operation flow; Section 2 explains the expression and symbol of the problem; the proposed algorithm is described in Section 3. Section 4 mainly analyzes the MCVS in detail with a case study, and the fifth part summarizes this paper.

2. Analysis of Coal Loading Operations

In the coal industry, the importance of coal loading operation is a key link between production and the market, which cannot be ignored. A systematic analysis of coal loading operations not only helps to improve loading efficiency, but also ensures the stability and economy of coal supply. Through the detailed analysis of the loading process, each procedure can be effectively identified and optimized, thereby reducing the waste of resources and operational risks, and improving the safety and reliability of the overall operation.

At present, traditional coal loading operations with manual interventions are facing many challenges. This method has insufficiently efficient, has high labor cost, and suffers from cheating behavior; in addition, there are many safety risks, and the method has become a bottleneck, restricting the further development of the coal industry. Therefore, the coal industry is in urgent need of transformation and upgrading. The introduction of intelligent technology could improve the efficiency and safety of loading operations, breaking this development bottleneck.

2.1. Loading Operation Process

The loading operation process incorporates almost all tasks undertaken by coal enterprises upon receipt of customer orders. These tasks involve loading coal onto vehicles according to particular specifications and subsequently delivering the coal to various customer locations. Key processes include order reception, coal blending and storage, loading operation notification, vehicle entry to the yard for skin removal and queuing, loading, weighing, quality inspection, and vehicle departure to destinations, as shown in Figure 1.

The coal loading operation process unfolds in the following manner: ① Upon receipt of customer orders, the enterprise obtains detailed specifications from each customer regarding coal type, quantity, and delivery schedule. ② Notify the coal preparation plant to meticulously blend the coal based on order details and store it in the loading bunker. ③ The designated personnel dispatch the loading operation notification to the customer and inform other staff members to ready themselves for the loading process. ④ Throughout the loading procedure, each customer’s vehicle proceeds to the electronic weighbridge along the specified route for skin removal before queuing up beneath the loading bunker for the loading task. ⑤ The customer’s vehicle undergoes the loading operation at the loading bunker. ⑥ Conduct quality inspections on the vehicle weight and coal to ensure that the quality standards specified in customer orders are met. Subsequently, the vehicle proceeds along the designated route towards the customer-specified destination.

2.2. Loading Operation Notification

Currently, in scenarios with multiple loading bunkers, customers, and vehicles, loading operation notifications are manually generated by staff, who rely on their own experience. This subjective and uncertain method frequently leads to extended vehicle queues at the loading bunker, awaiting their turn for loading. Hence, it is crucial to holistically consider customer orders, prioritization, vehicle loading capacity, arrival time window for loading, loading bunker capacity, and other variables to formulate an optimal loading schedule. This strategy enables efficient and strategic allocation of loading resources, thereby improving loading efficiency, guaranteeing prompt order deliveries, and mitigating resource squandering and cost escalation. Figure 2 illustrates the notification process for multi-customer loading operations within the coal intelligent loading system.

Coal commodities are traded via auctions, and customers receive notifications to dispatch vehicles for coal loading. Typically, the loading operation notification is issued by the coal enterprise following the customer orders attained from the coal auction transaction. It provides instructions to drivers and relevant personnel on coal loading. Assume the existence of customers indexed by $i(i=\mathrm{1,2},\cdots ,N)$, transport vehicles indexed by $j(j=\mathrm{1,2},\cdots ,M)$, and loading bunkers indexed by $k(k=\mathrm{1,2},\cdots ,K)$ in the enterprise. The multi-customer multi-vehicle configurations can be loaded at any of the $K$-loading bunkers. Establish the loading plan based on various factors to determine when the $j$ vehicle of customer $i$ will be loaded at the $k$ loading bunker, and subsequently issue the loading operation notification. The notification contains information such as the loading bunker serial number $k$, customer number $i$, vehicle number $j$, loading operation time $t_{ij}^k$, loading start time $t_s$, and loading end time $t_e$. The loading plan is issued as shown in

Table 1. Loading plan table.

Loading Bunker Serial Number	Loading Plan
$k$	$n$$\text{-}\mathrm{m}\underset{t_s}{\to }i$$\text{-}j$$\left(t_{ij}^k\right)$$\underset{t_e\left(T_{ij}\right)}{\to }$

.

$T_{ij}$ represents the delay time for vehicle loading in this context. Specifically, it specifies that after loading bunker $k$ is finished for customer $n$ vehicle $m$, the loading process of vehicle $j$ customer $i$ commences at time $t_s$. Subsequently, upon the completion of the loading process after a duration of $t_{ij}^k$, the vehicle departs from the enterprise. At this point, $T_{ij}$ signifies that the actual loading duration of vehicle $j$ serving customer $i$ exceeds the anticipated loading time upon arrival at the enterprise.

3. Construction of Vehicle Scheduling Optimization Model for Coal Mine Enterprises

In coal mining enterprises, vehicles play a key role, including coal mine transportation, material supply, personnel transportation, and waste disposal. Vehicle scheduling is the reasonable arrangement and management of coal loading vehicles to ensure that coal can be loaded quickly and efficiently and transported to customers on time. Vehicle scheduling is very important in the production and logistics management of coal mining enterprises, and its optimization has a far-reaching impact on improving operational efficiency and reducing transportation costs. This chapter will discuss how to build a scientific vehicle scheduling optimization model. First, determine the factors that affect the priority of the customer’s order and prioritize the order using the VIKOR method based on these factors. Then, according to the prioritization and the actual situation of the enterprise, an MCVS optimization model aiming at the minimum total cost is constructed to improve the overall operation efficiency.

3.1. Determination of Customer Order Priority

3.1.1. Analysis of Customer Order Priority Influencing Factors

When determining the loading sequence of multi-customer vehicles, it is important to consider the priority of customers. In this paper, the VIKOR method is used to evaluate the priority of customers and calculate the order of customers, which provides the basis for the subsequent vehicle scheduling model. The VIKOR method is suitable for dealing with multi-criteria decision problems with conflicts. In practical applications, different orders may have conflicts on multiple criteria. The VIKOR method is able to deal with these conflicts effectively by calculating the relative disadvantage value of each scheme and provide a balanced solution for decision-makers. When using the VIKOR method, relevant factors need to be selected according to industry characteristics and decision-maker preferences. Five primary factors are taken into account for coal mining enterprises, including the urgency of the delivery date, default penalty cost, cooperative relationship, product profit, and on-time delivery rate, as depicted in

Table 2. Description of customer priority indicators.

Influencing Factor	Indicators	Indicators Classification	Description
Urgency of delivery date	$X_1$	Cost indicator	The more urgent the delivery date of the order, the higher the level.
Default penalty cost	$X_2$	Cost indicator	The higher the default cost of the order, the higher the level.
Partnership with customers	$X_3$	Benefit indicators	The better the relationship between the enterprise and the customer, the higher the level.
Profit per product	$X_4$	Benefit indicators	The higher the profit of the product, the higher the level.
On-time delivery rate	$X_5$	Cost indicator	The more stringent the customer’s demand for punctuality, the higher the level.

.

The urgency of the delivery date and the cooperative relationship among the mentioned indicators are qualitative. It is necessary to transform them into quantitative measures and evaluate them using the evaluation level membership degree method. The membership degree indicates the degree to which the indicators belong to the set, with a range of [0, 1], as shown in

Table 3. Membership degree of evaluation level.

Evaluation Level	Very Bad	Bad	Normal	Good	Very Good
Membership degree	0.2	0.4	0.6	0.8	1

. Default penalty cost, product profit, and on-time delivery rate are quantitative indicators with distinct units. Hence, they must be normalized to facilitate comprehensive comparison and ranking on a uniform scale.

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:

$$x_{uv}={\displaystyle \frac{x_{uv}-min x_{uv}}{max x_{uv}-min x_{uv}}}$$

(1)

$$x_{uv}={\displaystyle \frac{max x_{uv}-x_{uv}}{max x_{uv}-min x_{uv}}}$$

(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).

(2)

Determine the Positive and Negative Ideal Solutions for Each Order

Positive ideal solution:

$$f_v^{+}=\left(f_1^{+},f_2^{+},\cdots ,f_5^{+}\right)$$

(3)

Negative Ideal Solutions:

$$f_v^{-}=\left(f_1^{-},f_2^{-},\cdots ,f_5^{-}\right)$$

(4)

where: $f_v^{+}={max}_v\left(f_{uv}\right)$,$f_v^{-}={min}_v\left(f_{uv}\right)$.

(3)

Group Benefit Value $S_u$, Individual Regret Value $R_u$, and Benefit Ratio $Q_u$ were calculated

$$S_u={\sum }_{u=1}^5\left[{\displaystyle \frac{f_v^{+}-f_{uv}}{f_v^{+}-f_v^{-}}}\right]$$

(5)

$$R_u=\underset{v}{\max }\left[{\displaystyle \frac{f_v^{+}-f_{uv}}{f_v^{+}-f_v^{-}}}\right]$$

(6)

$$Q_u=a{\displaystyle \frac{S_u-S^{-}}{S^{+}-S^{-}}}+\left(1-a\right){\displaystyle \frac{R_u-R^{-}}{R^{+}-R^{-}}}$$

(7)

where: $S^{+}={max}_u\left(S_u\right)$, $S^{-}={min}_u\left(S_u\right)$, $R^{+}={max}_u\left(R_u\right)$, $R^{-}={min}_u\left(R_u\right)$, $a$ represents the decision coefficient, and $a\in \left[\mathrm{0,1}\right]$ 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. The lowest priority order $u$ (customer $i$) has a penalty coefficient of $R_i=10$, followed by the lower priority customer $n$, with a penalty coefficient of $R_n=20$, and so forth.

3.2. Establishment of a Multi-Customer Vehicle Scheduling Model

3.2.1. Problem Description

The MCVS problem in the coal intelligent loading system is outlined as follows: On the $K$ loading bunkers, there exist $N$ customers requiring loading. Each customer possesses several vehicles that coal can be loaded into at different loading bunkers. Efficient reduction of the entire loading cycle and prevention of resource wastage is achieved through the provision of an explicit loading notification. This paper addresses a half-day cycle in which each customer’s driver arrives at the loading site based on the communicated date provided by the enterprise’s staff for loading. Owing to distance variances and departure times, the arrival times of drivers will vary accordingly. Hence, the driver shall inform the person in charge of the expected arrival loading time window in the previous cycle to allow for proper scheduling of the loading operation notice. Based on the present loading process conditions, the following assumptions are posited for addressing the MCVS problem:

(1)

All loading bunkers are of the same type and have the same loading rate;

(2)

The total amount of coal required by each customer’s vehicle is less than the total capacity of the K loading bunkers;

(3)

Each vehicle can only be loaded under one loading bunker;

(4)

The arrival time of all customer vehicles is known;

(5)

Loading of any vehicle cannot be interrupted.

3.2.2. Model Building

In traditional loading operations, the lack of proper vehicle loading notifications often causes customer vehicle congestion during loading wait times, leading to the failure to deliver the goods on time. This paper introduces a model aimed at minimizing overall costs, including operating expenses, carbon emission expenses, penalty costs, and more. Optimizing customers’ loading schedules and locations can enhance loading efficiency, decrease operational expenses, and improve service quality. The symbols used in the mathematical model are detailed in

Table 4. Description of related symbols.

Symbols	Definition
$K$	Number of loading bunkers available to the enterprise
$k$	$\mathrm{Loading} \mathrm{bunker} \mathrm{index} k=\mathrm{1,2},\cdots ,K$
$N$	Number of customers
$i,n$	$\mathrm{Customer} \mathrm{index}, i,n=\mathrm{1,2},\cdots ,N$
$M$	Number of vehicles
$j,m$	$\mathrm{Vehicle} \mathrm{index}, j,m=\mathrm{1,2},\cdots ,M$
$g_k$	$\mathrm{Operating} \mathrm{cost} \mathrm{of} \mathrm{loading} \mathrm{bunker} k$
$t_{ij}^k$	$\mathrm{Service} \mathrm{time} \mathrm{for} \mathrm{loading} \mathrm{vehicle} j$$\mathrm{to} \mathrm{customer} i$$\mathrm{at} \mathrm{loading} \mathrm{bunker} k$
$T_{ij}$	$\mathrm{Loading} \mathrm{delay} \mathrm{time} \mathrm{after} \mathrm{the} \mathrm{arrival} \mathrm{of} \mathrm{vehicle} j$$\mathrm{to} \mathrm{customer} i$
$\gamma$	Carbon tax
$\beta$	Carbon dioxide emission factor
$\epsilon$	Unit carbon emission cost factor
$P_1$	Fuel consumption per unit of time the vehicle waits
${\eta }_1$	Penalty cost factor for delayed loading
$\left[E{t}_{ij}^d, L{t}_{ij}^d\right]$	Range of time customer vehicles are expected to arrive at the business for loading services
$Q_{ij}$	$\mathrm{Load} \mathrm{capacity} \mathrm{of} \mathrm{vehicle} j$$\mathrm{to} \mathrm{customer} i$
$G$	Maximum capacity of the loading bunker
$R_i$	$\mathrm{Prioritization} \mathrm{penalty} \mathrm{factor} \mathrm{for} \mathrm{customer} i$
$x_{ij}^k$	$\mathrm{A} \mathrm{value} \mathrm{in} \mathrm{the} \mathrm{range} \{0,1\}, 1 \mathrm{if} \mathrm{vehicle} j$$\mathrm{to} \mathrm{customer} i$$\mathrm{is} \mathrm{loaded} \mathrm{on} \mathrm{loading} \mathrm{bunker} k$, 0 otherwise
$Z_k$	$\mathrm{Takes} \mathrm{a} \mathrm{value} \mathrm{in} \mathrm{the} \mathrm{range} \mathrm{of} \{0,1\}, \mathrm{where} 1 \mathrm{indicates} \mathrm{loading} \mathrm{bunker} k$ being loaded, and 0 indicates otherwise

.

In the loading process, the optimal number of loading warehouses will be determined according to demand to improve loading efficiency and reduce resource wastage. Additionally, the costs of carbon emissions and penalties need to be taken into account. In this context, the optimization objective is defined as minimizing the total cost $C$ with the following objective function:

$$C=C_1+C_2+C_3$$

(8)

where: $C_1$ represents operating costs, including labor costs, equipment costs, energy costs, maintenance costs, and management costs. $C_2$ represents the carbon emission cost, which is the carbon emission cost generated during the waiting period of the customer’s vehicle. $C_3$ represents the penalty cost incurred due to the failure to load the vehicle within the specified time range.

The operating cost, carbon emission cost, and penalty cost are calculated as follows:

$${ C}_1=\sum _{k=1}^K{g}_k{Z}_k$$

(9)

$$C_2=\sum _{i=1}^N\sum _{j=1}^M\sum _{k=1}^K{x}_{ij}^k\epsilon \gamma \beta p_1{T}_{ij}$$

(10)

$$C_3=R_i\sum _{k=1}^K\sum _{i=1}^N\sum _{j=1}^M\omega \left(t_{ij}^k\right)$$

(11)

The penalty cost function $\omega \left(t_{ij}^k\right)$ in Formula (11) is expressed as:

$$\omega \left(t_{ij}^k\right)=\left\{\begin{array}{c}F E{t}_{ij}^d>t_{ij}^k\\ 0 E{t}_{ij}^d<t_{ij}^k<L{t}_{ij}^d \\ {\eta }_1\left(t_{ij}^k-L{t}_{ij}^d\right) L{t}_{ij}^d<t_{ij}^k\end{array}\right.$$

(12)

$F$ is a significant constant, indicating that if the vehicle fails to load within the expected arrival loading time window, there will be a substantial penalty cost.

The constraints of this model are as follows:

The actual amount of coal loaded by customers is less than the coal reserves in the loading warehouse:

$$\sum _{i=1}^N\sum _{j=1}^M{Q}_{ij}{x}_{ij}^k\le G;\left(k=\mathrm{1,2},3,\dots ,K\right)$$

(13)

The number of vehicles loaded in the loading bunker does not exceed the total number of vehicles, namely:

$$\sum _{k=1}^K{x}_{ij}^k=1;\left(i=\mathrm{1,2},\cdots ,N;j=\mathrm{1,2},\cdots ,M\right)$$

(14)

$$\sum _{i=1}^N\sum _{j=1}^M{x}_{ij}^k=1;\left(k=\mathrm{1,2},\cdots ,K\right)$$

(15)

All customer vehicles can be loaded, namely:

$$\sum _{k=1}^K\sum _{i=1}^N{x}_{ij}^k=N$$

(16)

$$\sum _{k=1}^K\sum _{j=1}^M{x}_{ij}^k=M$$

(17)

Ensure continuity of loading, namely:

$$t_{uv}^k=t_{ij}^k+T_{uv}^k$$

(18)

The actual number of loading bunkers for coal loading vehicles does not exceed the total number of loading bunkers, namely:

$$\sum _{k=1}^K{x}_{ij}^k\le K;i=0,j=0$$

(19)

Constraints on customer priorities, namely:

$$x_{ij}^k{R}_{i+1}\ge {x_{\left(i-1\right)j}^{k}R}_i, \left(i=1,2,3,\cdots ,N;R_i=10,20,30,\cdots \right)$$

(20)

where, $R_{i-1}$ represents the penalty coefficient of the previous customer priority immediately adjacent to customer $i$.

4. Design of a Multi-Customer Vehicle Scheduling Algorithm Based on an Improved Sparrow Search Algorithm

4.1. Sparrow Search Algorithm

The Sparrow Search Algorithm (SSA) simulates the behavior of sparrows in foraging and collaborative group communication [32]. The algorithm categorizes individuals into discoverers, followers, and vigilantes [33]. Discoverers provide foraging information to the entire group, followers follow and forage, and vigilantes monitor the foraging area.

The current optimal scheduling plan (discoverer) position update can be expressed as in Formula (21):

$$X_{p,q}^{t+1}=\left\{\begin{array}{c}{X}_{p,q}^t·exp\left({\displaystyle \frac{-p}{\alpha \times {gen}_{max}}}\right),R_0\ge ST\\ X_{p,q}^t+H·L , R_2<ST\end{array}\right.$$

(21)

where: $t$ denotes the current iteration number, $X_{p,q}^t$ denotes the position of the $p\mathrm{t}\mathrm{h}$ plan in the $q\mathrm{t}\mathrm{h}$ dimension in the $t\mathrm{t}\mathrm{h}$ generation, $\alpha \in \left(\mathrm{0,1}\right)$, ${gen}_{max}$ is the maximum number of iterations, $R_0$ denotes the alarm value, $ST$ denotes the safety threshold, $H$ is a random number obeying the normal distribution, and $L$ is a 1-dimensional all-1 matrix.

Other scheduling plans (follower) position updates can be expressed as in Formula (22):

$$X_{p,q}^{t+1}=\left\{\begin{array}{c}Q·exp\left({\displaystyle \frac{{X_{worst}^t-X}_{p,q}^t}{p^2}}\right) ,p>{\displaystyle \frac{l}{2}}\\ X_p^{t+1}+\left|X_{p,q}^t-X_c^{t+1}\right|·A^{\mathrm{*}}·L, p\le {\displaystyle \frac{l}{2}}\end{array}\right.$$

(22)

where: $X_{worst}^t$ denotes the location of the scheduling plan with the worst fitness in generation $t$, and $X_c^{t+1}$ denotes the location of the scheduling plan with the best fitness in generation $t+1$. $A$ denotes a 1-dimensional matrix, where each element is randomly predefined as −1 or 1, $A^{\mathrm{*}}=A^T{\left(A{A}^T\right)}^{-1}$, and $l$ is the population size. When $p>{\displaystyle \frac{l}{2}}$, it means that the $p\mathrm{t}\mathrm{h}$ scheduling plan has low fitness; when $p\le {\displaystyle \frac{l}{2}}$, the scheduling plan will be close to the optimal plan $X_c$.

The potential scheduling plan for updating the position (vigilant) can be expressed as in Formula (23):

$$X_{p,q}^{t+1}=\left\{\begin{array}{c}{X}_{best}^t+ϵ·\left|X_{p,q}^t-X_{best}^t\right|, f_p\ne f_e\\ X_{best}^t+s\left({\displaystyle \frac{{X_{p,q}^t-X}_{best}^t}{\left|f_p-f_w\right|+\sigma }}\right), f_p=f_e\end{array}\right.$$

(23)

where: $X_{best}^t$ denotes the global optimal position in generation $t$, $ϵ$ is a random number that controls the step size and follows a normal distribution with a mean of 0 and variance of 1, $s\in [-\mathrm{1,1}]$, and $\sigma$ is a smaller constant to prevent the denominator from being 0. $f_p$ denotes the fitness value of the current scheduling plan, while $f_e$ and $f_w$ represent the fitness values of the current global optimal and worst scheduling plans, respectively. When $f_p\ne f_e$, the scheduling plan keeps changing its position and tries to find a better fit; when $f_p=f_e$, the scheduling plan moves closer to the nearby plans to avoid the danger zone.

4.2. Improvement Strategy of Sparrow Search Algorithm

The SSA is highly reliant on the selection of the initial solution. If the initial solution is far from the optimal solution, the algorithm requires more iterations to achieve a better solution. Therefore, the uniformized distribution Chebyshev chaotic mapping system is utilized [34]. Chebyshev mapping is a prime example of chaotic mapping. In comparison to one-dimensional mappings like Tent mapping and Logistic mapping, it exhibits superior chaotic properties, a broader range of value domains, and notably enhances the uniformity of sequence distribution. The expression of the uniformized distribution Chebyshev mapping system is as follows:

$$\left\{\begin{array}{c}{x}_{t+1}=\cos \left[t·\arccos \left(x_t\right)\right],-1\le x_t\le 1\\ y_t=x_{t+1},t=\mathrm{0,1},2,\cdots ,w\\ y_{t+1}=\left({\displaystyle \frac{2}{\pi }}\right)\arcsin \left[\cos \left(y_t\right)\right]+D,-1\le y_t\le 1\end{array}\right.$$

(24)

where: $y_{t+1}$ represents the scheduling plan after the $t+1$ mapping iteration and $D$ is an arbitrary constant. The process of population initialization is as follows: first, a $d$-dimensional vector is randomly generated in the range of [−1,1] as the initial scheduling plan. This vector is then substituted into the first formula of Formula (24). Iteratively, a new scheduling plan of $w-1$ is generated for each dimension. Subsequently, the new scheduling plan is substituted into the second formula to map the variable value generated by Chebyshev mapping to the scheduling plan.

4.3. Improved Sparrow Search Algorithm Design

(1)

Encoding and Decoding

The MCVS problem refers to the loading sequence of multiple customer vehicles in the warehouse. This paper encodes the vehicle sequence using non-negative integers. Ten customer loading vehicles are taken as the coding plan, and the coding indicates that the loading sequence of the ten vehicles is 1-3-7-10-4-5-8-2-6-9, as shown in Figure 3. The diagram illustrates that the customer’s first vehicle, labeled as vehicle number 1, is loaded first in a loading bay, followed by vehicle number 3, and so on.

(2)

Cross Operation

Based on an adaptive crossover operator, a location-based crossover method is selected. Assuming that there are 10 loading vehicles to be sorted, the specific steps are as follows:

Step 1: Determine the intersection points of parent $P_1$ and $P_2$. Assume that the intersection points involve vehicles position 2, 4, 5, and 9;

Step 2: Randomly generate child $Q_1$ and $Q_2$, ensuring that the vehicles at the intersection point in $Q_1$ match those in $P_1$;

Step 3: Insert the vehicles of $P_2$, excluding the crossing points, into $Q_1$ sequentially. The resulting child $Q_1$ is 2-3-5-10-4-8-1-7-6-9;

Step 4: Repeat Step 2 and Step 3 for child $Q_2$ to obtain the sequence 3-5-7-8-1-10-4-2-6-9.

According to the cross-operation process described above, the uniform cross diagram is illustrated in Figure 4.

(3)

Variation Operation

The reverse variation method is adopted, assuming that the number of loading vehicles is 10. Two integers, $a=5$ and $b=7$, are selected from the range [1, 10] to represent the variation position and generate the variation interval. The reverse of the gene interval, (4, 5, 8), results in (8, 5, 4). Consequently, the offspring chromosome sequence becomes 1-3-7-10-8-5-4-2-6-9. The detailed operation is shown in Figure 5.

The flowchart of the enhanced SSA is depicted in Figure 6.

5. Case Verification

To verify the effectiveness of the MCVS method in actual loading processes, this study takes the loading process of a coal mining enterprise as an example. Combined with the VIKOR method, the order prioritization is calculated and the MCVS model is constructed based on customer priority. On this basis, related methods are applied to solve the model, and the optimal customer vehicle loading scheme is obtained, which could solve the problems of low customer satisfaction, long waiting time for vehicles, and low loading efficiency.

5.1. Case Background

A coal mining enterprise is a coal supplier. Coal products are traded through auctions. After the transaction is completed, customers are notified to send vehicles to load coal. The enterprise has a total of 12 coal bunkers, including 2 original coal bunkers, 6 coal storage bunkers, 1 gangue bunker, and 3 loading bunkers for customers to load coal. In the morning, a total of seven customers received order information, which included customer number, vehicle number, customer vehicle number, load capacity, expected arrival loading time window, and loading operation time. As 66 groups have too many data points, only a portion of the customer information is displayed in

Table 5. Customer information table.

Serial Number	$\mathbf{Customer} \mathbf{Number} \mathit{i}$	$\mathbf{Vehicle} \mathbf{Number} \mathit{j}$	$\mathbf{Customer} \mathbf{Vehicle} \mathbf{Number} \mathit{i}$$\text{-}\mathit{j}$	$\mathbf{Load} \mathbf{Capacity} {\mathit{Q}}_{\mathit{i}\mathit{j}}$ (ton)	$\mathbf{Expected} \mathbf{Arrival} \mathbf{Loading} \mathbf{Time} \mathbf{Window} \left[\mathit{E}{\mathit{t}}_{\mathit{i}\mathit{j}}^{\mathit{d}},\mathit{L}{\mathit{t}}_{\mathit{i}\mathit{j}}^{\mathit{d}}\right]$	$\mathbf{Loading} \mathbf{Operation} \mathbf{Time} {\mathit{t}}_{\mathit{i}\mathit{j}}^{\mathit{k}}\left(\mathbf{m}\mathbf{i}\mathbf{n}\right)$
0	-	-	-	-	[08:00, 18:00]	-
1	1	1	1-1	40	[08:30, 09:00]	12
2	1	2	1-2	40	[09:00, 09:30]	12
3	1	3	1-3	40	[09:00, 09:30]	12
4	1	4	1-4	30	[09:30, 10:00]	8
5	1	5	1-5	40	[08:40, 09:10]	12
6	1	6	1-6	30	[10:10, 10:40]	8
7	1	7	1-7	40	[11:00, 11:30]	12
8	1	8	1-8	40	[10:20, 10:50]	12
…	…	…	…	…	…	…
16	2	7	2-7	35	[11:00, 11:30]	10
…	…	…	…	…	…	…
65	7	8	7-8	35	[11:00, 11:30]	10
66	7	9	7-9	45	[11:30, 12:00]	13

; the complete information is shown in the Supplementary Materials.

When the relevant personnel receive the customer information, they arrange the vehicles based on their experience. The loading plan before optimization is depicted in

Table 6. Loading plan before optimization.

Loading Bunker Serial Number	Loading Plan
Loading bunker 1	$4\text{-}4\left(10\right)\underset{8:10}{\to }$$7\text{-}3\left(10\right) \underset{8:20}{\to }$$3\text{-}1\left(10\right)\underset{8:30}{\to }$$4\text{-}3\left(13\right) \underset{8:43}{\to }$3-2(10)$\underset{8:53}{\to }$1-5(12)$\underset{9:05}{\to }7$-4(13)$\underset{9:18}{\to }$1-2(12)$\underset{9:30}{\to }$4-6(10)$\underset{9:40}{\to }$3-4(10)$\underset{9:50}{\to }$5-1(12)$\underset{10:02\left(2\right)}{\to }$4-12(10)$\underset{10:12}{\to }$6-6(13)$\underset{10:25}{\to }$1-6(8)$\underset{10:33}{\to }$4-8(10)$\underset{10:43}{\to }$6-4(10)$\underset{10:53}{\to }$1-8(12)$\underset{\mathbf{\text{11}}\mathbf{:}\mathbf{\text{05}}\mathbf{\left(}\mathbf{\text{15}}\mathbf{\right)}}{\to }$7-5(10)$\underset{11:15}{\to }$3-6(10)$\underset{11:25}{\to }$1-7(12)$\underset{11:37\left(7\right)}{\to }$5-7(8)$\underset{11:45\left(5\right)}{\to }7$-9(13)$\underset{11:58}{\to }$
Loading bunker 2	$4\text{-}1\left(13\right) \underset{8:13}{\to }$4-2(13)$\underset{8:26}{\to }$2-4(10)$\underset{8:36}{\to }$6-2(13)$\underset{8:49}{\to }$1-1(12)$\underset{9:01\left(1\right)}{\to }$5-4(13)$\underset{9:14}{\to }$3-3(10)$\underset{9:24}{\to }$5-2(12)$\underset{9:36\left(6\right)}{\to }$7-7(13)$\underset{9:49}{\to }$1-9(8)$\underset{9:57}{\to }2$-1(8)$\underset{10:05\left(5\right)}{\to }$4-10(13)$\underset{10:18}{\to }$7-6(13)$\underset{10:31\left(1\right)}{\to }$5-5(13)$\underset{10:44\left(4\right)}{\to }$3-8(10)$\underset{10:54}{\to }$5-6(8)$\underset{11:02\left(2\right)}{\to }$6-7(13)$\underset{11:15}{\to }$7-8(10)$\underset{11:25}{\to }2$-5(8)$\underset{11:33\left(3\right)}{\to }6$-9(10)$\underset{11:43\left(3\right)}{\to }$ 2-9(10) $\underset{11:53\left(3\right)}{\to }5$-9(13)$\underset{12:06\left(6\right)}{\to }$
Loading bunker 3	$6\text{-}1\left(13\right) \underset{8:13}{\to }$7-1(13)$\underset{8:26}{\to }$5-3(8)$\underset{8:34\left(4\right)}{\to }$4-5(13)$\underset{8:47}{\to }$3-5(10)$\underset{8:57}{\to }$2-3(8)$\underset{9:05}{\to }$6-3(13)$\underset{9:18}{\to }$1-3(12)$\underset{9:30}{\to }$7-2(13)$\underset{9:43}{\to }$1-4(8)$\underset{9:51}{\to }$2-2(8)$\underset{09:59}{\to }$4-7(10)$\underset{10:10}{\to }$6-5(10)$\underset{10:20}{\to }$3-7(10)$\underset{10:30}{\to }$2-6(8)$\underset{10:38}{\to }$4-11(13)$\underset{10:51}{\to }$6-8(10)$\underset{11:01\left(1\right)}{\to }$4-9(10)$\underset{11:11}{\to }$3-9(10)$\underset{11:21}{\to }2$-7(10)$\underset{11:31\left(1\right)}{\to }$2-8(10)$\underset{11:41\left(1\right)}{\to }$5-8(8)$\underset{11:49}{\to }$

.

In Table 6, the loading scheduling plan for the three loading bunkers of the enterprise can be observed. The specific plan is represented as follows: loading bunker 1 starts at 8:00 a.m. and first loads 4-4 with a loading time of 10 min, ending loading at 8:10 a.m., and then loads 7-3. The expected arrival loading time for 1-8 is between 10:20 and 10:50, but the end time of coal loading is 11:05, which is 15 min later than the expected arrival loading time, resulting in penalty costs. According to the loading plan mentioned above, the loading operation notification table is obtained. Due to the large amount of data, let us consider the loading operation notification for the nine vehicles of customer 1, as shown in

Table 7. Notification of loading operation before optimization.

$\mathbf{Loading} \mathbf{Bunker} \mathbf{Serial} \mathbf{Number} \mathit{k}$	$\mathbf{Customer} \mathbf{Number} \mathit{i}$	$\mathbf{Vehicle} \mathbf{Number} \mathit{j}$	$\mathbf{Load} \mathbf{Capacity} {\mathit{Q}}_{\mathit{i}\mathit{j}}$ (ton)	$\mathbf{Loading} \mathbf{Start} \mathbf{Time} {\mathit{t}}_{\mathit{s}}$	$\mathbf{Loading} \mathbf{End} \mathbf{Time} {\mathit{t}}_{\mathit{e}}$
2	1	1	12	8:49	9:01
1	1	2	12	9:18	9:30
3	1	3	12	9:18	9:30
3	1	4	8	9:43	9:51
1	1	5	12	8:53	9:05
1	1	6	8	10:25	10:33
1	1	7	12	11:25	11:37
1	1	8	12	10:53	11:05
2	1	9	8	9:49	9:57

.

Table 7 specifies that the loading operation started at 8:49 under loading bunker 2 for 1-1. After 12 min of loading coal, the operation was completed, and the vehicle left at 9:01.

It can be seen that this plan resulted in a total delay of 70 min in loading for all customers, meaning that customer satisfaction was low. Therefore, it is essential to utilize the MCVS optimization method proposed in this paper to schedule the vehicles in order to generate a rational and efficient scheduling plan.

5.2. Customer Prioritization

Aiming at the order information of seven customers, the evaluation grade membership degree method is used for evaluation, and the obtained customer order evaluation indicator information is shown in

Table 8. Customer order evaluation indicator information.

	Evaluation Indicators	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$
Customer Orders
1		0.8	0.6	0.6	0.4	0.4
2		0.8	0.8	0.4	0.4	1
3		0.4	0.6	0.6	0.8	0.6
4		0.2	0	1	1	0
5		1	1	0.2	0	0.8
6		0.2	0.4	1	0.8	0.2
7		0.2	0.4	0.8	0.8	0.4

.

Because each indicator unit is different, the data normalization process is carried out. Here, $X_3$ and $X_4$ are benefit indicators, which are converted by Formula (1); $X_1$, $X_2$, and $X_5$ are cost indicators, converted by Formula (2). Formulas (3) and (4) were used to calculate the positive and negative ideal solutions for each index, as shown in

Table 9. Normalization treatment and table of positive and negative ideal solutions.

	Evaluation Indicators	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$
Customer Orders
1		0.2	0.4	0.5	0.4	0.6
2		0.2	0.2	0.25	0.4	0
3		0.6	0.4	0.5	0.8	0.4
4		0.8	1	1	1	1
5		0	0	0	0	0.2
6		0.8	0.6	1	0.8	0.8
7		0.8	0.6	0.75	0.8	0.6
Each index positive and negative ideal solution	Positive ideal solutions	0.8	1	1	1	1
	Negative ideal solutions	0	0	0	0	0

.

Formulas (5)–(7) were used to calculate the group benefit value, individual regret value, benefit ratio sum, and order ranking, as shown in

Table 10. Group benefit value, individual regret value, interest ratio, and order ranking.

	Evaluation Indicators	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$	Group Benefit Value	Individual Regret Value	Interest Ratio	Order Ranking
Customer Orders
1		0.8	0.6	0.6	0.4	0.4	2.85	0.75	0.6719	5
2		0.8	0.8	0.4	0.4	1	3.9	1	0.9062	6
3		0.4	0.6	0.6	0.8	0.6	2.15	0.6	0.5239	4
4		0.2	0	1	1	0	0	0	0	1
5		1	1	0.2	0	0.8	4.8	1	1	7
6		0.2	0.4	1	0.8	0.2	0.8	0.4	0.2833	2
7		0.2	0.4	0.8	0.8	0.4	1.25	0.4	0.3302	3

.

According to the ordering result, it can be seen that $r_4>r_6>r_7>r_3>r_1>r_2>r_5$, and the order priority of customer is Order 4 > Order 6 > Order 7 > Order 3 > Order 1 > Order 2 > Order 5. Therefore, it can be inferred that each customer’s prioritization penalty coefficients are as follows: $R_1$= 30, $R_2$= 20, $R_3$= 40, $R_4$= 70, $R_5$= 10, $R_6$= 60, and $R_7$= 50.

5.3. Vehicle Scheduling Plan

The data in Table 5 are plugged into the established vehicle scheduling model, Formulas (8) to (20), and the model is solved by the enhanced SSA to generate the vehicle scheduling plan.

(1)

Parameter Setting

The model is solved in MATLAB 2019. The initial values and units of each parameter of the model are set as shown in

Table 11. Model parameter settings.

Parameter	Numerical Value	Unit
The number of loading bunkers $\mathrm{available} \mathrm{to} \mathrm{coal} \mathrm{mining} \mathrm{companies} K$	3	--
$\mathrm{Loading} \mathrm{bunker} \mathrm{operating} \cos \mathrm{t} g_k$	300	CNY/hour
$\mathrm{Maximum} \mathrm{capacity} \mathrm{of} \mathrm{loading} \mathrm{bunkers} G$	8600	tons
$\mathrm{Penalty} \cos \mathrm{t} \mathrm{coefficient} \mathrm{for} \mathrm{delayed} \mathrm{loading} {\eta }_1$	1500	CNY/hour
$\mathrm{Carbon} \mathrm{tax} \gamma$	20	CNY/ton
$\mathrm{Unit} \mathrm{carbon} \mathrm{emission} \cos \mathrm{t} \mathrm{coefficient} \epsilon$	250	CNY/ton
Carbon dioxide emission factor β	3.095	kilogram
$\mathrm{Fuel} \mathrm{consumption} \mathrm{of} \mathrm{vehicles} \mathrm{waiting} \mathrm{per} \mathrm{unit} \mathrm{time} P_1$	84	kg/hour

. The algorithm parameters are set as shown in

Table 12. Algorithm parameter settings.

Parameter	Parameter Value
Number of populations	300
Number of iterations	150
Early warning value ST	0.6
Proportion of discoverers PD	0.7
Proportion of vigilantes SD	0.2
Crossover probability	0.9
Mutation probability	0.01

.

Some of the key parameters and behaviors of the SSA are described in Table 12. This algorithm searches using a population of 300 sparrows for a maximum of 150 iterations per iteration. The algorithm will issue an alert when the searched target value is greater than or equal to 0.6. In each iteration, 70% of the sparrows will follow the optimal strategy for the search, while 20% of the sparrows will remain vigilant to avoid falling into local optimal solutions. In addition, there is a 0.9% probability for two sparrows to cross over and a 1% probability for each sparrow to mutate.

(2)

Comparison of Algorithms

To evaluate the effectiveness of the enhanced algorithm, Chebyshev chaotic mapping and cross mutation improved Sparrow search algorithm (CCM-SSA), Sparrow search algorithm (SSA) and NSGA-II algorithm were applied to solve the MCVS model to minimize the customer penalty cost. The specific results are illustrated in Figure 7.

According to the comparison results in Figure 7, the CCM-SSA algorithm can find a superior solution in fewer iterations compared to the traditional SSA algorithm and the NSGA-II, showing higher global search capability and efficiency. Therefore, by employing the CCM-SSA algorithm combined with sample data to solve the model presented in this paper, a more optimized scheduling plan can be achieved.

(3)

Scheduling Plan

According to the parameter settings in Table 11 and Table 12 above, and the example data of coal mining enterprises in Table 5, the model is solved using the CCM-SSA algorithm.

According to the iteration graph shown in Figure 8, the total cost of the scheduling plan gradually decreases as the number of iterations increases. The CCM-SSA algorithm converges after about 57 iterations, reducing the total cost of the scheduling plan to CNY 9012. This result demonstrates the capability of the CCM-SSA algorithm to generate outcomes in fewer iterations. The loaded scheduling plan after optimization is generated by the CCM-SSA algorithm, as depicted in

Table 13. Loaded vehicle plan after optimization.

Loading Bunker Serial Number	Loading Plan
Loading bunker 1	$4\text{-}1\left(13\right)\underset{8:13}{\to }$$3\text{-}1\left(10\right) \underset{8:23}{\to }$$2\text{-}4\left(10\right)\underset{8:33}{\to }$$4\text{-}5\left(13\right) \underset{8:46}{\to }$$3\text{-}2\left(10\right) \underset{8:56}{\to }$$1\text{-}5\left(12\right) \underset{9:08}{\to }$$3\text{-}3\left(10\right) \underset{9:18}{\to }$$1\text{-}2\left(12\right) \underset{9:30}{\to }$$7\text{-}2\left(13\right) \underset{9:43}{\to }$$2\text{-}2\left(8\right) \underset{9:51}{\to }$$4\text{-}6\left(10\right) \underset{10:01}{\to }$$4\text{-}10\left(13\right) \underset{10:14}{\to }$$6\text{-}6\left(13\right) \underset{10:27}{\to }$$5\text{-}5\left(13\right) \underset{10:40}{\to }$$4\text{-}8\left(10\right) \underset{10:50}{\to }$$6\text{-}4\left(10\right) \underset{11:00}{\to }$$5\text{-}6\left(8\right) \underset{11:08\left(8\right)}{\to }$$7\text{-}8\left(10\right) \underset{11:18}{\to }$$1\text{-}7\left(12\right) \underset{11:30}{\to }$$3\text{-}6\left(10\right) \underset{11:40}{\to }$$2\text{-}8\left(10\right) \underset{11:50}{\to }$$5\text{-}9\left(13\right) \underset{12:03\left(3\right)}{\to }$
Loading bunker 2	$4\text{-}4\left(10\right) \underset{8:10}{\to }$$7\text{-}3\left(10\right) \underset{8:20}{\to }$$4\text{-}2\left(13\right) \underset{8:33}{\to }$$4\text{-}3\left(13\right) \underset{8:46}{\to }$$3\text{-}5\left(10\right) \underset{8:56}{\to }$$2\text{-}3\left(8\right) \underset{9:04}{\to }$$6\text{-}3\left(13\right) \underset{9:17}{\to }$$1\text{-}3\left(12\right) \underset{9:29}{\to }$$3\text{-}4\left(10\right) \underset{9:40}{\to }$$2\text{-}1\left(8\right) \underset{9:48}{\to }$$5\text{-}1\left(12\right) \underset{10:00}{\to }$$4\text{-}7\left(10\right) \underset{10:10}{\to }$$6\text{-}5\left(10\right) \underset{10:20}{\to }$$3\text{-}7\left(10\right) \underset{10:30}{\to }$$2\text{-}6\left(8\right) \underset{10:38}{\to }$$1\text{-}8\left(12\right) \underset{10:50}{\to }$$6\text{-}8\left(10\right) \underset{11:00}{\to }$$4\text{-}9\left(10\right) \underset{11:10}{\to }$$7\text{-}5\left(10\right) \underset{11:20}{\to }$$3\text{-}9\left(10\right) \underset{11:30}{\to }$$6\text{-}9\left(10\right) \underset{11:40}{\to }$$2\text{-}9\left(10\right) \underset{11:50}{\to }$
Loading bunker 3	$6\text{-}1\left(13\right) \underset{8:13}{\to }$$5\text{-}3\left(8\right) \underset{8:21}{\to }$$7\text{-}1\left(13\right) \underset{8:34}{\to }$$6\text{-}2\left(13\right) \underset{8:47}{\to }$$1\text{-}1\left(12\right) \underset{8:59}{\to }$$5\text{-}4\left(13\right) \underset{9:12}{\to }$$7\text{-}4\left(13\right) \underset{9:25}{\to }$$5\text{-}2\left(12\right) \underset{9:37\left(7\right)}{\to }$$1\text{-}4\left(8\right) \underset{9:45}{\to }$$7\text{-}7\left(13\right) \underset{9:58}{\to }$$1\text{-}9\left(8\right) \underset{10:06}{\to }$$4\text{-}12\left(10\right) \underset{10:16}{\to }$$7\text{-}6\left(13\right) \underset{10:29}{\to }$$1\text{-}6\left(8\right) \underset{10:37}{\to }$$4\text{-}11\left(13\right) \underset{10:50}{\to }$$3\text{-}8\left(10\right) \underset{11:00}{\to }$$6\text{-}7\left(13\right) \underset{11:13}{\to }$$2\text{-}5\left(8\right) \underset{11:21}{\to }$$\mathbf{\text{2-7}}\mathbf{\left(}\mathbf{\text{10}}\mathbf{\right)} \underset{\mathbf{\text{11}}\mathbf{:}\mathbf{\text{31}}\mathbf{\left(}\mathbf{\text{1}}\mathbf{\right)}}{\mathbf{\to }}$$5\text{-}7\left(8\right) \underset{11:39}{\to }$$7\text{-}9\left(13\right) \underset{11:52}{\to }$$5\text{-}8\left(8\right) \underset{12:00}{\to }$

.

According to Table 13, the loading scheduling plan for the three loading bunkers of the enterprise can be observed. The specific plan is represented as follows: loading bunker 1 starts at 8:00 a.m. and first loads 4-1 with a loading time of 13 min, ending loading at 8:13 a.m., and then loads 3-1. The expected arrival loading time for 2-7 is between 11:00 and 11:30, but the end time of coal loading is 11:31, which is 1 min later than the expected arrival loading time, resulting in penalty costs.

According to the loading plan mentioned above, the loading operation notification table is obtained. Due to the large amount of data, the loading operation notification for customer 1 is shown in

Table 14. Notification of loading operation before scheduling.

$\mathbf{Loading} \mathbf{Bunker} \mathbf{Serial} \mathbf{Number} \mathit{k}$	$\mathbf{Customer} \mathbf{Number} \mathit{i}$	Vehicle $\mathbf{Number} \mathit{j}$	$\mathbf{Load} \mathbf{Capacity} {\mathit{Q}}_{\mathit{i}\mathit{j}}$ (ton)	$\mathbf{Loading} \mathbf{Start} \mathbf{Time} {\mathit{t}}_{\mathit{s}}$	$\mathbf{Loading} \mathbf{End} \mathbf{Time} {\mathit{t}}_{\mathit{e}}$
3	1	1	12	8:47	8:59
1	1	2	12	9:18	9:30
2	1	3	12	9:17	9:29
3	1	4	8	9:37	9:45
1	1	5	12	8:56	9:08
3	1	6	8	10:29	10:37
1	1	7	12	11:18	11:30
2	1	8	12	10:38	10:50
3	1	9	8	9:58	10:06

as a representative, which has nine vehicles.

Table 14 specifies that the loading operation started at 8:47 under loading bunker 3 for 1-1. After 12 min of loading coal, the operation was completed, and the business left at 8:59.

(4)

Comparison Before and After Optimization

The total loading delay time of each customer before and after optimization was compared, as shown in

Table 15. Comparison of the customers total loading delay time before and after optimization.

Customer Number	Loading Delay Time
	Before Optimization	After Optimization
1	23	-
2	13	1
3	-	-
4	-	-
5	29	18
6	4	-
7	1	-
Total	70	19

.

According to Table 15, a total of five customer orders were delayed before optimization, with a total delay time of 70 min. Two customer orders were delayed after optimization, totaling a delay of 19 min. The plans before and after optimization are compared, and the comparison results of each cost and total cost are shown in Figure 9.

It can be observed from Figure 9 that the operating cost before and after optimization is CNY 3600. However, the carbon emission cost after optimization was CNY 412, which was reduced by CNY 1105, or 72.8%, compared to CNY 1517 before optimization. The penalty cost after optimization was CNY 5000, compared to CNY 37,750 before optimization, resulting in a decrease of CNY 32,750, which represents an 86.8% decrease. Overall, the total cost of the optimized plan is reduced by CNY 33,855, or 79%, compared to the pre-optimization plan. Therefore, the scheduling plan addressed by the MCVS model can offer enterprises loading operation notifications, enabling them to efficiently accomplish vehicle loading tasks and effectively reduce overall costs.

The MCVS optimization method of intelligent coal loading system proposed in this paper provides a new way for coal mining enterprises to transform into intelligent operations. Although the MCVS method proposed in this paper uses enhanced customer priority and the sparrow search algorithm to obtain an optimized vehicle scheduling plan, there are still some challenges and limitations in practical application.

The model proposed in this paper can solve the MCVS problem in the coal intelligent loading system to a certain extent, but in practical applications, customer demand and the scheduling environment may be complex and changeable, and the data required for vehicle scheduling (such as customer demand, vehicle capacity, etc.) may be inaccurate or incomplete, which may affect the effectiveness of the model and the quality of the scheduling plan. In addition, models have limitations in responding to unexpected events or unusual situations. For example, unforeseen issues such as vehicle breakdown, traffic congestion, or order cancellations can affect scheduling results. Therefore, future research should focus on improving the adaptability of the model and enhancing the ability to deal with emergencies so as to improve the practical application effect and reliability of the scheduling plan.

6. Conclusions

In this paper, the MCVS problem of coal intelligent loading systems is studied, and a MCVS method considering customer priority is proposed. By enhancing the SSA, the optimal vehicle scheduling scheme is obtained. Finally, the proposed method is verified through the case of enterprise A as an example. The main conclusions are as follows:

(1) To address the issues of unclear customer priority and low satisfaction, the enterprise customer priority is obtained by using the VIKOR method, which provides a foundation for MCVS.

(2) In light of the poor quality of the traditional SSA solving plan, the Chebyshev chaotic mapping and cross-mutation operations are introduced into the traditional SSA algorithm. This improvement aims to boost the solving speed and search capability of the algorithm, ultimately validating its effectiveness.

(3) Aiming to address the issues of low efficiency in vehicle scheduling and long waiting times for customers, a vehicle scheduling plan is proposed for coal mining enterprises through the construction of the MCVS model. The total cost of this plan is reduced by 79% compared to the pre-optimization plan.

The MCVS method proposed in this paper provides a scientific, efficient, and intelligent scheduling plan for coal mining enterprises. However, the current research mainly focuses on the real-time scheduling of customer arrival times and actual demand, and has not yet involved the demand prediction and path uncertainty. The specific outlook is as follows:

(1) Future research should introduce demand forecasting methods to predict customer demand in advance by analyzing historical data and market trends [35]. This will make the scheduling plan more forward-looking, reduce response time to sudden changes in demand, and improve overall scheduling efficiency.

(2) Vehicles may encounter uncertain factors such as traffic congestion and weather changes on their way to coal mining enterprises. These factors may have an impact on scheduling. Therefore, subsequent studies should adjust the model by combining it with these uncertainties and explore robust optimization or real-time adjustment mechanisms to improve the flexibility and adaptability of scheduling systems.

All in all, although the MCVS method proposed in this paper provides strong support for the vehicle scheduling of coal mining enterprises, there is still room for improvement in demand forecasting and uncertainty processing. Future research will focus on these problems, provide more perfect and efficient scheduling plans for coal mining enterprises, and further promote the sustainable development and competitiveness of coal mining enterprises in the complex operating environment.