Green Transportation Model in Logistics Considering the Carbon Emissions Costs Based on Improved Grey Wolf Algorithm

Abstract

The use of new energy vehicles in transportation can effectively promote the development of green logistics. This study selects heavy–duty diesel trucks as traditional logistics vehicles and heavy–duty electric trucks as new energy logistics vehicles. A green transportation model considering carbon emission costs is established to analyze whether new energy logistics vehicles should be used in long–distance freight delivery and how to arrange the use of two types of logistics vehicles. The model is solved using a grey wolf optimization algorithm, which incorporates good point sets, dynamic adaptive inertia weights, and memory–guided location update equations. The model is then applied to three logistics companies in Zhejiang province, China. In addition, considering the time constraints of the logistics industry, the model is used to simulate the arrangement of logistics transport companies for two types of vehicles in long–distance transportation of goods under realistic situations. Finally, this paper studies the future arrangements for long–distance transportation of goods by logistics companies considering the growing popularity of charging piles and advancements in production technology for new energy vehicles. The results show that the involvement of more new energy logistics vehicles in long–distance transport results in lower transportation costs and reduced pollution generated during transportation.

1. Introduction

Frequent logistics activities increase fuel consumption, air pollution, and resource waste, negatively impacting sustainable economic development. Transportation is one of the major causes of pollution in the logistics industry. Therefore, we must prioritize the development of green transportation in logistics. New energy electric vehicles have excellent development potential due to low noise and pollution during operation. China recognizes the importance of environmental protection and encourages using new energy vehicles. However, while new energy electric vehicles have been widely used for near–distance transportation in the logistics industry, they are rarely used for long–distance transportation. This paper examines the feasibility of incorporating new energy logistics vehicles in long–distance cargo transportation from the logistics center to the distribution point and establishes a mathematical model that minimizes the sum of transportation costs of two types of logistics vehicles, carbon emission costs, charging time costs, and wages of transportation personnel. This paper designs an improved grey wolf optimization algorithm to solve the problem and applies Zhejiang Province as a logistics center of long–distance transportation. Analyzing the development status and future direction of new energy logistics vehicles guides logistics companies in arranging transportation.

2. Literature Review

The concept of green logistics was introduced in the 1990s and received attention from scholars. Researchers have studied green logistics in different regions, such as Jiangxi [1] and Henan [2] provinces in China and the logistics companies of Lithuania [3] and Poland [4]. These studies have explored the efficiency, characteristics, and applications of green logistics, respectively. The application of green logistics in different industries has also been studied by researchers, for example, the auto parts industry [5], the chemical industry [6], and agriculture [7,8]. These studies provide a reference for the future development of green logistics.

Green logistics includes resource pooling, green transportation, green storage, green packaging, and waste streams (reverse logistics). De Souza et al. [9] used hierarchical analysis to normalize and rank 27 green practice indicators in green logistics performance. The results showed that green transportation had the worst results. Shah et al. [10] conducted a study on the sustainability of green transportation and found that an effective green transportation system can reduce risk, congestion, and pollution and improve safety while optimizing travel speeds and traffic flow. Therefore, further research on green transportation is necessary.

In terms of research methodology, The qualitative study of green transport focuses on the importance of implementing green transport [11], exploring the application of green transportation and the problems to be faced from different perspectives, such as economy [12] and resource conservation [13]. The quantitative study of green transport has two main aspects. The first aspect involves the application of relevant knowledge, such as econometrics and statistics, to analyze green transport. For example, Hussain et al. [14] used the autoregressive distributed lag model to evaluate the contribution of environmental spending and green transportation to transportation emissions. Wang et al. [15] and Liu et al. [16] used the Global Malmquist–Luenberger index to study the relationship between transportation infrastructure and green total factor productivity. Almatar et al. [17] explored the benefits of green transport implementation by distributing questionnaires to those involved in the environmental protection sector. The second aspect is to develop a green transportation model using intelligent optimization algorithms to solve it. For instance, Wu et al. [18] combined fourth–party logistics with green transportation of goods and solved it using an improved particle swarm optimization algorithm. Jiang et al. [19] addressed the multi–vehicle and one–cargo green transport problem by creating a dual–objective model that minimized travel time and total emissions. Salehi et al. [20] developed a dual–objective model to minimize carbon emissions and total transportation costs. Li et al. [21] developed a nonlinear programming model that considered carbon emissions and utilized an adaptive genetic algorithm for optimization. Xin et al. [22] developed a green transportation model considering the impact of solid waste management and air pollution on urban operations and solved it using heuristic algorithms.

In terms of research objectives, It mainly includes the impact of green transportation on different elements [12,13,14,15,16], how to reduce the cost of carbon emissions, which leads to green transportation [19,20,21], and the use of new energy vehicles in transport. For example, Han et al. [23] concluded from a study of the energy transition in the Chinese transportation sector that electric vehicles were feasible for public passenger and freight transport applications. Chen [24] focused on using new energy vehicles in public transportation in Guangdong Province. Zhang [25] investigated the application of new energy vehicles in public transportation and provided recommendations for the sustainable development of Shenzhen’s new energy vehicle industry.

Most research on new energy vehicles in transportation focuses on small and medium–sized vehicles, although heavy trucks are responsible for most cargo transportation. Heavy trucks generally use diesel engines, which emit high levels of nitrogen oxides and particulate pollutants during operation, posing a threat to human health, contributing to global warming, and negatively impacting ecological sustainability. Therefore, it is necessary and meaningful to include heavy–duty electric trucks to participate in the study of cargo transportation. Currently, the research on heavy–duty trucks is focused on feasibility analysis. For example, Qiu et al. [26] evaluated the economic viability of electrified highways as a supplement to heavy–duty electric trucks. By modeling the applicability and feasibility of decarbonization strategies for energy and emission impacts at different time points, Khanna et al. [27] made short and long–term projections for decarbonizing heavy–duty trucks in China. Yaïci et al. [28,29] studied the feasibility of building a heavy–duty truck hydrogen refueling infrastructure. However, less research has been done on heavy–duty electric trucks in the transportation sector.

From the above review, we can conclude that the study of green logistics has encompassed diverse fields, including ecological and environmental science, engineering, mathematics, and economics, producing significant research outcomes that have significantly advanced green logistics. Nevertheless, there is not enough research in the field of transportation for green logistics. The current research on green transportation primarily focuses on the relationship between transportation modes and the environment. Limited research has been conducted on the role of electric trucks in green transportation, particularly in specific industries such as logistics. Furthermore, the feasibility of implementing heavy–duty electric trucks in long–distance cargo transportation has received little attention. Most existing research on heavy–duty electric trucks centers around the batteries used in future heavy–duty trucks and the decarbonization of heavy–duty trucks. Therefore, there is a need for more studies on the feasibility of applying heavy–duty electric trucks in specific industries.

This paper proposes a model considering new energy logistics vehicles (heavy–duty electric trucks) involved in long–distance cargo transportation to determine the type of logistics vehicles selected by the logistics center and the number of goods to be distributed. The ultimate goal of the model is to minimize the total cost. In the construction of the model, the transportation cost of two kinds of logistics vehicles, the carbon emission cost of traditional logistics vehicles, the charging time cost of new energy logistics vehicles, and the wages of transportation personnel are considered. The model is applied to the cargo transportation of three logistics companies in Zhejiang Province, China, to verify the model’s validity. Finally, this paper discusses the future use of new energy logistics vehicles for long–distance transportation.

3. Mathematical Modeling

3.1. Problem Description

This paper explores the feasibility of using heavy–duty electric trucks for long–distance cargo transportation and examines how logistics centers can arrange the use of traditional logistics vehicles and new energy logistics vehicles to reduce costs and pollution. We abstract the green transportation problem as a multi–vehicle, multi–supply point, and multi–demand point vehicle scheduling problem, where the supply point represents the logistics center, and the demand point represents the distribution area. Each logistics center has a certain number of traditional logistics vehicles and new energy logistics vehicles. This paper explores the many–to–many transportation between logistics centers and distribution areas, which implies that each logistics center can transport goods for all distribution areas, and each distribution area can accept goods from all logistics centers. For conventional logistics vehicles, consider the fuel consumption and carbon emission cost. For new energy logistics vehicles, consider the cost of electricity consumption and the charging time. Moreover, the pay of the driving staff is also taken into account to provide a more comprehensive analysis.

3.2. Model Assumptions

For modeling, the following assumptions are made in this paper:

• Traditional logistics vehicles operate on diesel fuel.
• Only one type of vehicle is used to transport cargo from logistics center i to distribution location j.
• The vehicles are loaded to full capacity at the point of departure and return empty.
• All vehicles move at a constant speed.
• Each vehicle has a driver.
• The vehicles depart from and return to the logistics center i.
• Supply and demand are expressed in terms of the number of fully loaded vehicles.
• Both types of vehicles have the same cargo capacity.

3.3. Parameter and Variable

The parameters and variables in the model are described in

Table 1. Parameters and variables description.

Parameter, Variables	Description
$I$	Set of logistics centers, $i\in I$
$J$	Set of distribution points, $j\in J$
$S_i$	The total number of fully loaded vehicles owned by logistics center i, where STra represents the number of fully loaded conventional logistics vehicles, and SNew represents the number of fully loaded new energy logistics vehicles.
$D_j$	Number of fully loaded vehicles required at distribution point j.
$d_{ij}$	Distance between logistics center i and distribution location j
$Q_{ij}$	The number of logistics vehicles is arranged by logistics center i to distribution location j.
$k_{ij}$	The number of times the new energy logistics vehicle is charged from distribution center i to distribution location j.
$t_{ij}$	Time from logistics center i to distribution location point j
$q_{Tra}$	Loading capacity of conventional logistics vehicles
$q_{New}$	Loading capacity of new energy logistics vehicles
$a_{Tra}$	Per fuel consumption of a conventional logistics vehicle
$a_{New}$	Per electricity consumption of a new energy logistics vehicle
$c_{Tra}$	Unit oil price
$c_{N\mathrm{e}w}$	Unit electricity price
$f$	The unit cost of carbon emissions
$v_{Tra}$	The average speed of traditional logistics vehicles
$v_{New}$	The average speed of new energy logistics vehicles
$c_t$	Unit time wage for transport staff
$R{\mathrm{co}}_2$	The amount of CO2 produced per kilometer of diesel fuel
$T_{N\mathrm{e}w}$	One charge time for new energy logistics vehicles
$c_T$	The unit time cost of charging new energy logistics vehicles
$d_T$	Endurance ability of new energy logistics vehicles
$\rho$	The density of diesel
$q$	The calorific value per unit of diesel
$W_{Tra}$	The conversion efficiency of the calorific value
$W_{B\mathrm{at}}$	Battery cycle efficiency
$W_{Em}$	Motor efficiency
$x_{ij}$	Distribution point j is set to 1 for distribution by traditional logistics vehicles and 0 for new energy logistics vehicles.
$y_{ij}$	$\left\{\begin{array}{c}{y}_{ij}=1 Logistics center i to distribution site j\\ y_{ij}=0 Logistics center i not distribution site j \end{array}\right.$

.

3.4. Green Transportation Model with Total Cost Minimization

This paper aims to study the feasibility of incorporating new energy logistics vehicles in long–distance cargo transportation and proposes an optimal allocation strategy for two types of logistics vehicles to minimize total cost. This study considers five cost factors and presents their corresponding expressions:

$$z_1={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J(1+q_{Tra})a_{Tra}{c}_{Tra}{x}_{ij}{y}_{ij}{d}_{ij}}}{Q}_{ij}$$

(1)

$$z_2={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J(1+q_{New})a_{New}{c}_{New}(1-x_{ij})y_{ij}{d}_{ij}}}{Q}_{ij}$$

(2)

$$z_3={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^{J}2c_t{t}_{ij}{Q}_{ij}}}$$

(3)

$$z_4={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^{J}2c_T{T}_{New}{k}_{ij}{Q}_{ij}}}$$

(4)

$$z_5={\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^{J}2R_{c{o}_2}f{Q}_{ij}{x}_{ij}{y}_{ij}{d}_{ij}}}$$

(5)

Z₁ represents the round–trip transportation costs for traditional logistics vehicles. Z₂ represents the round–trip transportation costs for new energy logistics vehicles. Z₃ represents the salary of transportation personnel. Z₄ represents the charging time cost for new energy logistics vehicles. Z₅ represents the carbon emission cost associated with traditional logistics vehicles.

The objective of the green transport model is to minimize total cost, which is expressed as follows:

$$z_1+z_2+z_3+z_4+z_5\ge \min z$$

(6)

The unit fuel consumption of traditional logistics vehicles can be quantified using a specific formula. However, no direct formula is available for calculating the unit power consumption of new energy logistics vehicles. As a result, the unit power consumption of new energy logistics vehicles can only be estimated from the unit fuel consumption of traditional logistics vehicles, and the expression is displayed below:

$$a_{New}=\frac{a_{Tra}\rho q{W}_{Tra}}{\beta W_{Bat}{W}_{Em}}$$

(7)

Because 1 kwh is equivalent to 3.6 MJ, β is 3.6.

According to the BP China Carbon Emissions Calculator, 1 L of diesel produces 2.63 kg of CO₂. The formula for calculating the amount of CO₂ produced per kilometer by a diesel vehicle is as follows:

$$R_{c{o}_2}=2.63a_{Tra}$$

(8)

The remaining expressions of the green transport model are presented below:

$$t_{ij}=\frac{d_{ij}{y}_{ij}}{v_{Tra}{x}_{ij}+v_{New}(1-x_{ij})}$$

(9)

$${\displaystyle \sum _{j=1}^J{Q}_{ij}{x}_{ij}{y}_{ij}\le S_{Tra}i}$$

(10)

$${\displaystyle \sum _{j=1}^J{Q}_{ij}(1-x_{ij})y_{ij}\le S_{N\mathrm{ew}}i}$$

(11)

$${\displaystyle \sum _{\mathrm{i}=1}^I{Q}_{ij}{y}_{ij}=D_j}$$

(12)

$$k_{ij}=\left[\frac{d_{ij}(1-x_{ij})y_{ij}}{d_T}\right]+1$$

(13)

$${\displaystyle \sum _{i=1}^I{y}_{ij}\ge 1}$$

(14)

$${\displaystyle \sum _{j=1}^J{y}_{ij}\ge 1}$$

(15)

$$y_{ij}=\left\{\begin{array}{ll}0& Q_{ij}=0\\ 1& Q_{ij}\ne 0\end{array}\right.$$

(16)

$$a_{Tra},a_{New},c_{Tra},c_{New},f>0$$

(17)

Equation (9) represents the time from logistics center i to distribution location j. Equations (10) and (11) indicate that the number of two types of logistics vehicles involved in transportation does not exceed the number of the logistics center i. According to Equation (12), the demand for goods at all distribution locations is satisfied. Equation (13) represents the number of times that the new energy logistics vehicle is charged from distribution center i to distribution point j. Equation (14) shows that all distribution locations have received the goods. All logistics centers are involved in transportation, according to Equation (15).

4. Grey Wolf Optimization Algorithm

4.1. Standard Grey Wolf Optimization Algorithm

Mirjalili et al. [30] proposed the grey wolf optimization algorithm (GWO) in 2014, which the gray wolf inspired. Currently, GWO and its hybrid or improved technologies are being used in many various fields, such as engineering [31], computer science [32], energy fuels [33], transportation [34], agriculture [35], and medicine [36], with successful outcomes. The effectiveness of GWO in solving problems highlights its potential, making it the chosen algorithm to solve the model in this paper.

The algorithm simulated the leadership hierarchy and hunting mechanism of the grey wolf in nature. α, β, δ, and ω denote the first, second, third, and fourth–ranked grey wolves, respectively. Grey wolf α has a minor proportion in the group, but it has absolute dominance over grey wolves β, δ and ω. Grey wolf ω has the most significant proportion in the group, but it has the least power and must follow the command of the grey wolves α, β and δ. Thus, the grey wolves α, β and δ guide the hunting behavior of the grey wolf packs.

During hunting, grey wolves round up their prey, and their behaviors are defined as follows:

$$D=\left|C·X_{p(t)}-X(t)\right|$$

(18)

$$X(t+1)=X_{p(t)}-A·D$$

(19)

$$A=2a·r_1-a$$

(20)

$$C=2·r_2$$

(21)

Equation (18) defines the distance calculation between a grey wolf and its prey. Equation (19) represents the position of the grey wolf when the algorithm iterates to generation t + 1. Equations (20) and (21) are the computational coefficient vectors A and C.

When hunting, grey wolves α will identify the location of their prey and lead β and δ grey wolves to surround the target. The mathematical model of this process is shown below:

$$D_{\alpha }=\left|C_1·X_{\alpha }-X\right|$$

(22)

$$D_{\beta }=\left|C_2·X_{\beta }-X\right|$$

(23)

$$D_{\delta }=\left|C_3·X_{\delta }-X\right|$$

(24)

$$X_1=X_{\alpha }-A_1·D_{\alpha }$$

(25)

$$X_2=X_{\beta }-A_2·D_{\beta }$$

(26)

$$X_3=X_{\delta }-A_3·D_{\delta }$$

(27)

$$X(t+1)=\frac{X_1+X_2+X_3}{3}$$

(28)

Equations (22)–(24) represent the distances between grey wolves α, β, and δ and other individuals, respectively. Equations (25)–(27) represent the direction and step length of ω grey wolves toward α, β, and δ grey wolves, respectively, and Equation (28) determines the final position of ω grey wolves.

The grey wolf approaches its prey gradually when the prey stops moving. The formula for the convergence factor is given below, representing the grey wolf approaching the target.

$$a=2-2\frac{t}{T_{\max }}$$

(29)

Tmax denotes the maximum number of iterations.

4.2. Improved Grey Wolf Optimization Algorithm

The GWO uses a random method to initialize the population, and the evolution of the population is guided only by high–quality solutions, which makes the grey wolf optimization algorithm fall into the local optimum during the search process. This paper constructs the initial solution using the good point set. Inspired by the idea of setting inertia weights and memory preservation of the optimal solutions of the motion history of the particle in the particle swarm algorithm, dynamic adaptive inertia weights and memory–guided position–updated equations are introduced to change the individual position–update process of the GWO. This approach enhances the local exploitation capability of the GWO and makes the algorithm jump out of the local optimum.

4.2.1. Good Point Set

Compared to the random method’s initial population distribution, the populations initialized with good point sets exhibit a more uniform distribution. The distribution of the initial population in the search space is a crucial factor that determines the algorithm’s global search ability. The more evenly the population distribution is, the higher the population diversity is and the stronger the global search ability of the algorithm is. So using the good point set method to initialize the population can improve the algorithm’s stability. Figure 1 illustrates the population distribution for random initialization (a) and good point set initialization (b).

4.2.2. Dynamic Adaptive Weights and Memory–Guided Location Update Equation

This paper uses the position update method of the particle swarm algorithm to update the position of ω grey wolf to improve the local exploration capability of the GWO. The position update equation is shown as follows:

$$w=w_{\min }+(w_{\max }-w_{\min })(1-\exp (1-T_{\max }/t))$$

(30)

$$P=\frac{w(X_1+X_2+X_3)}{3}+c_1{r}_1(X_1-P)+c_2{r}_2(X_2-P)+c_3{r}_3(X_3-P)$$

(31)

W_max denotes the maximum inertia weight, while W_min represents the minimum. The maximum number of iterations is T_max, and the current iteration is t. The learning factors of the three grey wolf individuals are designated as c₁, c₂, and c₃, respectively. r₁, r₂, and r₃ represent random numbers between 0 and 1.

4.3. GWO and Improved GWO

This paper presents test experiments on GWO and IGWO, which are based on the Windows 11 operating system and simulated using MATLAB 2016a. The study focuses on verifying the optimization capability of IGWO and GWO in eight test functions, which include single–peaked functions (F₁, F₂, F₃, and F₄) and multi–peaked functions (F₅, F₆, F₇, and F₈).

Table 2. Test functions.

Test Function	Range	Global Minimal
$F_1(x)={\displaystyle {\sum }_{i=1}^n{x}_i^2}$	[−100, 100]	0
$F_2(x)={\displaystyle {\sum }_{i=1}^n\left|x_i\right|}+{\displaystyle {\prod }_{i=1}^n\left|x_i\right|}$	[−10, 10]	0
$F_3(x)=\underset{i}{\max }\left\{\left|x_i\right|,1\le i\le n\right\}$	[−100, 100]	0
$F_4(x)={\displaystyle {\sum }_{i=1}^{n}i{x}_i^4}+random[0,1)$	[−1.28, 1.28]	0
$F_5(x)={\displaystyle {\sum }_{i=1}^n[x_i^2}-10\cos (2\pi x_i)+10]$	[−5.12, 5.12]	0
$\begin{array}{l}{F}_6(x)=-20\exp (-0.2\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{x}_i^2}})-\\ \exp (\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\cos (2\pi x_i))+20+e}\end{array}$	[−32, 32]	0
$F_7(x)=\frac{1}{4000}{\displaystyle {\sum }_{i=1}^n{x}_i^2}-{\displaystyle {\prod }_{i=1}^n\cos (\frac{x}{\sqrt{i}}})+1$	[−600, 600]	0
$\begin{array}{l}{F}_8(x)=\left[1+{(x_1+x_2+1)}^2\left(19-14x_1+3x_1^2-14x_2+6x_1{x}_2+3x_2^2\right)\right]\\ \left[30+2{\left(x_1-3x_2\right)}^2\left(18-32x_1+12x_1^2+48x_2-36x_1{x}_2+2\right)\right]x_2^2\end{array}$	[−5, 5]	3

displays each function’s expressions, ranges, and global minimum.

In this experiment, n = 30, and the test functions F₁−F₈ are solved 50 times using IGWO and GWO, respectively. The mean and standard deviation of the 50 optimal solutions are shown in

Table 3. Function optimization results of GWO and IGWO.

Test Function	GWO		IGWO
	Mean	SD	Mean	SD
F1	1.1 × 10−8	8.5 × 10−9	4.3 × 10−109	1.74 × 10−108
F2	7.2 × 10−6	4.3 × 10−6	1.4 × 10−12	1.1 × 10−12
F3	0.03	0.02	1.2 × 10−8	1.2 × 10−8
F4	7 × 10−3	4.5 × 10−3	9.3 × 10−4	7.0 × 10−4
F5	14.0	7.0	1.8	3.6
F6	1.9 × 10−5	1.1 × 10−5	6.8 × 10−11	8.3 × 10−11
F7	9 × 10−3	0.01	2.3 × 10−3	6.9 × 10−3
F8	5.7	14.8	3	1 × 10−4

.

Figure 2 illustrates the relationship between the number of iterations and the minimal value of the optimal solution for each test function.

In solving the minimal value problem, the smaller the mean value, the better the algorithm’s average performance. The smaller the standard deviation, the more stable the algorithm. The results in Table 3 show that IGWO outperforms GWO in terms of the mean and standard deviation of optimal solutions for functions F₁–F₈. Figure 2 further illustrates that the minimum values obtained from IGWO are smaller than those obtained from GWO solutions. Therefore, IGWO is superior in performance and stability to GWO.

5. Example Analysis

5.1. Data

This study explores the need for new energy logistics vehicles in long–distance transportation and the arrangement of two different types of logistics vehicles. The research assumes that the goods transported are identical and employs a many–to–many distribution method. The required goods at each distribution point are expressed as the number of fully loaded vehicles to simplify calculations. This paper takes three logistics transportation companies in Zhejiang Province as logistics centers. Shandong, Henan, Beijing, Guangzhou, and Hunan are set as distribution points. M₁, M₂, and M₃ denote the three logistics companies. The distribution points in Shandong, Henan, Beijing, Guangzhou, and Hunan are denoted by N₁, N₂, N₃, N₄, and N₅, respectively.

Table 4. Vehicle stock in logistics companies.

	M1	M2	M3
STra	60	30	50
SNew	40	50	50

displays the reserves of new energy logistics vehicles and traditional logistics vehicles for each of the three logistics companies.

Table 5. Distance and demand from each province to Zhejiang.

Province	Shandong	Henan	Beijing	Guangzhou	Hunan
Distance/km	851.4	922.4	1247.6	1253.2	878.8
Demand/Vehicle	20	25	30	15	20

provides information on the cargo demand of each region and the distance between the logistics companies and each area.

Distance from Zhejiang to Shandong, Henan, Beijing, Guangzhou, and Hunan are taken from the Baidu map.

5.2. Result and Analysis

The distribution center has sufficient cargo volume. Both traditional and new energy logistics vehicles are trucks with a capacity of 20 tons. According to the price of 0# diesel, industrial electricity, and the unit fuel consumption of a 20−ton truck in Zhejiang Province, this paper establishes the following values: c_Tra = 1.058 USD/L, c_New = 0.126 USD/kwh, a_Tra = 0.25 L/km. Based on relevant research and the real situation, V_New and V_Tra are set to 70 km/h. c_T sets to 8 USD/h. c_t sets to10 USD/h. T_New sets to 8 h. d_T sets to 200 km. The fuel density is ρ = 0.72 kg/L, and the energy content of the fuel is q = 33 MJ/kg. As W_Tra ∈ [34%, 45%], W_Tra sets to 40%. W_Bat and W_Em are set to 90%. Rennert et al. [37] concluded from a study of the social cost of carbon emissions that the actual social cost of carbon emissions should be 3.6 times higher than the USD 51 set by the US government, which is USD 185 per ton of CO₂. Therefore, this paper takes the carbon emission cost as USD 185/ton, which is f = 0.185 USD/kg.

The experimental results of using IGWO and GWO solved 30 times are shown in

Table 6. Experimental results.

	Minimal Total Cost	Mean	SD
GWO	1.495 × 107	1.582 × 107	1.937 × 106
IGWO	1.491 × 107	1.508 × 107	0.380 × 106

, Figure 3 and Figure 4.

The transport options corresponding to the minimal total cost are shown in

Table 7. Transportation options.

	N1	N2	N3	N4	N5
M1	0	8	8	0	20
M2	0	0	20	15	0
M3	20	17	2	0	0

and

Table 8. Distribution of different types of logistics vehicles.

	N1	N2	N3	N4	N5
M1	x	0	0	x	0
M2	x	x	0	0	x
M3	0	0	0	x	x

.

Table 7 shows the number of new energy logistics vehicles and traditional logistics vehicles arranged for each province by the three logistics transport companies. Table 8 provides information on the types of vehicles the three logistics transport companies utilize. ‘0’ indicates that logistics company Mi has assigned new energy logistics vehicles to transport goods to distribution point Nj. ‘1’ means that traditional logistics vehicles have been arranged to transport goods to distribution point Nj. ‘×’ signifies that logistics company Mi does not transport goods to distribution point Nj.

The results presented in Table 6 demonstrate that the IGWO solution yields smaller values for minimal total cost, mean, and standard deviation compared to the GWO solution. Figure 3 and Figure 4 show that the IGWO solution shows faster convergence and higher stability. These findings indicate that the improved algorithm is effective in solving the actual problem. Table 7 and Table 8 reveal that all logistics transport companies arrange new energy logistics vehicles to participate in cargo transportation to achieve the lowest total cost. It shows that new energy logistics vehicles can not only join in transporting goods over long distances but should also be dispatched as far as possible to transport goods. But the time constraints of logistics transportation often lead companies to opt for traditional logistics vehicles in long–distance cargo transportation. The main reason why logistics companies rarely choose new energy logistics vehicles to participate in long–distance transportation is that the charging facility network is not perfect, the charging piles are not widespread, the endurance ability of new energy logistics vehicles is not strong, long–distance transportation requires multiple charging, the charging time is too long, and the timeliness of transportation is not guaranteed.

To better reflect the impact of time on the selection of vehicle types by logistics companies in practical scenarios, this paper sets to c_T = 80 USD/h and keeps the other variables constant. The IGWO is used for solving. The total cost is 1.458 × 10⁸ USD.

Table 9. Transportation options.

	N1	N2	N3	N4	N5
M1	20	12	18	1	0
M2	0	0	0	14	0
M3	0	13	12	0	20

and

Table 10. Distribution of different types of logistics vehicles.

	N1	N2	N3	N4	N5
M1	1	1	1	1	x
M2	x	x	x	1	x
M3	x	1	1	x	1

depict the number and types of logistics vehicles the three logistics companies dispatched.

Table 9 and Table 10 indicate that all logistics companies arrange traditional logistics vehicles to participate in cargo transportation. It shows that time is the main reason logistics transport companies do not choose new energy logistics vehicles.

As the country attaches importance to new energy, the production technology of new energy vehicles is constantly improving, and charging piles are gradually becoming popular. In the future, the endurance ability and speed of new energy logistics vehicles will increase significantly, and the charging time will reduce progressively. This paper takes T = 2 h, d_T = 400 km, and keeps the values of the remaining variables constant to forecast how logistics transport companies will arrange their transport vehicles. The IGWO solution gets a minimal total cost of 7.806 × 10⁵ USD, corresponding to the transportation scheme shown in

Table 11. Transportation options.

	N1	N2	N3	N4	N5
M1	0	10	10	5	7
M2	17	0	12	10	0
M3	3	15	8	0	13

and

Table 12. Distribution of different types of logistics vehicles.

	N1	N2	N3	N4	N5
M1	x	0	0	0	0
M2	0	x	0	0	x
M3	0	0	0	x	0

.

As seen from Table 11 and Table 12, all the vehicles involved in transportation are new energy logistics vehicles. The total transportation cost will be significantly reduced when the transportation demand is met. When the endurance ability of new energy logistics vehicles continues to increase, charging time continues to shorten, and charging piles become prevalent, new energy vehicles are the optimal choice for logistics companies, whether for near–distance transport or long–distance transport.

6. Conclusions

This paper establishes a logistics transportation model considering the transportation cost, charging cost, carbon emission cost, and the salary of transportation staff. The objective is to assess the viability of utilizing new energy logistics vehicles for long–distance cargo transportation and how to arrange the number of new energy logistics vehicles and traditional logistics vehicles. According to the results obtained from the IGWO, it shows that long–distance cargo transportation should arrange new energy logistics vehicles. The more new energy logistics vehicles are involved in transportation, the lower the total transportation cost. The wide use of new energy logistics vehicles can reduce the environmental pollution caused by transportation and the transportation costs of logistics companies. Therefore, the state should actively promote the development of new energy logistics vehicles and the popularity of charging piles. Logistics transport companies should prioritize using new energy logistics vehicles for goods transportation while ensuring time is not exceeded.