Logistics Distribution Path Optimization Considering Carbon Emissions and Multifuel-Type Vehicles

Abstract

With the development of a sustainable economy, higher requirements are put forward for logistics enterprises, which not only need to meet the requirements of profit growth but also to meet the need of sustainable development. A vehicle routing problem (VRP) optimization model considering carbon emissions and multifuel-type vehicles (VRP-CEMF) is proposed to solve the problems of air pollution and high transportation cost in the current logistics distribution. An improved genetic algorithm (IGA) is designed to solve the VRP-CEMF. The impact of carbon emissions and multifuel-type vehicles on the logistics distribution path is explored by a real example simulation. The results show that the logistics distribution path optimization considering carbon emissions and multifuel-type vehicles including hybrid electric vehicles and hydrogen-fueled vehicles can significantly reduce carbon emissions on the premise of ensuring the lowest total cost. Furthermore, the impact of carbon emissions, hydrogen fuel price, and customer demand on the logistics distribution path is discussed by sensitivity analysis. The research results of this paper provide an effective reference for enterprises to control carbon emissions in the process of logistics distribution and promote the green transformation of logistics.

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1. Introduction

With the growth of the economy, the logistics industry is developing rapidly [1]. However, the development of the logistics industry has brought environmental problems. A large amount of carbon dioxide is generated during the logistics transportation [2–4]. Under the circumstances, low-carbon logistics has become a new direction and an inevitable choice for the logistics industry [5].

In order to achieve low-carbon logistics, reducing carbon emissions in logistics distribution is becoming an important measure [6] In logistics distribution, the logistics distribution path optimization is the key. Many scholars have studied the logistics distribution path optimization considering carbon emission, obtaining a reduction in carbon emission while reducing the operating costs of distribution vehicles [7–10]. Moreover, in order to further reduce carbon emissions in logistics distribution, vehicles with different capacities are taken into account in the logistics distribution path optimization, and better effects are achieved [11–14]. However, the vehicles for logistics distribution in these studies are mainly petrochemical fuel vehicles. With the development of new energy technologies, vehicles with different fuel types have emerged in recent years, such as new energy vehicles with hydrogen and electricity as the main power [15, 16]. New energy vehicles have obvious low-carbon advantages [17, 18] and begun to attract the attention of the logistics transportation industry [19, 20]. The impacts of these vehicles with different fuel types on logistics distribution paths, carbon emissions, and cost require further research. Based on this, carbon emissions and multifuel-type vehicles are considered in logistics distribution path optimization, and their impacts are explored. The main contributions involve the following three aspects:

1. Considering carbon emissions and multifuel-type vehicles, a logistics distribution path optimization model, vehicle routing problem optimization model considering carbon emissions and multifuel-type vehicles (VRP-CEMF), is established, and an improved genetic algorithm (GA) (IGA) is designed to solve the model.

2. The impact of carbon emissions on the logistics distribution path is explored, and the results show that by taking carbon emissions into account in the logistics distribution path optimization, both the total cost and carbon emissions are reduced.

3. The impact of multifuel-type vehicles on the logistics distribution path is explored, which includes diesel-fueled vehicles, hybrid electric vehicles, and hydrogen-fueled vehicles. The results show that the logistics distribution path optimization considering multifuel-type vehicles can significantly reduce the carbon emissions on the premise of ensuring the lowest total cost.

The remainder of the paper is organized as follows. Section 2 provides an overview of related literature. Section 3 presents the problem description. Section 4 presents the mathematical model of VRP-CEMF. Section 5 proposes the IGA algorithm to solve the model. Section 6 reports simulation and discussion of a real example. Finally, some conclusions are presented in Section 7.

2. Literature Review

The logistics distribution path optimization belongs to the VRP. A lot of research results have been achieved and generally include the traditional logistics distribution path optimization, the logistics distribution path optimization considering multiple types of vehicles, and the logistics distribution path optimization considering carbon emissions.

2.1. The Traditional Logistics Distribution Path Optimization

In the traditional logistics distribution path optimization, single-fuel type vehicles are typically considered. Wang and Li [21] proposed a VRP-based discrete variable multiobjective problem model considering total delivery distance and customer satisfaction, and a hybrid algorithm based on a GA is proposed to solve the model. Mohammed et al. [22] applied an IGA to the capacitated VRP, which considered vehicle capacity and travel time to ensure customer satisfaction, and optimal vehicle travel paths are achieved. Kassem and Chen [23] studied the VRP with simultaneous pickup and delivery in closed-loop logistics network optimization and proposed a mixed-integer programming model to express the routing problem. Ehmke et al. [24] introduced a planning system for city logistics service providers, in which travel time is considered and a heuristic method is adopted, and more realistic vehicle routes are obtained.

As the scale of VRP continues to expand, the solution algorithms become more and more intelligent. For example, Gil et al. [25] studied the multidepot green VRP with pick-up and delivery and developed a mathematical programming and metaheuristic method to tackle the problem. Wang and Luo [26] proposed a model for cold-chain logistic distribution path optimization with time windows, and the improved intelligent water drop algorithm was applied to the model. Xu et al. [27] designed a vehicle routing optimization model and introduced an ant colony optimization algorithm to solve the model. Liu [28] used the recursive fuzzy neural network algorithm to optimize the logistics distribution path of e-commerce, and optimal distribution paths with different characteristics are obtained. Qi and Li [29] proposed a hybrid method that combines iterated local search with the traditional ant colony algorithm for vehicle routing optimization. Experimental results show that this method achieves high optimization efficiency in standard tests. By studying the VRP in cross-docked distribution networks, Ahkamiraad and Wang [30] proposed a mixed-integer linear programming model that incorporates pickup, delivery, capacity, and time windows. A hybrid algorithm combining GA and particle swarm optimization was proposed to solve the model. Guo et al. [31] studied the location–inventory routing problem in a closed-loop supply chain and formulated the problem as a nonlinear integer programming model. A novel heuristic approach that combines simulated annealing with an adaptive GA was developed to solve the model. Ren et al. [32] proposed a mathematical model for logistics distribution path planning that comprehensively considers road characteristics and distance and used an adaptive GA to solve the model.

The above literature has established an optimization model for the VRP of a single vehicle type and has formed a relatively complete research system. However, these traditional models often fall short in adapting to the inherent variability and complexity of modern logistics, particularly regarding the increasing need for environmental considerations. This highlights the limitations of single-fuel-type vehicles in today’s distribution networks and lays the direction for research into multifuel-type vehicles that account for varying load capacities and requirements.

2.2. The Logistics Distribution Path Optimization Considering Multiple Types of Vehicles

With the in-depth research on the VRP and the widespread application of multifuel-type vehicles in practical logistics distribution, the optimization of logistics vehicle distribution routes that considers multifuel configurations has attracted significant research attention. Song and Ko [33] proposed a vehicle routing optimization model considering the refrigerated and nonrefrigerated vehicles and developed a heuristic algorithm to resolve the model. The practitioner can decide on a suitable number of both refrigerated and nonrefrigerated vehicles based on the performance and the availability. Huai et al. [34] constructed a multiobjective integer programming model under the premise of considering the coexistence of multiple types of vehicles to study the path optimization problem in the cold-chain logistics system, and a GA is designed to solve the problem. Wang et al. [35] extended the traditional VRP to a heterogeneous multitype fleet VRP with time windows and incompatible loading constraints and developed a mathematical mode to solve this problem. Yang et al. [36] studied the routing optimization problem with soft time windows and the constraints on vehicle capacity. The vehicle types were discussed, and the impacts of different vehicle types on operating cost, customer satisfaction, and environmental pollution were also analyzed. Gong and Liu [37] fully considered the needs of various vehicle types and customers in the distribution process and established a multivehicle transportation model for simultaneous picking and distribution with different capacities.

Significant progress has been achieved in multifuel vehicle routing optimization studies, demonstrating practical applicability by considering various vehicle types. However, despite these advancements, a critical gap persists: these investigations insufficiently address environmental sustainability perspectives. Specifically, the explicit integration of carbon emissions, differentiated by vehicle types, into the overall cost functions remains largely unexamined. This oversight limits their applicability in “green logistics” contexts, which the present study aims to specifically address.

2.3. The Logistics Distribution Path Optimization Considering Carbon Emission

Environmental improvement has been one of the important goals of the logistics industry, and more and more scholars are focusing on the issue of the logistics distribution path optimization considering carbon emissions. Sbihi and Eglese [38] proposed to produce and distribute goods in a sustainable manner and achieved green logistics by reducing energy use and other emission reduction measures in logistics activities. Erdoğan and Miller-Hooks [39] researched the green VRP and developed solution techniques to help fleets in overcoming difficulties that exist as a result of limited vehicle driving range in conjunction with limited refueling infrastructure. Sun and Lang [40] established a node-arc-based mixed-integer nonlinear programming model on the basis of full consideration of carbon emission and customer demand and developed a linearization method. The computational experiment results show that the proposed model and method can effectively solve the transportation routing problem with carbon emission. Kumar et al. [41] studied the multiobjective VRP and the relationship between fuel consumption and carbon emission and reduced total carbon emissions by minimization of total operational costs and fuel consumption. Xi and Li [42] studied the logistics distribution vehicle path optimization problem under a time-dependent transportation environment and established a model considering customer service time windows. The experiment results prove that the proposed model can minimize carbon emissions and total travel time. Chen et al. [43] obtained the functional relationship between transportation distance, carrying capacity, and carbon emissions through regression analysis, so as to solve the problem of agricultural product logistics distribution path planning considering carbon emissions. Su and Fan [44] combined with the concept of sustainable development to study the dynamic capacitated VRP, which is helpful to reduce carbon emissions and improve customer satisfaction. Furthermore, the relationship between carbon emissions and logistics costs was studied. Jabali et al. [45] proposed a vehicle routing model considering travel time, fuel, and carbon dioxide emissions costs. The simulation results show that fuel consumption was correlated with carbon dioxide emissions, and carbon emissions reduction led to cost reduction. Wang et al. [46] studied the VRP with time windows for cold-chain logistics based on carbon tax and discussed changes of distribution paths with different carbon emissions under different carbon taxes and their influence on the total distribution cost. Wang et al. [47] have proposed a cold-chain distribution method for fresh agricultural products under the carbon tax mechanism for the problem of large carbon emissions in the cold-chain distribution mechanism, which can effectively optimize the distribution path and reduce the carbon tax. Li et al. [48] established a logistics heterogeneous fleet VRP model to reduce carbon emissions while reducing logistics distribution costs. Wu et al. [49] proposed that in cold-chain logistics, there is a certain opposing principle between pursuing low distribution costs, high freshness, and low-carbon emissions, and a comprehensive carbon emission model is proposed to describe and quantify carbon emissions.

The above literature provides a comprehensive overview of research in logistics distribution path optimization, revealing significant advancements in various aspects. While some studies have begun to incorporate carbon emissions into path optimization, others have considered multiple vehicle types (primarily refrigerated/nonrefrigerated or petrochemical fuel vehicles with varying load capacities), a notable void that exists at the intersection of these two critical areas. Specifically, the existing literature largely overlooks the integrated impact of emerging new energy vehicles (such as electric [50], biofuel [51], and gasoline–electric hybrid vehicles [52]), which produce fewer carbon emissions, on logistics distribution path optimization when simultaneously considering their diverse capacities and environmental footprints.

Therefore, VRP-CEMF is proposed to solve the problems of air pollution and high transportation cost in the current logistics distribution by considering the following:

1. Multiple vehicle types, including both traditional and new energy vehicles.

2. The loading capacity of different types of vehicles.

3. Vehicle-type-specific integration of carbon emissions into the cost function.

3. Problem Description

The VRP considering carbon emissions and multifuel-type vehicles can be described as follows: there are multiple fuel types of distribution vehicles in the distribution center of the logistics system, which are different in terms of the maximum load, carbon emissions, and cost. The distribution center derives customer demand and location information from received orders and then uses multiple types of fuel vehicles to complete the distribution task, with carbon emissions being considered. Distribution vehicles start from the distribution center according to the planned optimal path and return to the distribution center after serving all customers.

The problem has the following characteristics:

1. Vehicles provide unidirectional distribution services to customers during the distribution process.

2. A single distribution center is considered. All vehicles depart from the center to perform tasks and return to the same center upon completion.

3. Customer locations and demands are predetermined, and each customer is only served by one distribution vehicle.

4. The distribution center has sufficient multifuel-type vehicles.

5. The total demand assigned to each vehicle must not exceed its capacity constraint.

As shown in Figure 1, the schematic diagram of the VRP considering carbon emissions and multifuel-type vehicles is illustrated, taking a scenario with one distribution center, nine customers, and three types of distribution vehicles (diesel-fueled vehicle, hybrid electric vehicle, and hydrogen-fueled vehicle) as an example. Figure 1(a) illustrates the distribution scheme utilizing single-fuel vehicles, specifically using three diesel-fueled vehicles to complete the distribution tasks via three distinct routes. Figure 1(b) presents the distribution scheme combining diesel-fueled and hybrid electric vehicles, where one diesel-fueled vehicle and two hybrid electric vehicles are deployed. Figure 1(c) demonstrates the mixed distribution scheme involving diesel-fueled and hydrogen-fueled vehicles, employing two diesel-fueled vehicles and one hydrogen-fueled vehicle. Furthermore, it is also shown in Figure 1 that the distribution paths obtained by considering different vehicle fuel types are different.

[figure(s) omitted; refer to PDF]

4. Mathematical Model

4.1. Parameter and Variable Definitions

The parameters used in this paper are defined as follows:

  C: set of distribution centers and customers, C = {0, 1, 2, …, N}, where 0 represents the distribution center, and the rest represent the customers

  M: set of vehicle types, M = {1, 2, …, m}

  K: set of vehicle numbers, K = {1, 2, …, k}

  $Q_m$: the capacity of type m vehicle

  $q_i$: the demand of customer i, i ∈ C

  $L_{\text{ij}}^m$: the load capacity of the type m vehicle when departing from customer i to customer j, i ∈ C, j ∈ C, i ≠ j

  $d_{ij}^m$: the distance traveled by the type m vehicle between customer i and customer j, i ∈ C, j ∈ C, i ≠ j

  $f^m$: the unit fixed cost of type m vehicle, ¥/vehicle

  $C_d^m$: the unit distance cost of type m vehicle, ¥/km

  $C_e^m$: the unit fuel consumption cost of type m vehicle, ¥/L

  $C_c^m$: the unit carbon emission cost of type m vehicle, ¥/kg

  $C_r^m$: the unit electricity price of type m vehicle, ¥/km

  $u_i$: sequence of vehicle i distribution to customers

  $X_{ijk}^m$: decision variable, if the vehicle k of type m travels from customer i to customer j, $X_{ijk}^m$ = 1; otherwise, $X_{ijk}^m$ = 0

4.2. Mathematical Model Formulation

A mathematical model for the logistics distribution path optimization considering carbon emissions and multifuel-type vehicles is formulated, and the objective function is to minimize the total costs of fixed cost, transportation cost, fuel consumption cost, and carbon emission cost.

4.2.1. Fixed Cost

Fixed cost, which is usually related to the number and type of vehicles, includes driver wages, vehicle purchase, maintenance, and insurance. These factors are taken into account and attributed to a constant according to the type of each vehicle, that is $f^m$. Thus, the fixed cost of the distribution vehicles, labeled as $C_1$, can be calculated as follows:$$\begin{array}{}\text{(1)}& C_1={\displaystyle \sum }_{m\in M}{\displaystyle \sum }_{k\in K}{\displaystyle \sum }_{j\in C}{f}^m{X}_{0jk}^m,\end{array}$$where $X_{0jk}^m$ is the type m vehicle departing from the distribution center and heading to customer j.

4.2.2. Transportation Cost

The transportation cost, labeled as $C_2$, is the sum of the cost of all vehicles’ travel distances in the logistics distribution process, which can be calculated according to the unit distance cost of each type of vehicle. The calculation formula is as follows:$$\begin{array}{}\text{(2)}& C_2={\displaystyle \sum }_{m\in M}{C}_d^m{\displaystyle \sum }_{k\in K}{\displaystyle \sum }_{i\in C}{\displaystyle \sum }_{j\in C}{d}_{ij}^m{X}_{ijk}^m.\end{array}$$

4.2.3. Fuel Consumption Cost

The fuel consumption cost is calculated using the load-based fuel consumption model (LFCM) [53]. In LFCM, there is a linear relationship between vehicle unit distance fuel consumption and load capacity. Based on this linear relationship, the unit distance fuel consumption $f_e$, whose unit is L/km, is calculated as follows:$$\begin{array}{}\text{(3)}& f_{e}Y=F_{e1}+\frac{F_{e2}-F_{e1}}{Y_{\max }}Y,\end{array}$$where Y is the vehicle load and its unit is ton, $Y_{\max }$ is the vehicle capacity and its unit is ton, $F_{e2}$ is the fuel consumption per kilometer when the vehicle is in full load and its unit is L/km, and $F_{e1}$ is the fuel consumption per kilometer when the vehicle is empty and its unit is L/km.

Then fuel consumption of the vehicle $F_e$ between customer i and j can be calculated as follows:$$\begin{array}{}\text{(4)}& F_e{L}_{ij}^m=f_e{L}_{ij}^m{d}_{ij}^m.\end{array}$$

According to formulas (3) and (4), the fuel consumption cost of all vehicles in the whole distribution process, labeled as $C_3$, can be calculated as follows:$$\begin{array}{}\text{(5)}& C_3={\displaystyle \sum }_{m\in M}{C}_e^m{\displaystyle \sum }_{k\in K}{\displaystyle \sum }_{i\in C}{\displaystyle \sum }_{j\in C}{F}_{e1}+\frac{F_{e2}-F_{e1}}{Q_m}{L}_{ij}^m{d}_{ij}^m{X}_{ijk}^m.\end{array}$$

4.2.4. Carbon Emission Cost

The carbon emission cost is calculated on the basis of carbon emissions. Vehicle carbon emissions E are mainly related to fuel consumption and fuel type, usually calculated according to the carbon emission coefficient [54], and the calculation formula is as follows:$$\begin{array}{}\text{(6)}& E=\delta \mathrm{\ast }{F}_e,\end{array}$$where $\delta$ represents the coefficient of carbon dioxide emission, which is determined by the type of fuel, and its unit is kg/L.

Based on formulas (4) and (6), the carbon emission cost of all distribution vehicles, labeled as $C_4$, can be calculated as follows:$$\begin{array}{}\text{(7)}& C_4=\delta {\displaystyle \sum }_{m\in M}{C}_c^m{\displaystyle \sum }_{k\in K}{\displaystyle \sum }_{i\in C}{\displaystyle \sum }_{j\in C}{F}_{e1}+\frac{F_{e2}-F_{e1}}{Q_m}{L}_{ij}^m{L}_{ij}^m{X}_{ijk}^m.\end{array}$$

In summary, based on formulas (1), (2), (5), and (7), the mathematical model for the logistics distribution path optimization considering carbon emissions and multifuel-type vehicles, that is, VRP-CEMF, is obtained as follows:$$\begin{array}{}\text{(8)}& \mathrm{Min}Z=C_1+C_2+C_3+C_4.\end{array}$$

Subject to,$$\begin{array}{}\text{(9)}& {\displaystyle \sum }_{kϵK}{X}_{0jk}^m=1,j\in C;m\in M,\text{(10)}& {\displaystyle \sum }_{kϵK}{X}_{i0k}^m=1,i\in C;m\in M,\text{(11)}& {\displaystyle \sum }_{i,jϵc}{X}_{ijk}^m=1,k\in K;m\in M,\text{(12)}& {\displaystyle \sum }_{jϵC}{X}_{0jk}^m\le 1,k\in K;m\in M,\text{(13)}& {\displaystyle \sum }_{iϵC}{X}_{i0k}^m\le 1,k\in K;m\in M,\text{(14)}& {\displaystyle \sum }_{i\in C}{\displaystyle \sum }_{jϵC}{L}_{ij}^m{X}_{ijk}^m\le Q_m,k\in K;m\in M,\text{(15)}& {\displaystyle \sum }_{jϵC}{L}_{ij}^m={\displaystyle \sum }_{i\in C}{L}_{ij}^m=q_{ij},i\in C;j\in C,\text{(16)}& {\displaystyle \sum }_{jϵC}{\displaystyle \sum }_{kϵK}{X}_{0jk}^m\le K,m\in M,\text{(17)}& Q_m\ge 0,m\in M,\text{(18)}& X_{ijk}^m\in 0,1,i\in C;j\in C;m\in M,\text{(19)}& u_i-u_j+N{X}_{ijk}^m\le N-1{,u}_i\ge 0.\end{array}$$

Formula (8) is the objective function with the minimum total cost. Formulas (9) and (10) indicate that each customer is served and to be served only once. Formula (11) indicates the customer’s out-degree and in-degree constraints. Formulas (12) and (13) indicate that the vehicle starts from the distribution center and finally returns to the distribution center. Formula (14) indicates that the demand of all customers in a distribution path does not exceed the capacity of the vehicle. Formula (15) represents that the vehicle meets the demands of all customers along the distribution path in one-way distribution. Formula (16) ensures the number of paths is not greater than the number of vehicles in the distribution center. Formulas (17) and (18) describe customer demand constraints and decision variable constraints. Formula (19) is a subtour elimination constraint.

5. IGA

The VRP-CEMF is an NP-hard combinatorial optimization problem, whose computational complexity increases exponentially with the expansion of customer numbers or vehicle types. Exact algorithms (e.g., branch-and-bound) struggle to obtain solutions for this problem. Metaheuristic algorithms, such as GA [55], exhibit strong global search capabilities and serve as powerful tools for solving optimization problems. Therefore, GA is used to solve VRP-CEMF. Furthermore, in order to improve the quality of the solution, the GA is improved.

5.1. The Principle of the IGA

A local search operation [56] is added after selection, crossover, and mutation operators to improve the global search ability of the GA, and an IGA is obtained. The IGA combines the advantages of GA, which can solve multiobjective problems in a large range and the advantages of a local search strategy with fast search speed and good search effect, and can effectively solve the logistics distribution path optimization problem considering carbon emissions and multifuel-type vehicles. According to the design idea of IGA, the calculation flow of the algorithm can be obtained, which includes setting IGA parameters, coding and initializing populations, and calculating fitness value, selection operation, crossover operation, mutation operation, and local search operation. Figure 2 shows the IGA flowchart, and Algorithm 1 presents the pseudocode.

[figure(s) omitted; refer to PDF]

Algorithm 1: IGA.

1: Initialize parameters: Population size, generations, mutation rate, crossover rate, number of vehicles, and number of customers

2: Initialize population P with random solutions where each solution is a set of vehicle routes covering all customers

3: for gen = 1 to generations do

4:  for each individual ind in population P do

5:   Calculate the cost Z of the routes in individual ind

6:   Set fitness f(ind) = 1/$Z_{ind}$

7:  end for

8:  Create an empty list P′ for the new population

9:  Calculate the total fitness F = ${{\displaystyle \sum }}_{ind\in p}find$

10:  for i = 1 to population size/2 do

11:   generate a random number r between 0 and F

12:   Initialize cumulative fitness

13:   for each individual ind in population P do

14:    Update cumulative fitness

15:    if r < cumulative fitness, then

16:     Select ind as parent P1

17:     Break the loop (as P1 is selected)

18:    end if

19:   end for

20:   if r < crossover rate then

21:    Perform crossover on P1 and P2 to generate offspring O1 and O2

22:   else

23:    Set O1 ⟵ P1 and O2 ⟵ P2 (clone the parents)

24:   end if

25:   Add O1 and O2 to P′

26:  end for

27:  for each individual ind in P′ do

28:   if r < mutation rate then

29:    Apply mutation to ind (swap two customers)

30:    if improvement is found in local search on mutated ind, then

31:     Update ind

32:    end if

33:   end if

34:  end for

35:  P ⟵ P′

36:  Output the best solution found in P with the highest fitness (min Z)

37: end for

38: Return the optimal path solution

5.2. The Step Description of IGA

1. Coding. The natural number encoding method is used, the natural number itself has the order, in the face of multiple constraints, where the time zone is strong. The distribution vehicles, distribution centers, and customers can be matched to the natural series. In natural number coding, the natural number 0 corresponds to the distribution center, and other natural numbers correspond to customers. The specific coding process is as follows.

  First, a random sequence of natural numbers is generated based on the number of customers. This sequence of natural numbers is the sequence of chromosomes.

  Second, “0” representing a distribution center is inserted into the chromosome sequence to form a complete path in the form of “distribution center, customer, customer, distribution center.” The order in which the customer is placed on the chromosome is the order in which the vehicle is distributed.

  For example, if a chromosome code is “0510698204370,” it means that the services of 9 customers are completed by three vehicles, and three distribution paths are generated. That is, Path 1: 0-5-1-0; Path 1 represents the first vehicle that departs from the distribution center and returns to the distribution center after serving Customers 5 and 1. Path 2: 0-6-9-8-2-0; Path 2 represents the second vehicle that departs from the distribution center and returns to the distribution center after serving Customers 6, 9, 8, and 2. Path 3: 0-4-3-7-0; Path 3 represents the third vehicle that departs from the distribution center and returns to the distribution center after serving Customers 4, 3, and 7. The type of distribution vehicle is determined by customer demand along the three distribution paths.

2. Population initialization: Population initialization is a process of generating several distribution paths according to the constraints and forming several complete distribution schemes. That is, according to the coding rules, a specified number of chromosomes is randomly generated to form the initial population.

3. Fitness function: The fitness calculation of the population is needed, leaving the chromosome with a large fitness within the population and eliminating the chromosome with a small fitness. This can make the iterative chromosome of high quality, which facilitates the generation of the global approximate optimal solution. The objective of the model of VRP optimization for logistics distribution (formula (8)) is to minimize the total cost, so its reciprocal is used as the fitness function of the chromosome. The fitness function $F_i$ of the ith chromosome can be formulated as follows:$$\begin{array}{}\text{(20)}& F_i=\frac{1}{Z_i},\end{array}$$

  where $Z_i$ is the value of the objective function obtained by formula (8).

4. Select operation: The roulette method is used for the selection operation, which can make the algorithm better traverse all customers. The specific process of the select operation is as follows:

① Calculate the fitness of each chromosome in the population.

② Calculate the retention probability of each chromosome, and the corresponding formula for calculating is as follows:$$\begin{array}{}\text{(21)}& P{x}_i=\frac{f{x}_i}{{\displaystyle \sum }_{i=1}^{N}f{x}_i},\end{array}$$

  where f($x_i$) is the fitness value of the chromosome i and N is the population size.

③ Calculate the cumulative retention probability of each chromosome, and the corresponding formula is as follows:$$\begin{array}{}\text{(22)}& q_i={\displaystyle \sum }_{j=1}^{i}P{x}_j,\end{array}$$

  where $q_i$ is the cumulative fitness value of the chromosome j.

④ A random number within the range [0,1] is generated and compared with the cumulative retention probability to determine whether the chromosome is retained.

⑤ Repeat Step ④ until the desired population size is achieved.

5. Crossover operation: The partial matching cross strategy is used. The process is as follows:

  First, two intersection positions are randomly generated for Parent chromosome I (Parent I) and Parent chromosome II (Parent II), respectively. The segment between two intersection positions represents a complete distribution path.

  Second, the segment between two intersection positions of Parent I, that is, the selected path is kept in the preceding part of Offspring II (Offspring II) and that between two intersection positions of Parent II, that is, the selected path is kept in the preceding part of Offspring I (Offspring I).

  Finally, other gene positions of Offspring I are filled with different genes of Parent I to obtain Offspring I. Also, Offspring II is obtained.

  For example, Parent I is “0510698204370,” Parent II is “0380416207950,” and the process of Offspring I and Offspring II produced by the crossover operation is shown in Figure 3.

6. Mutation operation: According to the characteristics of the research problem, the swapping mutation is adopted. That is, in the process of mutation operation, randomly select two genes and swap their positions. For example, the original chromosome is “0416205980370,” and the two genes “6” and “3” are selected, and the process of the mutant chromosome obtained by the mutation operation is illustrated in Figure 4.

7. Local search operation: The process of the local search operation is as follows:

  First, randomly select a gene (customer) from the chromosome as the first gene of the new chromosome.

  Second, the correlation between the remaining genes and the selected gene is calculated. The calculation of the correlation between customers is shown in the following equation: $$\begin{array}{}\text{(23)}& R_{ij}=\frac{1}{c+V},\end{array}$$

  where $R_{ij}$ represents the correlation between customer i and customer j, c represents the value that standardizes the shortest distance between customer i and j, V indicates whether the path passes through customer i and customer j at the same time, if the customer is in the same path, V = 0, otherwise V = 1.

  Finally, all the remaining genes are inserted into the new chromosome in ascending order according to the correlation with the selected gene, and a new chromosome is obtained.

  For example, the selected chromosome is “0510698204370,” and the gene “6” is selected as the first one of a new chromosome, and the process of the new chromosome obtained by the local search operation is illustrated in Figure 5.

8. Termination conditions: The number of iterations is set as the termination condition of the algorithm. Then, the optimal solution in the last generation population is outputted.

[figure(s) omitted; refer to PDF]

6. Example and Discussion

6.1. Example and Simulation

A real logistics distribution path optimization example of a milk company in Qingdao, China, is selected to simulate the VRP-CEMF. In this example, there is one distribution center and 22 customers. There are two types of diesel-fueled vehicles in the distribution center, set as Type A and Type B, with capacities of 1.6 tons and 2 tons, respectively. Customer demand, latitude and longitude coordinates of the distribution center, and each customer are shown in Table 1. According to the positional relationship between the distribution center and customers, a topology map is obtained, as shown in Figure 6. In Figure 6, $C_0$ is the distribution center, $C_1$, $C_2$, …, $C_{22}$ are customers, and the number between the two customers is the shortest distance. The specific parameter settings of the vehicle in the example are shown in Table 2.

Table 1

Distribution center and customer location and demand.

Customer	Longitude coordinates	Latitude coordinates	Demand (ton)
0	120.421294	36.119016	—
1	120.515991	36.198949	0.5
2	120.434057	36.243062	0.6
3	120.395065	36.149074	0.6
4	120.393555	36.196650	0.4
5	120.369142	36.111246	0.3
6	120.315378	36.064058	0.8
7	120.440442	36.158492	0.4
8	120.406935	36.064891	0.5
9	120.441712	36.116115	0.7
10	120.382593	36.236073	0.5
11	120.467422	36.174333	0.3
12	120.428541	36.162590	0.4
13	120.340855	36.089279	0.6
14	120.471119	36.108027	0.5
15	120.533803	36.105500	0.7
16	120.518228	36.167939	0.3
17	120.46046	36.163334	0.3
18	120.479528	36.193143	0.4
19	120.466283	36.124938	0.5
20	120.542798	36.221232	0.8
21	120.488527	36.185508	0.6
22	120.405068	36.246085	0.4

[figure(s) omitted; refer to PDF]

Table 2

Specific parameter settings of vehicles.

Parameter	Parameter value	Unit
$Q_A$	1.6	Ton
$Q_B$	2.0	Ton
$F_{e1}^A$	0.07	L/km
$F_{e2}^A$	0.09	L/km
$F_{e1}^B$	0.1	L/km
$F_{e2}^B$	0.12	L/km
$f^A$	100	¥/vehicle
$f^B$	110	¥/vehicle
$C_d^m$	1	¥/km
$C_e^m$	7.06	¥/L
$\delta$	3.096	kg/L
$C_c^m$	0.6	¥/kg

The example is modeled based on formula (8) and simulated using MATLAB software. The parameters of the IGA are set through multiple experimental verifications, and the crossover rate and mutation rate are selected from candidate values of [0.7, 0.8, 0.85, 0.9, 0.95] and [0.05, 0.1, 0.15, 0.2], respectively. The final parameter configuration is determined as follows: the initial population is 100, the maximum number of iterations is 500, the crossover probability is 0.9, and the mutation probability is 0.1. After 50 simulations, the best result is obtained, which includes the number of the two types of vehicles required for the example, the corresponding distribution paths, and the costs, as shown in Table 3. Vehicle paths from Table 3 are represented on the map as shown in Figure 7.

Table 3

Simulation results.

Vehicle type	Distribution path	Fixed cost (¥)	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)
A	Path 1: 0 ⟶ 15 ⟶ 16 ⟶ 21 ⟶ 0	640	214.3	143.94	37.87
	Path 2: 0 ⟶ 8 ⟶ 6 ⟶ 5 ⟶ 0
B	Path 3: 0 ⟶ 4 ⟶ 10 ⟶ 22 ⟶ 2 ⟶ 0
	Path 4: 0 ⟶ 17 ⟶ 19 ⟶ 14 ⟶ 9 ⟶ 0
	Path 5: 0 ⟶ 13 ⟶ 3 ⟶ 12 ⟶ 7 ⟶ 0
	Path 6: 0 ⟶ 20 ⟶ 1 ⟶ 18 ⟶ 11 ⟶ 0
Total cost (¥)		1036.11

[figure(s) omitted; refer to PDF]

As can be seen from Table 3, six vehicles including two Type A vehicles and four Type B vehicles are needed to complete the distribution task under the consideration of carbon emission, and six distribution paths are obtained. Based on these six paths, the distribution distance of each path can be calculated as 39.2 km, 34.2 km, 41.5 km, 26.6 km, 34.3 km, and 38.5 km, respectively. The loading rates of each distribution vehicle are 100%, 100%, 95%, 100%, 100%, and 100%, respectively. It can be seen that the loading on each distribution path does not exceed the capacity of the vehicle, in which the Type A vehicle shows a loading rate of 100% and the Type B vehicle shows an average loading rate of 98.75%, which indicates a high vehicle utilization rate.

In addition, in order to verify the effect of the proposed model considering carbon emissions, the simulation is also performed for the example without considering carbon emissions, and the corresponding results are obtained, as shown in Table 4. Vehicle paths from Table 4 are represented on the map as shown in Figure 8.

Table 4

Simulation results without considering carbon emissions.

Vehicle type	Distribution path	Fixed cost (¥)	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)
B	Path 1: 0 ⟶ 13 ⟶ 6 ⟶ 8 ⟶ 0	660	205.4	151.47	39.86
	Path 2: 0 ⟶ 9 ⟶ 15 ⟶ 14 ⟶ 0
	Path 3: 0 ⟶ 16 ⟶ 1 ⟶ 20 ⟶ 11 ⟶ 0
	Path 4: 0 ⟶ 7 ⟶ 2 ⟶ 22 ⟶ 10 ⟶ 0
	Path 5: 0 ⟶ 17 ⟶ 18 ⟶ 21 ⟶ 19 ⟶ 0
	Path 6: 0 ⟶ 12 ⟶ 4 ⟶ 3 ⟶ 5 ⟶ 0
Total cost (¥)		1056.73

[figure(s) omitted; refer to PDF]

As can be seen from Table 4, when carbon emissions are not considered in the optimization objective, six vehicles are required to complete distribution tasks, but only Type B vehicles are needed to complete them. The distribution distances of each path are 32.1, 26.1, 41.5, 41.3, 32.2, and 32.2 km, respectively. The loading rates of each distribution vehicle are 95%, 95%, 95%, 95%, 90%, and 95%, respectively. The average loading rate is 94.2%.

Furthermore, it can be found from Tables 3 and 4 that it is effective to take carbon emissions into account in the optimization of the logistics distribution path. When carbon emissions are considered in the optimization objective, the travel distance increased by 8.9 km, resulting in a slightly higher transportation cost. However, due to the changes in the type of distribution vehicles, the carbon emissions reduced by 5% and the total cost reduced by 2%. Moreover, the change in distribution customer orders leads to the change in vehicle load, and the average loading rate is higher when considering carbon emissions. This indicates that by taking carbon emissions into account in the logistics distribution path optimization, both the total cost and carbon emissions are reduced.

6.2. IGA Performance Analysis

In order to verify the performance of the IGA, diesel-fueled vehicles Type A are used to simulate the example. IGA and GA are simulated 500 times, respectively, and the best results are obtained, as shown in Table 5. The iterative convergence curves for GA and IGA are shown in Figure 9.

Table 5

The simulation results of IGA and GA.

Algorithm	Number of vehicles	Fixed cost (¥)	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)	Total cost (¥)
GA	8	800	284.7	149.42	39.32	1273.44
IGA	7	700	246.5	129.82	34.16	1110.48

[figure(s) omitted; refer to PDF]

As can be seen from Table 5, the number of vehicles required by the two algorithms to complete the distribution task is different, and the transportation cost, fuel consumption cost, and carbon consumption cost obtained by IGA are lower than those of GA. In addition, as can be seen from Figure 9, GA does not converge in the 500th generation, while IGA starts to converge around the 200th generation, and the convergence rate is obviously fast. Overall, the results obtained by IGA are better than those by GA, and this indicates that IGA can overcome the shortcomings of the inadequate local search ability of GA and is suitable for solving the problems studied in the paper.

6.3. Impact of Multifuel-Type Vehicles on the Distribution Paths

Using different fuel type of vehicles to complete transportation will produce different carbon emissions. In addition to diesel-fueled vehicle, new energy vehicles such as hybrid electric vehicles and hydrogen-fueled vehicles have gradually emerged [57, 58]. In this section, hybrid electric vehicles and hydrogen-fueled vehicles are used to investigate the impact of multifuel-type vehicles on the logistics distribution path.

6.3.1. Comparative Analysis of Hybrid Electric Vehicles

A hybrid electric vehicle is based on a pure electric vehicle and equipped with an engine that can be powered by diesel when the battery is about to run out. The diesel oil and electricity consumed by transportation are affected by many factors, such as the driving cycle, transport distance, driver preference, and battery capacity. In order to more clearly explore the impact of different fuel types of vehicles on logistics distribution paths, this paper ignores the impact of vehicle miles traveled variations over time and drivers [57], and the average of unit diesel consumption cost and unit electricity price is used to calculate the fuel consumption cost of hybrid electric vehicles, as shown in formulas (24)–(26).$$\begin{array}{}\text{(24)}& C_e^C=\frac{C_e^A+C_r^C\mathrm{\ast }{E}^{\mathrm{\ast }}}{2},\end{array}$$where $E^{\mathrm{\ast }}$ represents the actual power generation per liter of diesel.$$\begin{array}{}\text{(25)}& E^{\mathrm{\ast }}=E\mathrm{\ast }m\mathrm{\ast }\eta ,\end{array}$$where E represents the power generation per kilogram of diesel [59], m represents the mass per liter of diesel, and $\eta$ represents the heating efficiency of the engine.$$\begin{array}{}\text{(26)}& E=\frac{\overline{q}}{3600},\end{array}$$where $\overline{q}$ is the average low calorific value of diesel.

Hybrid electric vehicles are set as Type C, and the related parameters are shown in Table 6. After simulating, the results are obtained, as shown in Table 7.

Table 6

The related parameters of the Type C vehicle.

Parameter	Parameter value	Unit
$F_{e1}^C$	0.05	L/km
$F_{e2}^C$	0.065	L/km
$Q_C$	1.8	Ton
$f^C$	130	¥
$C_d^C$	0.8	¥/km
$C_e^C$	4.42	¥/L
$\delta$	3.096	kg/L
$C_c^m$	0.6	¥/kg
$\eta$	31%	—
$\overline{q}$	42,652	kJ/kg
m	0.835	kg
$C_r^C$	0.58	¥/kwh

Table 7

The simulation results of the Type C vehicle.

Vehicle type	Distribution path	Fixed cost (¥)	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)
Type C	Path 1: 0 ⟶ 3 ⟶ 10 ⟶ 2 ⟶ 0	910	187.92	54.73	23
	Path 2: 0 ⟶ 18 ⟶ 1 ⟶ 20 ⟶ 0
	Path 3: 0 ⟶ 8 ⟶ 15 ⟶ 16 ⟶ 11 ⟶ 0
	Path 4: 0 ⟶ 5 ⟶ 13 ⟶ 16 ⟶ 0
	Path 5: 0 ⟶ 22 ⟶ 4 ⟶ 21 ⟶ 17 ⟶ 0
	Path 6: 0 ⟶ 14 ⟶ 19 ⟶ 7 ⟶ 12 ⟶ 0
	Path 7: 0 ⟶ 9 ⟶ 0
Total cost (¥)		1175.65

It can be seen from Table 7, seven Type C vehicles are needed to complete the distribution task, which is different from the number of vehicles required for distribution by Type A and B vehicles. When compared with Table 3, it can be found that the distribution paths of Type C vehicles are different from those of Type A and B vehicles, and the fuel consumption cost and carbon emission cost are significantly reduced. This shows that the use of Type C vehicles generates less fuel consumption and carbon emissions. In addition, the fixed cost of Type C vehicles is relatively high due to the impact of purchase cost, maintenance cost, and infrastructure construction cost, resulting in a 13.47% increase in total cost compared to Type A and B vehicles.

6.3.2. Comparative Analysis of Hydrogen-Fueled Vehicles

Hydrogen-fueled vehicles use hydrogen as the main fuel and do not produce carbon emissions during driving. Hydrogen-fueled vehicles are applied to the logistics distribution of the example and set as Type D, and their related parameters are shown in Table 8. The results are obtained by simulation, as shown in Table 9.

Table 8

The related parameters of the Type D vehicle.

Parameter	Parameter value	Unit
$F_{e1}^D$	0.04	L/km
$F_{e2}^D$	0.055	L/km
$Q_D$	2	Ton
$f^D$	150	¥/vehicle
$C_d^m$	0.6	¥/km
$C_e^m$	35	¥/L

Table 9

The simulation results of the Type D vehicle.

Vehicle type	Distribution path	Fixed cost (¥)	Transportation cost (¥)	Hydrogen fuel consumption cost (¥)	Carbon emission (kg)
Type D	Path 1: 0 ⟶ 8 ⟶ 6 ⟶ 13 ⟶ 0	900	126.12	318.43	—
	Path 2: 0 ⟶ 9 ⟶ 5 ⟶ 3 ⟶ 0
	Path 3: 0 ⟶ 17 ⟶ 18 ⟶ 20 ⟶ 19 ⟶ 0
	Path 4: 0 ⟶ 4 ⟶ 10 ⟶ 22 ⟶ 2 ⟶ 0
	Path 5: 0 ⟶ 14 ⟶ 15 ⟶ 16 ⟶ 1 ⟶ 0
	Path 6: 0 ⟶ 12 ⟶ 7 ⟶ 11 ⟶ 21 ⟶ 0
Total cost (¥)		1344.55

From Table 9, it can be seen that six Type D vehicles are required to complete this distribution task, which is the same as the number of vehicles required for distribution using Types A, B, and C. Comparing with Tables 3 and 7, it can be found that the paths of Type D vehicles also changed significantly, and only one path is the same with Type A, Type B, and Type C vehicles. The transportation cost of Type D is low and does not produce carbon emission costs. In addition, the total cost of Type D vehicles is the highest, which is caused by the current technical limitations. Limited hydrogen production methods and expensive production cost make it expend more fixed costs and hydrogen fuel costs to complete the distribution task, resulting in the total cost of distribution, 29.77% and 14.37%, being higher than Type A, Type B, and Type C vehicles, respectively.

6.3.3. Comparative Analysis of Combined Distribution of Multifuel-Type Vehicles

In order to further optimize the logistics distribution path and explore the impact of multifuel-type vehicles on the distribution path, the combined distribution of diesel-fueled vehicles, hybrid electric vehicles, and hydrogen-fueled vehicles is used for logistics distribution. The simulation results are shown in Table 10.

Table 10

The simulation results of multifuel-type vehicles.

Vehicle type	Distribution path	Fixed cost (¥)	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)
Type A	Path 1: 0 ⟶ 9 ⟶ 0	850	179.56	69.24	26.7
	Path 2: 0 ⟶ 19 ⟶ 14 ⟶ 8 ⟶ 0
Type C	Path 3: 0 ⟶ 20 ⟶ 16 ⟶ 15 ⟶ 0
	Path 4: 0 ⟶ 13 ⟶ 6 ⟶ 5 ⟶ 0
	Path 5: 0 ⟶ 21 ⟶ 1 ⟶ 18 ⟶ 17 ⟶ 0
	Path 6: 0 ⟶ 10 ⟶ 22 ⟶ 2 ⟶ 11 ⟶ 0
	Path 7: 0 ⟶ 3 ⟶ 4 ⟶ 12 ⟶ 7 ⟶ 0
Total cost (¥)		1125.5

From Table 10, it can be seen that two Type A and five Type C vehicles are required to complete this distribution task. Compared to the results in Tables 3 and 7, it is found that the carbon emissions are less than Type A, and the total cost is lower than Type C. This indicates that the combined distribution of Type A and Type C vehicles has the advantages of low cost of petrochemical fuel vehicles and less carbon emissions of new energy vehicles. In addition, it can be found that the Type D vehicle is not assigned to logistics distribution. This is because while the Type D does not produce carbon emissions, its fixed cost and hydrogen fuel consumption cost are too high, which results in an increase in the total cost.

Furthermore, in order to more clearly analyze the impact of diesel-fueled vehicles, hybrid electric vehicles, and hydrogen-fueled vehicles on the distribution path, the travel distance, fuel consumption, and carbon emissions are compared, as shown in Figure 10. As can be seen, if Type A vehicles are used to complete the distribution task, although the carbon emissions and fuel consumption are less than those of Type A and Type B, the travel distance is the longest among all distribution schemes, resulting in a high total distribution cost. If Type C vehicles are used to complete the distribution task, although their travel distance is 9.6% more than Type A and Type B vehicles, the fuel consumption is reduced by 39.31% and carbon emissions are reduced by 88.23%, which is less polluting to the environment. If Type D vehicles are used to complete the distribution task, the travel distance is the smallest, with 0.98% less than Type A and Type B vehicles, and 10.52% less than Type C vehicles, and no carbon emissions are produced at all. If Type A and C vehicles are used to complete the distribution task, which combine the advantages of low total cost of fuel vehicles and less carbon emissions of new energy vehicles, not only the travel distance is 7.88% less than that of Type C vehicles, but also the carbon emission is 84.86% less than that of Type A vehicles.

[figure(s) omitted; refer to PDF]

Overall, taking multifuel-type vehicles into consideration in the logistics distribution path optimization problem can significantly reduce the carbon emissions generated in the distribution process on the premise of ensuring the lowest total cost.

6.4. Sensitivity Analysis

In order to further explore the impact of carbon emissions on the logistics distribution path, carbon emission is selected for the sensitivity analysis. In addition, as can be seen from Sections 6.3.2 and 6.3.3 hydrogen-fueled vehicles without carbon emissions have greater application advantages in the future logistics distribution, and the hydrogen fuel price is an important factor affecting the application of hydrogen-fueled vehicles in logistics distribution. With the development of new energy technology, the problems of new energy vehicles’ high fixed costs and fuel consumption costs will be solved. Therefore, the hydrogen fuel price is also selected for the sensitivity analysis.

6.4.1. Carbon Emission Sensitivity Analysis

The carbon emission cost coefficient is introduced into the model to control the proportion of carbon emission, and the objective function (formula (8)) is revised as follows:$$\begin{array}{}\text{(27)}& \mathrm{Min}Z=C_1+C_2+C_3+\beta C_4,\end{array}$$where $\beta$ is the carbon emission cost coefficient.

The carbon emission cost coefficient is set as 0 to 1 (at 0.2 intervals), respectively, and simulated, where the carbon emission cost coefficient of 0 and 1 corresponds to the situation of not considering carbon emissions and considering carbon emissions, respectively. The results with carbon emission cost coefficients of 0.2, 0.4, 0.6, and 0.8 are shown in Figure 11 and Table 11. In Figure 11(a), Path 1 is distribution by Type A vehicle, and the others are by Type B. In Figure 11(b), Path 3 is distribution by Type A vehicle, and the others are by Type B. In Figure 11(c), Paths 1 and 5 are distribution by Type A vehicle, and the others are by Type B. In Figure 11(d), Path 1 is distribution by Type A vehicle, and the others are by Type B.

[figure(s) omitted; refer to PDF]

Table 11

Simulation results under different carbon emission cost coefficients.

Carbon emission cost coefficient	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)	Total cost (¥)
0.2	209.5	149.39	39.31	1048.2
0.4	209.6	148.90	39.18	1047.68
0.6	210	148.13	38.97	1037.1
0.8	214	145.41	38.26	1047.67

As can be seen from Figure 11, under different carbon emission cost coefficients, logistics distribution paths have changed. Meanwhile, although the number of vehicles required is the same (6 paths), the types of vehicles used have changed. Furthermore, it can be seen from Table 11 that the transportation cost, fuel consumption cost, and carbon emission cost vary with the carbon emission cost coefficient. When carbon emission cost coefficients are small, vehicles will prioritize paths that travel less distance to reduce the total cost, which results in shorter vehicle travel distances and higher carbon emissions. When carbon emission cost coefficients are large, vehicles will prioritize paths that have lower carbon emissions, which results in lower carbon emissions and longer travel distances.

6.4.2. Hydrogen Fuel Price Sensitivity Analysis

On the basis of the original price, the price of hydrogen fuel is reduced for simulation. Based on the limit of hydrogen fuel production cost, the price of hydrogen fuel is set as 90%–40% (at 10% intervals) of the original price and is simulated, respectively. The results are obtained and shown in Table 12.

Table 12

Simulation results under different hydrogen fuel prices.

Hydrogen fuel price (based on the original price) (%)	Number of vehicles	Vehicle type selection	Carbon emission cost (¥)	Total cost (¥)
90	7	A, C	26.34	1128.55
80	6	C, D	15.46	1137.06
70	6	C, D	17.65	1125.71
60	6	C, D	17.41	1103.78
50	6	A, C, D	11.42	1101
40	6	A, C, D	10.68	1080.64

As can be seen from Table 12, in the case of a small reduction in hydrogen fuel prices, such as the price of hydrogen fuel that reduces from the original 90%, Type A and C are used to complete the distribution task, to the original 80%, the total cost is high, which shows that the cost of hydrogen-fueled vehicles is still high and has no advantage over other types of vehicles. Furthermore, with the reduction of hydrogen fuel price, it is more inclined to choose hydrogen-fueled vehicles without carbon emissions to complete the distribution task. When the hydrogen fuel price is reduced to the original 70% and 60%, hydrogen-fueled vehicles demonstrate better economic advantages. At this point, Type C and D vehicles, which offer greater low-carbon advantages, can be efficiently deployed to complete the distribution task In addition, as can be seen from the table, as the price of hydrogen fuel is further reduced, such as to the original 50% and 40%, the distribution cost of using Type D vehicles’ distribution is greatly reduced, Types A, C, and D are applied to complete the logistics distribution. In general, with the reduction of hydrogen fuel price, the advantages of hydrogen-fueled vehicles without carbon emission in logistics distribution are more obvious, and will become the main choice of logistics distribution in the future.

6.4.3. Customer Demand Sensitivity Analysis

Customer demand is the main factor to be considered in the optimization of the logistics distribution path. It is generally assumed to be constant, but in reality, it often changes. The change in customer demand will lead to a change in distribution costs, which will affect the optimal distribution path. The customer demands in the example were, respectively, increased by 10%–100% (at 10% intervals) on the basis of their original demands. Simulations were conducted for these varied demands, and the simulation results are presented in Table 13. Furthermore, based on Table 13, the relationship between fuel consumption cost, carbon emission cost, and increased customer demand can be visualized as shown in Figure 12.

Table 13

Simulation results under different customer demands.

Customer demand	Number of vehicles	Fixed cost (¥)	Transportation cost (¥)	Fuel consumption cost (¥)	Carbon emission cost (¥)	Total cost (¥)
Original demand	7	700	305.77	73.88	28.68	1108.33
Increased 10%	8	800	352.58	108.56	34.50	1195.64
Increased 20%	8	800	327.19	102.90	34.38	1264.47
Increased 30%	9	900	408.35	133.78	43.11	1485.24
Increased 40%	10	1000	428.30	124.53	40.65	1593.48
Increased 50%	10	1000	434.00	110.96	39.01	1583.97
Increased 60%	11	1100	407.53	124.79	42.16	1674.48
Increased 70%	12	1200	462.49	127.90	42.94	1833.33
Increased 80%	13	1300	528.40	117.47	41.61	1987.48
Increased 90%	13	1300	528.50	107.29	41.03	1976.82
Increased 100%	13	1300	521.30	106.32	40.62	1968.24

[figure(s) omitted; refer to PDF]

As can be seen from Table 13, with the increase in customer demand, the various costs incurred also increase. When the customer demand increases from 10% to 20%, from 40% to 50%, and from 80% to 100%, the number of vehicles does not change. This indicates that the increase in customer demand in a certain range will not lead to an increase in the number of vehicles, the total cost of logistics distribution will not be greatly increased, and the vehicle utilization rate will be higher. When customer demand increases by 30% or more, in addition to the increase in the total cost of logistics distribution, the number of vehicles also increases. This indicates that a significant rise in customer demand leads to an increase in the number of vehicles, thus increasing the total cost of logistics distribution.

As can be seen from Figure 12, with the increase in customer demand, the fuel consumption cost and carbon emission cost generally show an increasing trend. Among them, when customer demand increases by 20%, compared to an increase of 10%, the fuel consumption cost and carbon emission cost decline slightly. Similarly, when customer demand increases by 90% and 100%, compared to an increase of 80%, the fuel consumption cost and carbon emission cost continue to decrease. This indicates that within a certain range, increasing demand can enhance vehicle utilization, thereby reducing carbon emissions and total costs.

7. Conclusion

In this paper, carbon emission and multifuel-type vehicles are considered to study the logistics distribution of VRP, and a mathematical model with the objective of minimizing the sum of fixed cost, transportation cost, fuel consumption cost, and carbon emission cost is established. In order to improve the accuracy of the solution, an IGA is designed by adding a local search operation on the basis of the traditional GA and applied to solve the mathematical model.

The simulation of the proposed model is carried out through a real example, and the results show that by considering carbon emissions in the logistics distribution path optimization, both the total cost and carbon emissions are reduced. In addition, it is found that the application of multifuel-type vehicles in logistics distribution can significantly reduce carbon emissions. Especially, the combined distribution of diesel-fueled vehicles and hybrid electric vehicles can not only reduce carbon emissions but also reduce the total cost. Furthermore, carbon emission, hydrogen fuel price, and customer demand are selected to make a sensitivity analysis. The results show that with the change of carbon emission proportion, the logistics distribution path changes greatly, the carbon emission cost coefficient is large, and the carbon emission decreases significantly. With the reduction of hydrogen fuel price, the advantages of hydrogen-fueled vehicles without carbon emission are more obvious, and will become the main choice for logistics distribution. With the increase in customer demand, various costs are also increasing. However, the increase within a certain range will not lead to an increase in the number of vehicles, and the total cost of logistics distribution will not increase significantly. Furthermore, it will result in higher vehicle utilization rates, reducing carbon emissions and total cost.

The study in this paper optimizes the logistics distribution path considering vehicle fuel consumption type. In practice, vehicle speed, traffic flow, and other dynamic factors have a significant influence on vehicle’s carbon emissions. Further research is needed to take these dynamic factors into account in the logistics distribution path optimization. Furthermore, due to the current technological limitations of new energy vehicles, the impact of driving range on logistics distribution distance is an area that requires further research.

Disclosure

A preprint has previously been published: Chuanxiang Ren, Juan Teng, Juntao Li, Haowei Ji, Xiaoqi Wang, and Fangfang Fu, “Logistics Distribution Path Optimization Considering Carbon Emissions and Multifuel-type Vehicles,” SSRN, 2023, doi: 10.2139/ssrn.4414839. It has been cited in reference [60].

Author Contributions

Chuanxiang Ren: conceptualization, data curation, formal analysis, writing–original draft, and writing–review and editing. Li Lu: software, writing–original draft, and writing–review and editing. Juan Teng: software, methodology, and writing–original draft. Changchang Yin: supervision, project administration, and writing–review and editing. Juntao Li: conceptualization, funding acquisition, and supervision. Haowei Ji: data collection and validation. Xiaoqi Wang: software. Fangfang Fu: investigation.

Funding

This research was funded by the National Natural Science Foundation of China (Grant nos. 72101033 and. 71831001).

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