Cold Chain Distribution Route Optimization for Mixed Vehicle Types of Fresh Agricultural Products Considering Carbon Emissions: A Study Based on a Survey in China

Abstract

With the improvement of people’s living standards and the widening of circulation channels, the demand for fresh agricultural products continues to increase. The increase in demand will lead to an increase in delivery vehicles, costs, and carbon emissions, among which the increase in carbon emissions will aggravate pollution and is not conducive to sustainable development. Therefore, it is very important to balance economic and environmental benefits in the distribution of fresh agricultural products. Based on the analysis of the distribution characteristics of fresh agricultural products, this paper studies the optimization of the cold chain distribution route of fresh agricultural products considering carbon emission. Firstly, the cold chain distribution route planning of fresh agricultural products was investigated and analyzed by the interview method, and the basis for establishing the model objective and constraint conditions was obtained. Then, taking the minimum total cost including carbon emission cost as the optimization goal, the cold chain distribution route optimization model for mixed vehicle types is established considering electric refrigerated vehicles, gasoline refrigerated vehicles, and so on. Genetic algorithm was used to solve the model, and MATLAB2018b was used to substitute specific case data for simulation analysis. The analysis results show that increasing the consideration of carbon emission and mixed vehicle types in the distribution route of fresh agricultural products can not only reduce the distribution cost but also reduce the carbon emission. To some extent, the research content of this paper can provide a reference for enterprises in planning cold chain distribution routes of fresh agricultural products.

1. Introduction

With the improvement of living standards and the upgrading of consumption structure, people’s demand for fresh agricultural products is increasing, and the demand for cold chain distribution of fresh agricultural products is rising higher and higher. According to the “China Cold Chain Logistics Development Report (2024 edition)”, the total demand for cold chain logistics in China in 2023 is about 350 million tons, of which food (vegetables, fruits, meat, aquatic products, and other fresh agricultural products) accounts for 90%. Due to the particularity of fresh agricultural products, in order to ensure the freshness of agricultural products, it is necessary to maintain a low-temperature distribution environment and efficient distribution efficiency. Compared with ordinary logistics, the cooling demand of vehicles makes the cold chain distribution of fresh agricultural products consume more energy and produce more carbon dioxide (CO₂). Reductions of between 210 and 460 billion tonnes of CO₂ equivalent emissions can be delivered over the next four decades through actions to improve the cooling industry’s energy efficiency together with the transition to climate-friendly refrigerants, according to the Cooling Emissions and Policy Synthesis Report from the United Nations Environment Programme (UNEP) and the International Energy Agency (IEA). How to plan the distribution route scientifically and reasonably, so as to improve the distribution efficiency and satisfaction, and reduce the distribution cost and carbon emission, is a very noteworthy problem.

Due to the enhancement of environmental awareness, the use of new energy vehicles is becoming more and more widespread, and many fresh agricultural products cold chain logistics enterprises are in the stage of mixed-use such as gasoline refrigerated trucks and electric refrigerated trucks. China’s “14th Five-Year Plan” Cold Chain Logistics Development Plan clearly points out that it is necessary to speed up the elimination of high-emission refrigerated vehicles and encourage new or updated refrigerated vehicles to adopt new energy models in order to meet the needs of urban green distribution development. According to statistics on the website, 3696 new energy refrigerated vehicles were sold in the first five months of 2024 in China (excluding exports), an increase of 310% compared with 2023. In this case, how to give full play to the advantages of various types of vehicles, use vehicles, and plan distribution routes reasonably is a practical problem worth considering. In view of these aspects, this paper comprehensively considers carbon emissions and mixed vehicle types and other factors to study the cold chain distribution route optimization of fresh agricultural products, so as to promote the high-quality development of agricultural cold chain logistics.

2. Literature Review

Since the Vehicle Routing Problem (VRP) was first proposed by Dantzig and Ramser in 1959, it has attracted much attention, and there have been many mature research results. Among them, many scholars have explored the optimization of the distribution route according to the characteristics of the cold chain of fresh agricultural products. For example, Tarantilis and Kiranoudis [1] planned the distribution route for manufacturers producing and selling fresh meat; Zhu et al. [2] optimized the distribution route of fresh agricultural products considering the input of preservation cost. Wang et al. [3] set minimization of distribution cost and maximization of customer satisfaction as the optimization objectives of intelligent distribution of fresh agricultural products. Yang and Tao [4] established a VRP model for cold chain logistics of fresh products with dual objective optimization. With the deepening of research, more and more scholars pay attention to the importance of time in VRP. Marius and Desrosiers [5] introduced the time window limit into vehicle routing research earlier. Ahkamiraad [6] established a mixed-integer linear programming model for a special capacity multi-hop library VRP with pick-up, delivery, and time window to achieve minimal transportation and fixed costs. Liu and Li [7] built a cold chain logistics distribution route optimization model considering the time window requirements. Ho et al. [8], Ding et al. [9], Wu et al. [10], and Wang et al. [11] combined the characteristics of fresh agricultural products to study the vehicle routing optimization problem considering time window constraints. As the cold chain distribution of fresh agricultural products has high timeliness requirements, this paper will consider the time window constraint in exploring the optimization of the cold chain distribution path.

With the increasing awareness of environmental protection, some scholars have begun to pay attention to the problem of carbon emissions in cold chain distribution. Lin et al. [12] took the lead in introducing carbon emission into logistics research, arguing that enterprises should not only consider traditional economic costs when making logistics decisions but also consider their impact on the ecological environment and society. Liu et al. [13] studied the influence of carbon trading mechanisms on cold chain distribution route planning. Ji et al. [14], Zhang et al. [15], and Yang et al. [16] discussed the optimization of low-carbon routes of cold chain logistics combined with traffic conditions. Demir et al. [17], Hariga et al. [18], Zhao et al. [19], Afra and Behnamain [20], Wu et al. [21], Jiang et al. [22], and Ma et al. [23] established a multi-objective cold chain distribution path optimization model by taking factors such as the lowest fuel consumption, the lowest carbon emission, and the lowest environmental pollution into the objective function. Fu et al. [24], Yao et al. [25], Feng et al. [26], and Pérez-Lechuga et al. [27] focused on the problem of green vehicle routing for fresh agricultural products. However, in general, there are relatively few studies on the optimization of the cold chain distribution path of fresh agricultural products considering carbon emissions, and there is a large research space.

In the actual distribution process, there are often different types of vehicles for distribution. Their rated load, fuel/power consumption, driving speed, etc., are different and have a greater impact on the distribution path and cost of logistics enterprises. So, it is of practical significance to consider the problem of mixed vehicles in the model. Golden et al. [28] took multi-vehicle factors into account in the model earlier and established the objective function of minimum total cost. Heiman et al. [29] studied the routing problems of traditional fuel vehicles, plug-in hybrid vehicles, and electric vehicles. Macrina et al. [30] studied the vehicle routing problem of a hybrid fleet consisting of electric vehicles and conventional vehicles. Ene et al. [31] established a heterogeneous vehicle fleet VRP multi-objective model. Kabadurmus and Erdogan [32] also considered allowing different vehicle types when studying the vehicle routing problem. Leung et al. [33] and Kwon et al. [34] studied the route optimization model of multi-type refrigerated vehicles. Chen et al. [35] discussed the cold chain distribution vehicle routing problem under heterogeneous fleet and parking constraints. Chen et al. [36] analyzed how to plan the green vehicle route using mixed fleets for cold chain distribution. Multiple studies have shown that the distribution of many types of vehicles can reduce the total distribution cost and reduce carbon emissions to a certain extent. Therefore, it is necessary to take mixed vehicle types into account in the optimization of cold chain distribution routes for fresh agricultural products.

To sum up, there are many research results on cold chain distribution route optimization, but the focus of attention is different. The comparison of existing studies is shown in

Table 1. Comparison of existing studies on cold chain distribution routes.

Document Number	Fresh Agricultural Products	Time Window	Carbon Emission	Multiple Vehicle Types
1–4	√
5–7		√
8–11	√	√
12–13			√
14–23		√	√
24–27	√	√	√
28–32				√
33–35	√	√		√
36		√	√	√

Note: A “√” indicates that this factor was taken into account in the relevant literature.

, depending on whether they are specific to fresh agricultural products, and whether time windows, carbon emissions, and multiple vehicle types are considered. It can be seen that time window constraints are basically considered, some studies specifically combine the characteristics of fresh agricultural products, carbon emission factors have attracted attention, and there are relatively few studies on multiple vehicle types. Studies that consider all four factors at the same time are lacking.

As the demand for cold chain distribution of fresh agricultural products is strong, and carbon emission and distribution of various vehicle types are realistic problems that have to be considered, this paper intends to comprehensively consider the four factors mentioned above, and explore the optimization of cold chain distribution path of mixed vehicle types of fresh agricultural products considering carbon emission, in order to provide decision-making reference for the sustainable development of cold chain of agricultural products. The main features of this study are as follows: (1) Considering the time window constraint in the optimization of the distribution path. Maximize customer requirements for delivery time and improve customer satisfaction. (2) Consider the carbon emissions in the cold chain distribution of fresh agricultural products. Pursue economic benefits while improving environmental benefits. (3) Consider the impact of the distribution of multiple types of vehicles. Rationally allocate vehicle resources according to realistic conditions.

3. Method

Establishing a mathematical model to guide decision-making is a common method in distribution route planning. Based on the existing decision-making model, this paper intends to establish a new cold chain distribution route optimization model for fresh agricultural products by comprehensively considering factors such as time window, carbon emission, and mixed vehicle types, and select a suitable solution algorithm. Since the factors and ideas considered in decision-making are reflected in the objective function and constraint conditions of the model, this paper, before establishing the model, mastered the core elements of cold chain distribution of fresh agricultural products through literature analysis and investigation, and provided a basis for setting the model’s objectives and constraint conditions.

3.1. Investigation and Analysis of Cold Chain Distribution Route Planning for Fresh Agricultural Products

3.1.1. Investigation Plan

Through the analysis of the existing literature, it is found that cost minimization is one of the main goals of cold chain distribution route optimization for fresh agricultural products. Almost all of the research is about how to reduce costs, but different studies focus on different types of costs, among which fixed cost and transportation cost are generally considered, and some involve penalty costs, refrigeration costs, cargo damage costs, etc., followed by what costs are considered by enterprises in reality, and what costs are worthy of attention. This study conducted a survey on cold chain logistics companies of fresh agricultural products in view of these problems; at the same time, through the investigation to understand the actual situation of enterprises and decision-making methods.

(1)

Investigation purpose: To understand the concerns and influencing factors considered by cold chain logistics companies of fresh agricultural products in the process of distribution route planning, and to find out what cost components they consider when calculating costs, so as to provide reference for the establishment of multi-objective cold chain logistics distribution route optimization model of fresh agricultural products.

(2)

Investigation object: The respondents were eight different fresh agricultural products cold chain logistics companies in Wuhan, China. All of them can provide distribution services of fresh agricultural products such as fruits, aquatic products, meat, eggs, and quick-frozen products within the city, and are equipped with cold storage, refrigerated trucks, distribution centers, and other facilities to ensure the quality of distribution services and the freshness of goods.

(3)

Investigation time and location: The survey was conducted from 25 February 2024, to 10 March 2024, over a period of 15 days. The respondents were distributed in 4 districts of Wuhan City, China, namely Hongshan District, Dongxihu District, Jiangxia District, and Hannan District.

(4)

Investigation content: The core content is the practice of cold chain logistics companies in planning distribution routes for fresh agricultural products. For example, what are the influencing factors they will consider? What are the delivery costs that they focus on? What types of refrigerated trucks do they use for distribution?

(5)

Investigation method: The survey was completed by interview. Through the communication with the company’s employees, we understand the influencing factors and distribution costs considered by cold chain logistics enterprises when making distribution route plans. The survey outline is in Appendix A.

3.1.2. Analysis of Cold Chain Distribution Route Planning Objectives

Regarding the goal of cold chain distribution route planning, the survey mainly understands the cost considered by the enterprise. The surveyors know what aspects of costs are mainly considered by enterprises in cost calculation through inquiry and record them. When the interviewees could not answer, the researchers would remind them based on the results of the literature analysis, such as whether the cost of carbon emissions was considered. Through sorting, it is found that the costs considered by the eight companies mainly involve fixed costs, transportation costs, penalty costs, refrigeration costs, cargo loss costs, and carbon emission costs, as shown in

Table 2. The main costs considered by the surveyed companies.

Company Number	Fixed Cost	Transportation Cost	Penalty Cost	Cargo Loss Cost	Refrigeration Cost	Carbon Emission Cost
1	√	√	√	√	√	√
2	√	√			√
3	√	√	√	√	√	√
4	√	√	√	√
5	√	√
6	√	√	√	√	√	√
7	√	√	√
8	√	√			√

Note: A “√” indicates that the company has taken this cost into account.

. Three companies accounted for all six costs at the same time, while the others accounted for only some of them.

From the above statistical results, it can be seen that fixed cost and transportation cost are the most important parts in the cost calculation of distribution route planning, and all eight companies have taken them into account, while only a few companies have taken other costs into account due to the difficulty of calculation and quantification. The cost of carbon emissions has attracted the attention of some companies due to increased environmental awareness, but the attention needs to be increased. In fact, the interviewer also found in the process of communication with staff that it is not that companies do not know what should be included in the calculation of the total cost of distribution, but because of the complexity of its calculation, and it is time-consuming and laborious, they choose to ignore it, or convert to other cost calculations, such as refrigeration costs often being converted into fuel costs. In addition, even for companies that fully consider the above six kinds of costs, in addition to transportation and fixed costs, the other costs are simple calculations and are not calculated scientifically, reasonably, and carefully.

3.1.3. Analysis of Constraints in Cold Chain Distribution Route Planning

In the investigation of 8 cold chain logistics companies, it was found that all companies took into account the constraints of vehicle use, drivers, and time windows acceptable to customers when carrying out goods distribution. In addition, in response to the call for low-carbon environmental protection and effectively reducing carbon emissions in the distribution process, four companies that have taken into account the cost of carbon emissions have introduced pure electric refrigerated vehicles and gas–electric dual-use refrigerated vehicles. Two other companies are also planning to introduce gas–electric refrigerated trucks. It can be predicted that the application of electric refrigerated trucks in the cold chain distribution of fresh agricultural products will be more and more extensive. Companies that use electric refrigerated trucks need to consider power constraints when planning distribution routes. Because electric refrigerated trucks are still in the development stage, most companies now have multiple vehicle types at the same time. Therefore, when studying the cold chain distribution of fresh agricultural products, it is of practical significance to consider the joint distribution of mixed vehicle types.

According to the literature analysis and investigation, in order to reduce the carbon emissions in the cold chain distribution of fresh agricultural products, the cost of carbon emissions can be calculated and controlled. At the same time, in order to achieve the overall optimization, the fixed cost, transportation cost, penalty cost, cargo loss cost, refrigeration cost, and carbon emission cost, which account for a relatively large proportion, should be considered comprehensively, and the total cost should be minimized. In terms of constraints, in addition to considering the time required by customers, how to rationally allocate a variety of vehicle resources such as gasoline refrigerated vehicles, pure electric refrigerated vehicles, and gas–electric dual-use refrigerated vehicles is a practical problem worth considering. In order to achieve both economic and environmental benefits and promote the sustainable development of cold chain logistics of fresh agricultural products, it is particularly necessary to consider the time window and mixed vehicle types when planning the distribution route, and to minimize the total cost including carbon emission cost as the optimization goal.

3.2. Model Construction

3.2.1. Problem Description and Model Assumptions

According to the investigation results, this paper aims to minimize the comprehensive distribution cost of fixed cost, transportation cost, penalty cost, cargo loss cost, refrigeration cost, and carbon emission cost, and establishes a cold chain distribution route optimization model for fresh agricultural products considering different vehicle types. Assume that a distribution center needs to provide distribution services for M demand points, and the distribution center can be equipped with K refrigerated trucks for the transportation of fresh agricultural products. The quantity demanded at each demand point is $Q_i$. The latest time for delivery of fresh agricultural products is $l_i$, and the earliest time is $e_i$, so the service time window is $\left(e_i, l_i\right)$. The staff driving the refrigerated vehicle should deliver the goods to the customer demand point within the prescribed time, and certain penalty costs will be incurred if the time is advanced or delayed. It is necessary to make a reasonable distribution route while meeting the time required by the demand point, so as to reduce the total cost in the distribution process. The assumptions are as follows: (1) Only one distribution center is considered, and the goods transported are fresh agricultural products. (2) There are many types of refrigerated trucks in the distribution center, and the load capacity is known. (3) The quantity of goods in the distribution center is sufficient. (4) The starting point and end point of the refrigerated truck are the distribution center, and each demand point can only be distributed once in a plan. (5) The service time window of each demand point is known. (6) The road conditions between the distribution center and the demand point are complicated, and the linear distance between two points on the map is considered in this paper. (7) The demand of goods will not change in the process of distribution. The relevant variables used in the model are shown in

Table 3. Variables in the model.

Symbol	Implication
m	Collection of demand points, where 0 represents the distribution center. $\mathrm{m}=\{0,1,2···,\mathrm{M}\}$.
k	Number of refrigerated trucks used for distribution, $\mathrm{k}=\{1,2···,\mathrm{K}\}$.
r	Refrigerated vehicle types, including gasoline refrigerated vehicles and electric refrigerated vehicles, etc., $\mathrm{r}=\{1,2···,\mathrm{R}\}$.
Kr	Number of refrigerated vehicles of type r, and the total number of vehicles is K.
$i,j$	Demand points.
${\mathrm{Z}}_1$	Cost objective function.
${\mathrm{Z}}_{11}$	Fixed cost.
${\mathrm{Z}}_{12}$	Transportation cost.
${\mathrm{Z}}_{13}$	Penalty cost.
${\mathrm{Z}}_{14}$	Cargo loss cost.
${\mathrm{Z}}_{15}$	Refrigeration cost.
${\mathrm{Z}}_{16}$	Carbon emission cost.
${\mathrm{Z}}_2$	${\mathrm{CO}}_2$ emissions generated during the distribution of refrigerated vehicles.
Gr	Full load of type r refrigerated vehicle.
gr	Load weight of type r refrigerated vehicle.
$V_{\max }^r$	Maximum speed of type r refrigerated vehicle.
$E_i$	The earliest service time allowed by demand point i.
$L_i$	The latest service time allowed by demand point i.
$e_i$	The earliest delivery time required by demand point i.
$l_i$	The latest delivery time required by demand point i.
dij	Distance between node i and node j.
$L_{\max }^r$	Maximum driving distance of type r refrigerated vehicle.
$Q_i$	Quantity of goods demanded at demand point i.
$M_0$	Minimum battery capacity of electric refrigerated vehicle.
$M_{\max }$	Maximum battery capacity of an electric refrigerated vehicle.
$f{\left(g\right)}_{1i}$	Electricity of electric refrigerated vehicle at node i.
$t_{ir}^k$	The time when the k refrigerated vehicle of type r is transported from i to j.
w1	Unit penalty cost of refrigerated vehicle arriving earlier than the specified time.
w2	Unit penalty cost of refrigerated vehicle being late to the specified time.
$x_{ijr}^k$	when the k refrigerated vehicle of type r goes from the demand point i to j, $x_{ijr}^k=1$, otherwise 0.
$y_{ir}^k$	If the k refrigerated vehicle of type r serves the demand point i, $y_{ir}^k=1$, otherwise 0.
p	Unit carbon trading price.

.

3.2.2. Target Analysis

In this paper, the cold chain distribution route of fresh agricultural products is studied, and various costs are analyzed to minimize the comprehensive distribution cost. This paper does not set the weight of all kinds of costs; in the actual application process, enterprises can set reasonable weights according to their own conditions and demand points. The total cost is calculated as follows:

$$Z_1=Z_{11}+Z_{12}+Z_{13}+Z_{14}+Z_{15}+Z_{16}$$

(1)

(1) Fixed cost

The fixed cost $Z_{11}$ is composed of the depreciation cost of refrigerated vehicle, the driver’s salary, and so on, generated in the process of distribution. It does not change with the transport distance or load. It is calculated as follows:

$$Z_{11}={\displaystyle \sum _{k=1}^{K_r}{\displaystyle \sum _{r=1}^R{Z}_{11r}}}\times k$$

(2)

where $Z_{11r}$ is the fixed cost of type r (gasoline or electric, etc.) refrigerated vehicle.

(2) Transportation cost

The transportation cost $Z_{12}$ is the fuel consumption or power consumption cost generated by the refrigerated vehicle in the process of distributing fresh agricultural products. The longer the distance the refrigerated vehicle travels, the higher the fuel consumption cost and power consumption cost. The calculation function expression of transportation cost is as follows:

$$Z_{12}={\displaystyle \sum _{i=0}^M{\displaystyle \sum _{j=0}^M{\displaystyle \sum _{r=1}^R{\displaystyle \sum _{k=1}^{K_r}{x}_{ijr}^k}{d}_{ij}{Z}_{12r}}}}$$

(3)

where $Z_{12r}$ is the transportation cost per unit distance for type r vehicle.

(3) Penalty cost

If the driver of the vehicle does not deliver the goods within the time window acceptable to the customer, there will be a certain penalty cost. The penalty cost $Z_{13i}\left(t_i\right)$ at demand point i is a linear function of vehicle arrival time $t_i$. There is a penalty if the vehicle arrives within the range of $\left[E_i,e_i\right]$ and $\left[l_i,L_i\right]$, while there is no penalty if it arrives within the time of $\left[e_i,l_i\right]$, and the penalty value beyond the range of $\left[E_i,L_i\right]$ is set to an infinite positive number M. The expression for penalty cost is as follows:

$$Z_{13i}=\{\begin{array}{l}M\left(t_i<E_i\right)\\ \left(e_i-t_i\right)\times w_1\left(E_i\le t_i<e_i\right)\\ 0\left(e_i\le t_i<l_i\right)\\ \left(l_i-t_i\right)\times w_2\left(l_i\le t_i<L_i\right)\\ M\left(t_i>L_i\right)\end{array}$$

(4)

$$Z_{13}={\displaystyle \sum _{i=1}^M{Z}_{13i}}$$

(5)

(4) Cargo loss cost

Due to the characteristics of fresh agricultural products and their distribution characteristics, the cargo loss cost will be generated in the distribution process. This paper considers the cost caused by natural loss of fresh agricultural products in the process of distribution and the cargo damage caused by the temperature difference between inside and outside the refrigerated vehicle during loading and unloading. The expression of cargo loss cost is as follows:

$$Z_{14}={\displaystyle \sum _{i=0}^M{\displaystyle \sum _{r=1}^R{\displaystyle \sum _{k=1}^{K_r}{y}_{ir}^k\times q_i\times \left(1-e^{-{\beta }_1\times t_{ir}^k}\right)\times N+}}}{\displaystyle \sum _{i=0}^M{\displaystyle \sum _{r=1}^R{\displaystyle \sum _{k=1}^{K_r}{y}_{ir}^k\times q_{it}\times \left(1-e^{-{\beta }_2\ast t_{ir}^k}\right)\times N}}}$$

(6)

${\beta }_1$ and ${\beta }_2$ indicate the rate of corruption during closing and loading, respectively. N is the unit value of the goods. $q_{it}$ is the weight at t time.

(5) Refrigeration cost

In the distribution process of fresh agricultural products, refrigerated vehicles are required to maintain a low temperature, which will generate refrigeration costs. The refrigeration cost has two parts, respectively, the cost in the closed state and the cost generated during the loading and unloading process. This paper ignores the cost of refrigeration in the loading and unloading process and only considers the cost of refrigeration in the closed state. The expression of refrigeration cost is as follows:

$$Z_{15}={\displaystyle \sum _{i=0}^M{\displaystyle \sum _{r=1}^R{\displaystyle \sum _{k=1}^{K_r}{\alpha }_r\times t_{ir}^k\times y_{ir}^k}}}$$

(7)

${\alpha }_r$ is the refrigeration cost per unit time of type r refrigerated vehicle.

(6) Carbon emission cost

It can be seen from the relevant information that under certain conditions such as road conditions, driving technology, speed, etc., the fuel consumption or power consumption per kilometer traveled by the vehicle has a linear relationship with the load capacity. The linear function is as follows:

$$f{(g)}_r=\left[f^{\prime }{(G)}_r-f{(0)}_r\right]/G\times g+f(0)$$

(8)

In the expression, $f^{″}{(G)}_r$ represents the fuel consumption or electricity consumption of the refrigerated vehicle when it is fully loaded; $f{(0)}_r$ represents the fuel consumption or electricity consumption of the refrigerated vehicle without load; g is the load of refrigerated vehicle; G is the full load of the refrigerated vehicle.

Then, based on vehicle fuel consumption or electric energy consumption in the distribution process, carbon dioxide emissions are calculated, and the calculation function expression is as follows:

$$Z_2={\displaystyle \sum _{i=0}^M{\displaystyle \sum _{j=0}^M{\displaystyle \sum _{r=1}^R{\displaystyle \sum _{k=1}^{K_r}f{(g)}_r\times d_{ij}}}}\times x_{ij}^{k_r}\times {\lambda }_r}$$

(9)

where $f{(g)}_r$ is the fuel or electricity consumption of the vehicle. ${\lambda }_r$ is the carbon dioxide emission coefficient of the refrigerated vehicle. The carbon emission cost expression is:

$$Z_{16}=Z_2\times p$$

(10)

3.2.3. Constraint Analysis

Considering the distribution characteristics of cold chain logistics of fresh agricultural products and the characteristics of vehicle path planning, the following constraints are set for the model.

(1)

Constraints of the customer time window. The delivery vehicle should arrive within the time limit required by the customer, otherwise it will be subject to corresponding penalties.

(2)

During the delivery process, a demand point is only served by one refrigerated vehicle and is only served once.

(3)

Constraints on the number of vehicles in the distribution center. The number of vehicles to complete the distribution task cannot exceed all the vehicles owned by the distribution center, otherwise the scheme cannot be implemented.

(4)

All refrigerated vehicles start from the distribution center and return to the distribution center after the end of service.

(5)

Each refrigerated vehicle has a load limit, so in the distribution process, it is necessary to ensure that the total weight of fresh products does not exceed the carrying capacity of the refrigerated vehicle.

(6)

In order to ensure driving safety, the total length of each refrigerated vehicle driving route shall not exceed its maximum mileage during the distribution process.

(7)

In order to ensure safety, during the distribution process, the speed of each refrigerated vehicle should not exceed its maximum speed.

(8)

Each electric refrigerated vehicle used for distribution work should not be lower than the minimum allowable power, nor higher than the maximum battery capacity.

3.2.4. Construction of Cold Chain Distribution Path Optimization Model

According to the above analysis, the objective function of the cold chain distribution route optimization model of fresh agricultural products considering mixed vehicle types and carbon emissions is as follows:

$$Z_1=Min(Z_{11}+Z_{12}+Z_{13}+Z_{14}+Z_{15}+Z_{16})$$

(11)

The constraints are as follows:

$$E_i\le t_{ir}^k\le L_i; \forall r\in R,\forall k\in K$$

(12)

$${\displaystyle \sum _{i=0}^{\mathrm{M}}{\displaystyle \sum _{k=1}^{K_r}{\displaystyle \sum _{r=1}^R{x}_{ijr}^k}}}=1; \forall j\in M$$

(13)

$${\displaystyle \sum _{j=0}^{\mathrm{M}}{\displaystyle \sum _{k=1}^{K_r}{\displaystyle \sum _{r=1}^R{x}_{ijr}^k}}}=1; \forall j\in M$$

(14)

$${\displaystyle \sum _{j=1}^M{\displaystyle \sum _{k=1}^K{x}_{ijr}^k}}\le K_r; i=0$$

(15)

$${\displaystyle \sum _{i=0}^M{\displaystyle \sum _{r=1}^R{x}_{ijr}^k}}={\displaystyle \sum _{i=0}^M{\displaystyle \sum _{r=1}^R{x}_{jir}^k}}; \forall k\in K,\forall i\in M$$

(16)

$${\displaystyle \sum _{i=1}^M{\displaystyle \sum _{r=1}^R{Q}_i\times y_{ir}^k}}\le G_r; \forall k\in K$$

(17)

$${\displaystyle \sum _{i=0}^M{\displaystyle \sum _{j=0}^M{x}_{ijr}^k\times }}{d}_{ij}\le L_{\max }^r; \forall r\in R,\forall k\in K$$

(18)

$${\displaystyle \sum _{i=0}^M{\displaystyle \sum _{j=0}^M{d}_{ij}/t_{ij}\times x_{ijr}^k}}\le V_{\max }^r; \forall r\in R,\forall k\in K$$

(19)

$$x_{ijr}^k=\left\{0,1\right\}; \forall r\in R,\forall k\in K$$

(20)

$$y_{ir}^k=\left\{0,1\right\}; \forall r\in R,\forall k\in K$$

(21)

$$M_0\le f{(g)}_{1i}\le M_{\max }$$

(22)

Formula (11) is the objective function with the lowest cost. The Formula (12) in the constraints indicates that the service time is within the time specified by the customer. Formulas (13) and (14) indicate that each customer point has only one refrigerated vehicle for service, and is only served once. (15) means that the number of distribution vehicles must not exceed the number of vehicles owned by the distribution center. (16) indicates that each vehicle starts from the distribution center and finally returns there. (17) means that the total demand for goods at customer demand points on the distribution path cannot be greater than the maximum load of the distribution refrigerated vehicle. (18) indicates that the total mileage of each refrigerated vehicle in the distribution process is not greater than its maximum allowable mileage. (19) means that the speed of each refrigerated vehicle in the distribution process cannot be greater than the fastest speed it is allowed. (20) and (21) are decision variable functions. (22) represents the power constraint of electric refrigerated vehicle at each node.

3.3. Model Solution Algorithm

3.3.1. Algorithm Selection

There are many common algorithms to solve the vehicle routing problem, such as precise algorithm, ant colony algorithm, genetic algorithm, tabu search algorithm, simulated annealing algorithm, particle swarm algorithm, and so on. Considering the established model, this paper adopts genetic algorithm to solve the established model for the following three reasons: First, the operation of genetic algorithm is simple, with strong robustness, and has a wider range of application. Secondly, it can deal with the objective function and fitness function well and minimize the probability of falling into the local optimal solution. Third, the model constructed in this paper is relatively complex, which is a multi-objective distribution route optimization model considering mixed vehicle types, and genetic algorithm is just suitable for large-scale path planning. Therefore, this paper designs the solution of genetic algorithm and then solves the constructed path optimization model.

3.3.2. Solution Steps

The operation process of the genetic algorithm includes the following steps: Firstly, the coding design is carried out, and then the initial group selection is carried out. Then, it is necessary to calculate according to the fitness of individuals and select appropriate operators for operation. In this process, operator crossover and operator variation are used to optimize the solution, followed by, according to the termination condition, ultimately judging whether the solution is complete, as shown in Figure 1.

3.3.3. Solution Design

(1) Coding Design

Common chromosome coding methods include natural number coding, binary coding, and data structure coding. It can be seen from the literature that most of the coding methods related to the distribution path optimization problem are natural number coding. In the distribution between the distribution center and the customer points, the node code can be continuous, and there is only one distribution to the customer point, so the natural number coding method is also adopted in this paper to encode the chromosome. The coding process is specifically expressed as follows: the number “0” represents the distribution center, and the number “n” represents the customer point, where the code length = the number of customer points + the number of vehicles used $\times 2 - 1$, that is, the code length = $n+2\times m-1$. The problem becomes any natural number from “1” to “$n+2\times m-1$”, where a number greater than “n” represents a split point of route information. If the chromosomes that meet the constraints are solved according to the rules, then the chromosomes form an alternative distribution path. The location of “0” is used to record which type of vehicle is selected. Suppose that there are two types of vehicles, before the appearance of the m-th “0”, the first type of vehicle is selected, and the second type of vehicle is selected later.

(2) Generate initial population

A population is a collection of all individuals, each representing a solution. The larger the size of the initial population, the greater the number of individuals in the population that can be selected, crossed, and mutated. It can reduce the possibility of falling into the local optimal solution and improve the efficiency of searching for the global optimal solution. Once the number and size of the population are determined, the corresponding number of gene sequences can be generated in a suitable way. For the model in this paper, an individual represents a cold chain distribution path scheme. A variety of constraints are set, and individuals that do not meet the requirements are removed to obtain a high-quality initial population.

(3) Fitness function

The evaluation of a solution by genetic algorithm does not depend on the structure of its solution, but depends on the fitness value of the solution, which reflects the characteristics of genetic algorithm “survival of the fittest”. Since the objective of the model established in this paper is to find the minimum cost, the reciprocal of the objective function is used to determine its adaptability.

(4) Selection

Chromosome selection is to select the most dynamic and potential chromosomes in the existing population. The roulette selection method was used in this study. The basic principle of this method is that whether a chromosome is selected has a certain correlation with its fitness function value, that is, the higher the fitness of the chromosome, the greater the probability of being selected. If the population size is i and the fitness function of individuals is ${\mathrm{f}}_{\mathrm{i}}$, then the probability of the solution of the distribution path optimization model being selected is:

$$p_i={\displaystyle \frac{f_i}{{\displaystyle {\sum }_i^n{f}_i}}}$$

(23)

(5) Crossover

Crossover is an important method to generate new individuals, which determines the global optimization ability of genetic algorithm. In this paper, the single-point crossover method is chosen, as shown in Figure 2. The greater the crossover probability, the more new solutions can be obtained to ensure the diversity of the population and avoid premature convergence of the algorithm. Therefore, the crossover probability chosen in this paper is 0.9.

Note: The arrow points to the crossover point, and the part after that point is swapped.

(6) Mutation

Mutation is to replace the gene value of a specific site that meets certain conditions in order to overcome premature maturity in crossover and improve the diversity of the population. The algorithm is based on real number coding, which randomly selects chromosome individuals through population mutation. In this paper, the probability of mutation is 0.5.

4. Example Analysis

4.1. Case Background

Company A is one of the cold chain distribution companies of fresh agricultural products in Wuhan, China, investigated in this study. One of its distribution centers provides distribution services for many customers every day. This paper chooses the business of the distribution center and 21 customer demand points around it as the object of analysis. Baidu map is used to query the longitude and latitude coordinates of each demand point and distribution center. The difference between geographic coordinates and plane coordinates is ignored, and the Baidu map query result is taken as plane coordinates. At the same time, through the function of Baidu map, the distance between the demand points and the distance from the distribution center to the demand points are measured. Taking P as the coordinate point of the distribution center, its coordinate is (64, 45). Take M1-M21 as the coordinates of the demand points, and related data are shown in

Table 4. Information about the demand points.

Demand Points Number	Demand Point Coordinates		Distance to Distribution Center (km)	Quantity Required (t)	Time Window		Maximum Tolerance Time (h)
	Abscissa	Ordinate
M1	87	37	19.5	0.98	7:30	9:00	1
M2	77	39	10.1	1.98	7:30	9:00	1
M3	79	36	16.4	3.26	7:30	9:00	1
M4	66	37	18.1	2.76	7:30	9:00	1
M5	75	44	8.8	0.88	7:30	9:00	1
M6	65	39	12.9	2.59	7:30	9:00	1
M7	66	41	15.6	1.5	7:30	9:00	1
M8	68	36	7.5	2.19	7:30	9:00	1
M9	81	39	15.1	3.11	7:30	9:00	1
M10	77	45	9.3	3.48	7:30	9:00	1
M11	70	35	9.4	1.35	7:30	9:00	1
M12	76	41	6.5	2.61	7:30	9:00	1
M13	71	44	4.8	3.41	7:30	9:00	1
M14	83	35	20.7	3.5	7:30	9:00	1
M15	80	38	16.2	2.83	7:30	9:00	1
M16	81	39	15.8	2.05	7:30	9:00	1
M17	73	42	6.5	2	7:30	9:00	1
M18	73	34	14.1	1.28	7:30	9:00	1
M19	87	38	20.2	2.625	7:30	9:00	1
M20	81	32	20.3	2.86	7:30	9:00	1
M21	75	36	12.6	2.1	7:30	9:00	1

. The distances between different demand points are shown in Appendix B.

According to the survey, the distribution center has a total of 140 refrigerated vehicles, of which the load capacities of 5 t gasoline refrigerated vehicles and 4t electric refrigerated vehicles are 70 each. The relevant data of fuel consumption and power consumption of refrigerated vehicles are shown in

Table 5. Data of fuel and electricity consumption of refrigerated vehicles.

Name	Numerical Value
Power consumption per 100 km when the 4t electric refrigerated vehicle is unloaded.	40
Power consumption per 100 km when the 4t electric refrigerated vehicle is fully loaded.	50
Fuel consumption per 100 km when the 5t gasoline refrigerated vehicle is unloaded.	10
Fuel consumption per 100 km when the 5t gasoline refrigerated vehicle is fully loaded.	13

.

From the investigation, the maximum speed of vehicles in the distribution center is 50 km per hour, while the maximum operating distance of vehicles is set at 110 km. The average sales price of fresh agricultural products is 30 yuan/kg. The fixed cost of a 4t electric refrigerated vehicle is 150 yuan, the transportation cost is 0.3 yuan per kilometer per hour, the maximum battery capacity of electric vehicles is 200 kWh, and the minimum allowable electricity is 30 kWh. The fixed cost of a 5t gasoline refrigerated vehicle is 200 yuan, and the transportation cost is 0.9 yuan per kilometer per hour. The loading and unloading rate of the vehicle is 6 t/h, and the refrigerated vehicle will start the delivery at 7 am. If the vehicle arrives early, the waiting fee is 2 yuan/h (less than 1 h is counted as 1 h), and the late penalty fee is 10 yuan/h (less than 1 h is counted as 1 h). The detailed relevant data are shown in

Table 6. Summary of relevant data.

Name	Numerical Value
Vehicle speed	50
Loading and unloading speed	6
Fixed cost of 5t gasoline refrigerated vehicle	200
Unit transportation cost of 5t gasoline refrigerated vehicle	0.9
Fixed cost of 4t electric refrigerated vehicle	150
Unit transportation cost of 4t electric refrigerated vehicle	0.3
Waiting cost	2
Penalty cost	10
Unit refrigeration cost of 4t electric refrigerated vehicle when closed	3.5
Unit refrigeration cost of 5t gasoline refrigerated vehicle when closed	4
Unit refrigeration consumption of 4t electric refrigerated vehicle when closed	0.5
Unit refrigeration consumption of 5t gasoline refrigerated vehicle when closed	0.6
Corruption rate when refrigerated vehicle is not opened	0.008
Corruption rate during loading and unloading of refrigerated vehicle	0.01
Unit carbon trading price	0.6
${\mathrm{C}\mathrm{O}}_2$ emission coefficient of electric refrigerated vehicle	0.0997
${\mathrm{C}\mathrm{O}}_2$ emission coefficient of gasoline refrigerated vehicle	0.2925

.

4.2. Solving Procedure

The relevant data of distribution center and demand points were substituted into the cold chain distribution path optimization model of fresh agricultural products, and MATLAB 2018b was used to solve the problem. The number of demand points is 21, and the distribution center has 4t electric refrigerated vehicles and 5t gasoline refrigerated vehicles. Chromosome coding is performed accordingly. The population size is 750. The fitness is $f={\displaystyle \frac{1}{Z}}$. The roulette method is used for selection, any number is generated between the range of [0,1], and it is used as a pointer to determine the number of chromosomes to be retained. The number of chromosomes selected to be retained is 70% of the initial population number. On this basis, a single point method is used to cross. Two chromosomes are randomly generated, and cross operation is performed between the two chromosomes. For chromosomes that do not meet the restriction requirements, the mutation operation is repeated until the chromosome that meets the restriction is obtained.

The number of iterations is set to 750. From the actual situation, with the increase in the number of iterations, the change in the optimal value gradually decreases, tends to be flat after 214 iterations, and reaches a stable and unchanged state after 500 iterations, that is, the optimal solution is reached.

4.3. Optimization Result Analysis

The solution results show that in order to serve 21 customer points, the distribution center needs to send 12 vehicles to form 12 routes, as shown in

Table 7. Optimized delivery path.

Serial Number	Type of Refrigerated Vehicle	Delivery Routes
1	5t gasoline refrigerated vehicle	0→ -> 8 → 6 → 0
2	5t gasoline refrigerated vehicle	0 → 5 → 9 → 0
3	5t gasoline refrigerated vehicle	0 → 15 → 2 → 0
4	5t gasoline refrigerated vehicle	0 → 11 → 14→ 0
5	5t gasoline refrigerated vehicle	0 → 18 → 19 →1 → 0
6	5t gasoline refrigerated vehicle	0 → 3 → 7 → 0
7	5t gasoline refrigerated vehicle	0 → 4 → 16→ 0
8	5t gasoline refrigerated vehicle	0 → 10→ 0
9	5t gasoline refrigerated vehicle	0 → 21 → 20 → 0
10	4t electric refrigerated vehicle	0 → 12 → 0
11	4t electric refrigerated vehicle	0 → 13 → 0
12	4t electric refrigerated vehicle	0 → 17→ 0

. The scheme generated a total distribution cost of 3233.7852 yuan and carbon emissions of 393.409 kg.

In particular, the various costs, the number of vehicles used, and the total mileage of distribution are shown in

Table 8. Comparison of results before and after optimization.

Type of Target	Before Optimization	After Optimization	Reduced Amount
Fixed cost	2400	2250	150
Transportation cost	286.2	279.42	6.78
Penalty cost	0	0	0
Cargo loss cost	47.428	39.4231	8.0049
Refrigeration cost	463.59	428.8967	34.6933
Carbon emission	533.37	393.409	139.961
Carbon emission cost	320.02	236.0454	83.9746
Number of vehicles used	13	12	1
Total delivery miles	374.4	334.2	40.2
Total delivery cost	3517.238	3233.7852	283.4528

. Comparing the data before and after optimization, it can be seen that some changes have occurred.

Although the model is only applied in a small range, the obvious optimization effect can still be seen. The total number of refrigerated vehicles required after optimization is one less than the original distribution route scheme. At the same time, in addition to the same penalty costs, other costs have been reduced by varying degrees, and carbon emissions and total miles of distribution have also been reduced. From these data and changes, it can be seen that the optimized scheme not only saves the distribution cost of fresh agricultural products but also reduces carbon emissions. This also shows that the optimized distribution route reduces some unnecessary transportation in the distribution process and improves the economic and environmental benefits of Company A in the cold chain distribution of fresh agricultural products. It can be seen that the cold chain distribution route optimization model established in this paper is effective and has application value, and can provide reference for the distribution route planning of cold chain logistics companies of fresh agricultural products.

5. Discussion

Reasonable planning of cold chain logistics distribution route is an important measure to save logistics resources, reduce the impact on the environment, and promote the sustainable development of agricultural cold chain logistics. On the basis of field investigation, this paper establishes a new optimization model of cold chain distribution route for fresh agricultural products, and carries out an example analysis. The results show that:

(1)

It is necessary and feasible for cold chain distribution route planning of fresh agricultural products to comprehensively consider factors such as carbon emissions and mixed vehicle types. In view of the high timeliness requirements and high energy consumption of cold chain distribution of fresh agricultural products, the planning of distribution routes should not only consider the constraints of the time window but also consider how to rationally use vehicle resources, give play to the advantages of different types of vehicles, in order to reduce distribution costs and reduce carbon emissions. This paper is a helpful supplement to the existing research. In the study of cold chain distribution route of fresh agricultural products, Ho et al. [8], Ding et al. [9], Wu et al. [10], and Wang et al. [11] took the time window constraint into consideration; Fu et al. [24], Yao et al. [25], Feng et al. [26], and Pérez-Lechuga et al. [27] considered the time window and carbon emissions; Leung et al. [33], Kwon et al. [34], and Chen et al. [35] consider the time window and mixed vehicle types. In this paper, the three factors mentioned above are taken into account to establish a decision-making model, which can better balance economic benefits and environmental benefits, and has good application value in the current practical conditions.

(2)

The optimal overall cost should be pursued in the cold chain distribution route planning of fresh agricultural products. The cold chain distribution process will produce a variety of costs; only paying attention to a few costs may lead to the increase in other costs, affecting the overall operation effect. Therefore, when planning the distribution route, we should fully understand the possible costs and pursue the minimum comprehensive cost. Previous studies have considered the cost of cold chain distribution of fresh agricultural products from different perspectives. For example, Wang et al. [11] took into account the cost of freshness loss, cold chain refrigeration cost, and delay penalty cost; Jiang et al. [22] took into account the cost of transportation, refrigeration cost, and carbon emission cost; Ma et al. [23] considered fixed transportation cost, variable transportation cost, time penalty cost, and carbon emission cost. This paper comprehensively considers six major costs in the cold chain distribution of fresh agricultural products, including fixed cost, transportation cost, penalty cost, cargo loss cost, refrigeration cost, and carbon emission cost, which is conducive to improving the effectiveness of decision-making.

(3)

Genetic algorithm is an effective method to solve the cold chain distribution route optimization model of fresh agricultural products. There are many methods to solve mathematical models, and each has its own advantages. Similar to the studies of Liu and Li [7], Jiang et al. [22], and Chen et al. [35], this paper selects genetic algorithm to solve the problem based on the characteristics of the model. From the algorithm design and practical application, the algorithm can explain the model decision thinking well and help find the optimal solution quickly, so it is an effective solution method. Of course, if the model is further optimized, genetic algorithms mixed with other methods can be tried to improve the ability to solve the problem.

6. Conclusions

In this paper, the cold chain distribution route optimization of fresh agricultural products is taken as the research object, with the minimum total cost including carbon emission cost as the optimization goal. The cold chain distribution route optimization model is constructed considering different types of refrigerated vehicles and is solved with the help of genetic algorithm. Finally, taking the distribution center of Company A as an example, the empirical analysis of the proposed method is carried out, and the results show that the method is effective. The main work completed in this paper includes:

(1) Through the investigation on the distribution route planning of eight fresh agricultural products cold chain logistics companies in Wuhan, China, it is learned that the costs related to decision-making include fixed cost, transportation cost, penalty cost, cargo loss cost, refrigeration cost, carbon emission cost, etc., but most companies do not consider comprehensively, especially that the carbon emission costs are relatively less. In addition, many companies have multiple vehicle types such as gasoline, electric, and hybrid vehicles, which need to be considered when optimizing distribution routes.

(2) Based on the investigation results and the literature, a cold chain distribution route optimization model for fresh agricultural products is established. The optimization goal of the model is to minimize the six total costs including carbon emission costs, and the constraints of the time window are emphasized, and the mixed vehicle types is also taken into account. According to the characteristics of the model, genetic algorithm is chosen as the method to solve the model.

(3) The validity and application value of the model are verified by the case data of a distribution center of Company A. Through the data comparison before and after optimization, it can be seen that the distribution route determined by the new model can effectively utilize vehicle resources and reduce various costs and carbon emissions in the distribution process. This is beneficial to improve the economic benefits of the distribution center and improve the social environmental benefits and can provide a reference for the distribution route planning of cold chain logistics companies of fresh agricultural products.

This paper fully combines the characteristics of cold chain distribution of fresh agricultural products, considers the current situation of coexistence of multiple vehicle types, and comprehensively considers how to rationally plan the cold chain distribution path from the perspective of low-carbon development, which helps to better improve the quality and efficiency of fresh agricultural products distribution. However, there are still some details that have not been carefully considered in this study, such as complex traffic conditions, sudden increase in order demand, etc. Further research can make a more comprehensive consideration around this problem and seek more efficient solution algorithms.