Optimizing Cold Chain Distribution Routes Considering Dynamic Demand: A Low-Emission Perspective

Abstract

Cold chain logistics, with its high carbon emissions and energy consumption, contradicts the current advocacy for a “low-carbon economy”. Additionally, in the real delivery process, customers often generate dynamic demand, which has the characteristic of being sudden. Therefore, to help cold chain distribution companies achieve energy-saving and emission-reduction goals while also being able to respond quickly to customer needs, this article starts from a low-carbon perspective and constructs a two-stage vehicle distribution route optimization model that minimizes transportation costs and refrigeration costs, alongside carbon emissions costs. This research serves to minimize the above-mentioned costs while also ensuring a quick response to customer demands and achieving the goals of energy conservation and emission reduction. During the static stage, in order to determine the vehicle distribution scheme, an enhanced genetic algorithm is adopted. During the dynamic optimization stage, a strategy of updating key time points is employed to address the dynamic demand from customers. By comparing the dynamic optimization strategy with the strategy of dispatching additional vehicles, it is demonstrated that the presented model is capable of achieving an overall cost reduction of approximately 17.13%. Notably, carbon emission costs can be reduced by around 17.11%. This demonstrates that the dynamic optimization strategy effectively reduces the usage of distribution vehicles and lowers distribution costs.

1. Introduction

As living standards and quality improve, the cold chain market has been experiencing continuous expansion, resulting in a year-on-year increase in demand. To meet this growing market demand, it is imperative to enhance the efficiency of cold chain distribution and place greater emphasis on addressing cold chain delivery issues. Given the perishable nature of fresh products, customers have heightened expectations for prompt and fresh deliveries, thereby making it crucial for cold chain distribution companies to prioritize the optimization of delivery routes as a means to secure a larger market share. Moreover, as a special branch of the logistics industry, cold chain distribution requires the use of refrigeration equipment during the delivery process. This not only increases fuel consumption but also may cause greater pollution to the surrounding environment. According to the statistics from relevant authorities, the fuel consumption of refrigeration units in refrigerated trucks is 2 to 4 L per hundred kilometers, increasing exhaust emissions by more than 30% compared to regular vehicles. Coupled with the continuous expansion of the cold chain logistics market in recent years, the demand for cold chain logistics is on a growing trend, thus making the carbon emission problem of cold chain distribution even more serious. Therefore, to obtain a higher market share, cold chain distribution enterprises first need to solve the problem of cold chain distribution path optimization. Especially on the basis of low carbon, achieving a balance between economic and environmental benefits has become a pressing issue in research on cold chain distribution. This can help cold chain enterprises to realize energy savings and emission reductions in their distribution process.

The vehicle routing problem [1] (VRP) has received extensive attention and studies from scholars since it was proposed by Dantzing and Ramser in 1959. Based on whether the routing of delivery vehicles needs to be dynamically adjusted, VRP can be divided into two categories: static vehicle routing problem (SVRP) and dynamic vehicle routing problem (DVRP). Significant research achievements have been made in SVRP. For example, Osvald and Stirn [2] constructed an objective model for minimizing the total delivery cost based on time windows. They employed a tabu search algorithm for solving the optimization problem. Shukla and Jharkharia [3] designed an artificial immune algorithm to solve the logistics transportation problem of delivering fresh agricultural products from wholesalers to retailers. Brito [4] considered vehicle capacity, time windows, and other factors and constructed the VRPCLD model to optimize the total delivery time using soft computing methods to solve it. Qi and Hu [5] addressed the emergency cold chain logistics problem, considering the urgency of time, and developed a mathematical model for emergency logistics, which was solved using a hybrid algorithm combining ant colony systems and local search. Song [6] considered customer satisfaction and established a mathematical model to maximize customer satisfaction, using the artificial fish swarm algorithm to solve it. Nader [7] tackled the last-mile delivery problem in the vaccine supply chain, building a mixed-integer programming model to achieve timely delivery for all customers and solving it using a greedy random search algorithm.

With a rise in mobile e-commerce platforms, customer orders are showing more flexible and dynamic characteristics, with customer demands displaying a trend in dynamic changes. Therefore, scholars have begun to conduct in-depth research on the DVRP. Specifically, the current research mainly focuses on the dynamic changes in customer demands [8,9] and driving speeds [10,11]. For example, the literature of [12,13,14,15,16,17] has utilized strategies such as iterative optimization, continuity, and periodic processing strategies to handle the dynamic information that arises during the delivery process. Building upon this, Abdel [18] has adopted a heavy optimization strategy in handling dynamic information, which can be timely and effective in processing dynamic information. However, if the adjustment of multiple dynamic events occurs, it will lead to the emergence of situations such as the cost becoming larger and the driver’s emotion being affected. Zhang J et al. [19] have considered the problem of vehicle routing with demand randomness and established a probability model. Lingkai L et al. [20] focused on the electric vehicle problem and built static and dynamic optimization models based on battery swap stations, incorporating demand forecasting and battery quantity analysis. Allahyari et al. [21] applied dynamic vehicle routing optimization to the transportation of valuable goods, aiming to reduce robbery risks and operational costs of distribution networks. They analyzed the impact of customer demand uncertainty and speed-time dependency on network transport efficiency, constructing a corresponding vehicle routing optimization model. Wang Feng et al. [22] studied multi-objective DDVRPTW problems and developed corresponding mathematical models. Meanwhile, the construction of the DVRP model is mainly based on a single-stage model [18,19,20,21,22], and there is a lack of study on the multi-stage model construction. Furthermore, scholars have primarily worked on solving DVRP models through either exact [23] or heuristic algorithms [24,25,26,27].

In recent years, with the worsening of environmental pollution, people have started to pay attention to environmental and energy issues. Energy savings and emission reductions have gradually become research hotspots in the field of logistics and distribution. Therefore, some scholars have conducted research on low-carbon logistics path optimization. For example, Poonthalir [28] constructed a multi-objective, low-carbon vehicle routing optimization model while considering the vehicle gear shifting problem to reduce the total vehicle distribution costs and fuel consumption and solved it using a particle swarm algorithm. Hasan [29], considering the impact of road gradients on vehicle fuel consumption in the TSP problem, designed a decision-making model for experimental analysis. Hamida [30] aimed to find a balance between the environmental and economic benefits, constructed a dual-objective vehicle routing optimization model and designed a hybrid genetic algorithm for solving it. Zhang [31] addressed the low-carbon vehicle routing optimization problem, constructed a low-carbon vehicle routing optimization model with carbon emission costs as objectives, and used a tabu search algorithm to solve the mathematical model. Kopfer [32] focused on green ecological issues, considering the environmental impact of different types of vehicles on carbon emissions and fuel consumption factors, and optimized the solution using the CPLEX tool 12.4. Kwon [33] focused on the optimization problem of irregular vehicle paths while considering carbon emissions and found that significant reductions in carbon emissions can be achieved through carbon emission trading without additional costs. In conclusion, the above study on the optimization problem of a low-carbon logistics path is mainly based on room temperature logistics, while the information on customer demand is mainly static. However, the current study of cold chain logistics and the dynamic change in customer demand information is still insufficient.

After summarizing and analyzing the pieces of literature above, it is evident that some progress has been achieved in the study of SVRP. However, there are three main shortcomings in the study of DVRP:

1. In the field of cold chain logistics delivery, there is limited research on VRP considering carbon emissions. Existing studies on carbon emissions in VRP are mainly focused on ambient temperature logistics delivery. There is still limited research on considering carbon emissions in the cold chain delivery field from a low-carbon perspective.

2. There are weaknesses in constructing DVRP models. The DVRP models constructed in the current study are mainly based on a single stage, with limited studies on constructing multi-stage models for DVRP. This leads to a decreased cohesion and coupling of the models, thereby reducing the performance of the algorithms.

3. Scholars have studied the cold chain distribution problem with less consideration given to the dynamic changes in customer demand. Existing research on cold chain delivery mainly focuses on static vehicle routing problems. However, in real life, customer demand is constantly changing. Incorporating dynamic customer demand into cold chain delivery problems can more realistically simulate the delivery process and make the research have strong practical application value.

In summary, this paper establishes a two-stage vehicle path optimization model with the objective of minimizing the total cost within the customer’s allowed time from a low-carbon perspective, focusing on the influencing factors such as the customer service time window, distance, and load capacity. Finally, we solve it by using an improved genetic algorithm.

2. Problem Description and Model Construction

2.1. Problem Description

The original vehicle routing problem is designed so that the vehicle routes can be optimized based on specific known basic conditions, such as the geographic locations of a distribution center (DC) and multiple customers, as well as the customers’ demand for products. It also considers constraints like time window limits and vehicle load capacity, ensuring that goods are delivered in an organized manner from the DC to multiple consumers. DVRP, for another, is a subcategory of VRP that takes into account dynamic consumer demands and time windows. Under the background of this research, DVRP considers that customer delivery demands change dynamically during the distribution process, such as fluctuations in customer demand, changes in delivery time windows, and the emergence of new customers. Therefore, it requires dynamic optimization of the original delivery routes to converge towards an optimal solution.

The DVRP studied in this paper can be described as follows: Consider a complete directed graph where $G=(A,V)$ and where $A=\left\{0\right\}\cup \left\{N\right\}\cup \left\{Y\right\}$ is the set of nodes, with $\left\{0\right\}$ being the distribution center, $N$ being the set of static phase customer points, and $Y$ being the set of customer points in the second phase. The working hours of the distribution center are $[ET,LT]$. The edge set is $V=\{(\mathrm{i},\mathrm{j})|\forall i,j\in A\}$, where $d_{ij}$ is the distance between points $i$ and $j$. The vehicle speed is v, the vehicle load capacity is $Q$, the total number of distribution vehicles is $K$, and the decision variable $x_{ijk}$ indicates whether the vehicle $k$ goes directly from point $i$ to point $j$, with 1 for yes and 0 for no.

Based upon the research of dynamic vehicle routing optimization, the related assumptions are listed:

• The research focuses on the optimization of routes from a DC to multiple customers.
• Delivery vehicles commence their journeys from the distribution center in a fully loaded state, delivering a single type of perishable product.
• Each customer point is only served once, and it is not possible to divide the customer’s demand.
• The vehicles available at the perishable DC belong to the same model and can meet all customers’ delivery requirements.
• Each vehicle leaves the DC, follows a single route to distribute the merchandise to consumers, and goes back to the DC after the deliveries.
• The road conditions for vehicle travel are favorable, allowing the vehicles to maintain a constant speed.
• All consumer points possess their own time window, which represents a strict time constraint.

Table 1. Model symbols and descriptions.

Typology	Symbol	Meaning
Collection	$N$	Collection of customer points served. $N=\{1,2,\dots ,n\}$
	$K$	Distribution center’s distribution vehicle pooling. $K=\left\{1,2,\dots ,k\right\}$
Variant	$t_i$	Delivery vehicle’s arrival time at customer point $i$
	$t_j$	Delivery vehicle’s arrival time at customer point $j$
	$q_i$	Demand at customer point $i$
	$d_{ij}$	Distance between customerpoints $i$ and $j$
	$Q$	Maximum load capacity of distribution vehicles
	$ET$	Customer’s left time window
	$LT$	Customer’s right time window
	$c_1$	Unit transportation costs
	$c_2$	Unit price of carbon emissions
	$c_3$	Unit cooling costs
	$v$	Travel speed of distribution vehicles
	$l$	Average efficiency of unloading
	$\alpha$	Degree of deterioration of the case
	$R$	Heat transfer rate
	$S_1$	Exterior area of distribution vehicles
	$S_2$	Internal surface area of distribution vehicles
	$\Delta T$	Temperature distinction inside and outside the compartment
	$v_k$	Vehicle $k$ refrigerated compartment volume
	$\beta$	Frequency coefficient of compartment door opening
	$w_{ijk}$	Transportation of vehicle k from customer $i$ to customer $j$
	$\gamma$	Carbon emission factor per unit of fuel
Decision-making variable	$x_{ijk}$	Vehicle $k$ arrives at customer $j$ from customer $i$
	$y_{ik}$	Customer $i$ is delivered by vehicle $k$

presents the symbols defined in this research based on the problem’s description and assumptions.

2.1.1. Considering the Background of Carbon Emissions

The low-carbon practice topic has gained prominent attention across various research fields. Many scholars have incorporated carbon emission costs into the objective function of the vehicle routing problem [34,35]. The key point is how to gauge the vehicle carbon emissions. This common approach is to use carbon tax rates to calculate carbon taxes, which are then directly included in the costs. However, this paper argues that simply converting carbon emissions into economic costs overlooks the goal of minimizing carbon emissions. As a matter of fact, carbon emissions during vehicle operations are affected by various elements, like load, speed, and distance, making the calculations more complex. To address this problem, this research introduces a fuel consumption model.

This research uses a fuel consumption model to estimate fuel consumption, where the fuel consumption of each unit distance is represented by Equation (1).

$$\rho \left(Q_k\right)=\left({\rho }^0+\frac{{\rho }^{\ast }-{\rho }^0}{Q}·Q_k\right)$$

(1)

where ${\rho }^0$ and ${\rho }^{\ast }$ are the mean fuel consumption percentages when the vehicle is empty or not, respectively, $Q$ is the maximum loading capacity of the vehicle, and $\rho \left(Q_k\right)$ means the fuel consumption in each unit mile traveled as the vehicle is equipped with $Q_k$.

Assuming the distance from point $i$ to $j$ is $d_{ij}$, the fuel consumption from point $i$ to $j$ can be calculated using Equation (2).

$${\rho }_{\mathrm{ij}}=\rho \left(Q_k\right)d_{ij}$$

(2)

For the cold chain logistics distribution course, the carbon emissions are calculated according to this formula: Carbon emissions = Fuel consumption × Carbon emission coefficient [36]. Therefore, based on the fuel consumption calculation, a further calculation model for carbon emissions E can be derived, as shown in Equation (3).

$$E=\rho \left(Q_k\right)d_{ij}{x}_{ij}\gamma$$

(3)

2.1.2. Refrigeration Cost Analysis

The most obvious distinction between cold chain distribution and general distribution is the perishable nature of the transported products. Therefore, it is necessary to use refrigerated vehicles for transportation. The key distinction between a refrigerated vehicle and a regular vehicle is the use of refrigeration machinery to create a low-temperature environment, achieved through the use of refrigerants. If there is a significant temperature difference between the vehicle’s compartment and the external environment, more refrigerants are required to effectively sustain the desired low temperature. During transportation, the closed doors of the refrigerated vehicle ensure stable temperature changes, resulting in relatively lower refrigeration costs. However, during unloading at the consumer’s position, when the doors are open, there exists a heat exchange between the compartment and the exterior environment, leading to the costs of higher refrigeration. The refrigeration costs are divided into two parts: refrigeration costs in the transportation with closed doors and refrigeration costs incurred in unloading when there is a heat exchange between the compartment and the external environment.

The refrigeration costs during transportation are represented by Equation (4).

$$C_{31}=c_3{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^K{d}_{ij}(1+\alpha )}}}·R(\sqrt{S_1-S_2})·\Delta T\frac{d_{ij}}{v}$$

(4)

The refrigeration costs during unloading are represented by Equation (5).

Table 2. β values.

Door Opening Frequency Coefficient	0 Times	1–5 Times	6–10 Times	10 or More Times
β	0.25	0.5	0.75	1

shows the β values.

$$C_{32}=c_3{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^K\beta (0.54v_k+3.22)·\Delta T{y}_{ik}\frac{q_i}{l}}}}$$

(5)

Therefore, the total cooling cost is as shown in Equation (6).

$$C_3=C_{31}+C_{32}$$

(6)

2.2. Model Construction

Based on the problem’s description and analysis mentioned above, this study constructs two-stage models for considering low-carbon static and dynamic vehicle routing problems, detailed in Section 2.2.1 and Section 2.2.2, respectively.

2.2.1. Static Vehicle Routing Problem Model

The mathematical model constructed in the first stage (i.e., the static stage) of this study is shown as follows:

$$\min \left\{\begin{array}{l}{c}_1{\displaystyle \sum _{\mathrm{i}=1}^N{\displaystyle \sum _{y=1}^N{\displaystyle \sum _{k=1}^K{x}_{ijk}{d}_{ij}}}}+c_2\gamma {\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^K\rho \left(Q_k\right)d_{ij}{x}_{ijk}}}}+\\ c_3[{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^K{d}_{ij}(1+\alpha )}}}·R(\sqrt{S_1-S_2})·\Delta T\frac{d_{ij}}{v}+{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^K\beta (0.54v_k+3.22)·\Delta T{y}_{ik}\frac{q_i}{l}}}}]\end{array}\right\}$$

(7)

$$s.t.{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{x}_{ijk}{q}_i}}\le Q,k=1,\dots ,K;$$

(8)

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

(9)

$${\displaystyle \sum _{j=1}^N{x}_{0jk}}={\displaystyle \sum _{i=1}^N{x}_{i0k}},k=1,\dots ,K;$$

(10)

$${\displaystyle \sum _{i=1}^N{\displaystyle \sum _{k=1}^K{x}_{ijk}}}=1,j=1,\dots ,N;i\ne j;$$

(11)

$${\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^K{x}_{ijk}}}=1,i=1,\dots ,N;i\ne j;$$

(12)

$${\displaystyle \sum _{i=1}^N{x}_{ijk}}(w_{ijk}-q_i)\ge 0;j=1,\dots ,N;k=1,\dots ,K;$$

(13)

$$t_j=t_i+\frac{q_i}{l}+\frac{d_{ij}}{v},i=1,\dots ,N;k=1,\dots ,K;$$

(14)

$$E{T}_i\le t_i\le L{T}_i$$

(15)

$$X=(x_{ijk})\in S$$

(16)

where Equation (7) represents the total cost function, which encompasses the vehicle transportation costs, carbon emission costs, and cooling costs, and Equation (8) illustrates that the total quantity of merchandise transported by the vehicles does not exceed the maximum payload capacity of the vehicle. Equation (9) states that the number of vehicles utilized by the DC should not surpass K. Equation (10) represents the vehicle return constraint. Equations (11) and (12) illustrate that each consumer point can just be served by one vehicle. Equation (13) states that the transportation quantity of vehicles ought not to be lower than any customer demand. Equation (14) represents the distribution vehicle’s arrival time at one customer, point j. Equation (15) implies that any distribution vehicle must deliver the goods within the time window. Equation (16) represents the sub-tour elimination constraint.

2.2.2. Dynamic Vehicle Routing Problem Model

When a dynamic event occurs, let us assume that at time $T_i$, a dynamic demand order, denoted as $H$, arises. At this point, the static stage has completed serving $h$ customers, and vehicle $K_V(K_V<K)$ has been dispatched based on the static routing plan. However, since the static routing plan has already been executed, dispatched vehicles cannot be directly rescheduled by the dispatch center. Therefore, let us assume that the dispatched vehicles, at critical time points, are treated as virtual distribution centers. $Q_{kv}$ denotes the remaining payload capacity of the dispatched vehicle at time $T_i$, and the quantity of unserved customers is referred to as $N-h+H$. The quantity of vehicles yet to be dispatched is $P$($k=K_v+1,K_v+1,\dots ,K_v+P$). The customer’s ID is $h,h+1,\dots ,N-h+H$, represented as $Y=N-h+H$.

$$\min \left\{\begin{array}{l}{c}_1{\displaystyle \sum _{\mathrm{i}=1}^Y{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{k=1}^{K_v}{x}_{ijk}{d}_{ij}}}}+c_2\gamma {\displaystyle \sum _{i=0}^Y{\displaystyle \sum _{j=0}^Y{\displaystyle \sum _{k=1}^{K_v}\rho \left(Q_k\right)}}}{x}_{ijk}{d}_{ij}+\\ c_3[{\displaystyle \sum _{i=1}^Y{\displaystyle \sum _{j=1}^Y{\displaystyle \sum _{k=1}^{K_v}{d}_{ij}(1+\alpha )}}}·R(\sqrt{S_1-S_2})·\Delta T\frac{d_{ij}}{v}+{\displaystyle \sum _{i=1}^Y{\displaystyle \sum _{j=1}^Y{\displaystyle \sum _{k=1}^{K_v}\beta (0.54v_k+3.22)·\Delta T{y}_{ik}\frac{q_i}{l}}}}]+\\ c_1{\displaystyle \sum _{\mathrm{i}=h+1}^Y{\displaystyle \sum _{y=h+1}^Y{\displaystyle \sum _{k=1}^{K_v+P}{x}_{ijk}{d}_{ij}}}}+c_2\gamma {\displaystyle \sum _{i=h+1}^Y{\displaystyle \sum _{j=h+1}^Y{\displaystyle \sum _{k=K_v+1}^{K_v+P}\rho \left(Q_k\right)}}}{x}_{ijk}{d}_{ij}\\ c_3[{\displaystyle \sum _{i=h+1}^Y{\displaystyle \sum _{j=h+1}^Y{\displaystyle \sum _{k=K_v+1}^{K_v+P}{d}_{ij}(1+\alpha )}}}·R(\sqrt{S_1-S_2})·\Delta T\frac{d_{ij}}{v}+{\displaystyle \sum _{i=h+1}^Y{\displaystyle \sum _{j=h+1}^Y{\displaystyle \sum _{k=K_v+1}^{K_v+P}\beta (0.54v_k+3.22)·\Delta T{y}_{ik}\frac{q_i}{l}}}}]\end{array}\right\}$$

(17)

$$s.t.{\displaystyle \sum _{j=h+1}^Y{x}_{0jk}}={\displaystyle \sum _{i=h+1}^Y{x}_{i0k}},k=1,\dots ,K_v+P;$$

(18)

$${\displaystyle \sum _{i=h+1}^Y{\displaystyle \sum _{k=K_v+P}^{K_v+P}{x}_{ijk}}}=1,j=h+1,\dots ,Y;i\ne j;$$

(19)

$${\displaystyle \sum _{j=h+1}^Y{\displaystyle \sum _{k=K_v+P}^{K_v+P}{x}_{ijk}}}=1,i=h+1,\dots ,Y;i\ne j;$$

(20)

$$t_j=t_i+\frac{q_i}{l}+\frac{d_{ij}}{v},i=h+1,\dots ,Y;k=K_v+1,\dots ,K_v+P;$$

(21)

$${\displaystyle \sum _{i=h+1}^Y{\displaystyle \sum _{j=h+1}^Y{x}_{ijk}{q}_i}}\le Q_{kv},k=1,\dots ,K_v+P;$$

(22)

$${\displaystyle \sum _{i=h+1}^Y{x}_{ijk}}(w_{ijk}-q_i)\ge 0;j=h+1,\dots ,Y;k=1,\dots ,K_v+P;$$

(23)

$$E{T}_i\le t_i\le L{T}_i$$

(24)

$$X=(x_{ijk})\in S$$

(25)

where Equation (17) represents the total cost function, with the first three terms corresponding to the transportation costs, carbon emission costs, and cooling costs of the dispatched vehicles and the last three terms corresponding to the transportation costs, carbon emission costs, and cooling costs of the newly dispatched vehicles, and Equation (18) represents the vehicle return constraint. Equations (19) and (20) illustrate that each consumer point can merely be served by a vehicle. Equation (21) represents the arrival time of the distribution vehicles at customer point j. Equation (22) implies that the remaining vehicle payload capacity can be determined before serving the next customer, ensuring that the vehicle can meet this customer’s demand. Equation (23) states that the transportation quantity of the vehicle should not be lower than the demand of any customer. Equation (24) implies that any distribution vehicle must deliver the goods within the time window. Equation (25) represents the sub-tour elimination constraint.

3. Research Methodology

3.1. Problem-Solving Strategies

A two-stage mathematical model is established in this research for the purpose of addressing the problem, consisting of a static stage and a dynamic optimization stage. In the static stage, the distribution center generates a static delivery route plan using an improved genetic algorithm based on known customer information. During the static delivery plan execution, on the condition that dynamic events occur, the dynamic optimization stage begins. In this stage, a route updating strategy is introduced to regulate the routes in real time for the purpose of accommodating the continuously generated dynamic demands. Currently, there are several existing one-time strategies, such as the first-come-first-serve strategy, random queue center location strategy, and nearest-neighbor priority strategy. Additionally, two main mechanisms are employed to initiate the route updates as follows: customer-based and time-based. When two customers are far apart and the travel time is longer, the customer-based mechanism requires more responses to the dynamic demands, resulting in poor service efficiency. On the other hand, time-based route updates occur at regular intervals. By setting different update times, this mechanism can avoid an excessive response to dynamic demands and has relatively practical utility. Therefore, this study selects time-based updates as the initiation mechanism for route updating. The specific steps and solution process are illustrated in Figure 1 below.

Step 1: Determine the initial delivery routes for the vehicles. Data initialization: Set the starting time for delivery from the distribution center as 0, and assume all vehicles are at the distribution center. Use the algorithm described in this article (see Section 3.2) to determine the static delivery plan for the vehicles based on the existing delivery information.

Step 2: Activate the real-time optimization service for dynamic events. Once the delivery vehicles start executing the static delivery plan, they activate multiple real-time optimization service windows, waiting for the occurrence of dynamic events.

Step 3: Update the relevant delivery information when a dynamic event occurs. This includes customer demand points and quantities, the status and location of vehicles in transit, and other pertinent details.

Step 4: Transform the problem based on the updated delivery information. Set virtual customer demand points and regenerate an array of consumer points that have not been delivered yet, obtaining a new set of customer points.

Step 5: Determine dynamically adjusted vehicle routes. Use the algorithm described in this article (see Section 3.2) to solve the new routing problem in step 4. Obtain the vehicle route arrangement after the i-th occurrence of a dynamic event and update the delivery plan.

Step 6: Determine if another dynamic event occurs. If yes, go back to step 2. If not, conclude the process and output the final vehicle travel routes obtained in step 5.

3.2. Improved Genetic Algorithm Design

Genetic algorithms are a random global search optimization approach that originated from computer simulations of biological systems, simulating phenomena such as natural selection, crossover, replication, and mutations investigated in genetics. Through beginning with a primary population, by means of random selection, crossover, and mutation operating, a group of people who are appropriate to the circumstance are generated. The population evolves and explores a specific region in the search space, continuously reproducing and evolving. Eventually, it converges to a group of people who are most highly adapted to the circumstance, generating high-quality solutions to the problem. However, the local operations of genetic algorithms tend to experience stagnation, which impacts the efficiency and accuracy of optimization solutions to some extent. Therefore, this study introduces the idea of disruptive and repair strategies from large-scale neighborhood search algorithms to improve the local operations of genetic algorithms, thereby enhancing the precision of problem-solving. This, in turn, helps increase the algorithm’s search space and variability, further improving its global search capabilities and convergence. With these enhancements, we can expect to obtain more accurate and efficient optimization solutions.

3.2.1. Chromosome Encoding

In order to improve the computational efficiency during the solving process, we have chosen to use real numbers for encoding, as the distribution center needs to deliver to multiple customer locations using vehicles. The DC is encoded as 0; moreover, the N customer locations to be delivered to are randomly encoded as $1,2,\dots N$. After completing the delivery tasks, the delivery vehicle $K$ demands to go back to the DC, thus completing one delivery route. Therefore, the length of the chromosome available for encoding is $N+K+1$.

3.2.2. Generate Initial Population

Before initializing the population, it is necessary to construct one initial solution for the purpose of handling the VRP. The constructed initial solution may not necessarily satisfy the capacity and time window constraints. However, a high-quality initial solution can somewhat reduce the difficulty of the genetic algorithm search. The strategy for generating the initial solution in this study is as follows:

Randomly generate a new route, and after adding each new customer location, check if the vehicle’s load exceeds the remaining cargo capacity. If not, add the customer location to the current vehicle’s delivery route. If yes, add it to the delivery route of the next vehicle. Repeat this process to attain the initial population.

3.2.3. Define the Fitness Function

Using the above encoding method does not guarantee that all decoded delivery routes will satisfy the capacity and time window constraints. To address this, a penalty function is incorporated into the objective function to ensure that the vehicle’s delivery routes minimize the violations of the constraints as much as possible. Considering that this study focuses on a minimization problem when searching for the minimum value, the objective function and the fitness function have opposite directions of change. In other words, as the value of the objective decreases, the value of the fitness function increases, thereby increasing the likelihood of an individual being passed on to the next generation. In this study, the fitness function is designated as the reciprocal of the objective function, as shown in Equation (26).

$$f(n)=\frac{1}{F(x)}$$

(26)

where $f(n)$ denotes the fitness function and $F(x)$ denotes the objective function.

3.2.4. Genetic Operations

(1)

Selection Operation

The selection operation in this study utilizes both the best individual preservation strategy and the roulette wheel selection strategy. Firstly, the individuals of each generation are sorted in descending order based on fitness, with the best individual ranked first. This best individual, which exhibits the highest performance, is then copied to the next generation (the population to undergo crossover) and placed in the first position to ensure its preservation. The remaining individuals for the next generation are selected using the roulette wheel selection approach based on their fitness.

(2)

Crossover Operation

The crossover operation involves exchanging selected genes between two paired parent chromosomes, resulting in two new offspring. The new offspring inherit some or all of the structural characteristics and effective genes from the parents. Since real-valued encoding is used in this study, a two-point crossover approach is adopted for the gene exchange between individuals to enhance the crossover operator’s search capability for the remaining space. The specific steps are as follows:

① Randomly set two crossover points in the coding strings of the two paired individuals.

② Exchange the segments between the two crossover points in the two individuals.

③ Store the two new offspring in the subgroup.

(3)

Mutation Operation

The mutation operation is primarily aimed at maintaining population diversity, allowing the algorithm to escape from local optima and avoid premature convergence. Given the encoding method used in this study, the following mutation strategy is adopted.

Randomly select a parent chromosome for mutation and generate two random numbers for the gene positions (regenerated if they are the same). Swap the genes corresponding to the two random numbers to create a new mutated individual.

3.2.5. Local Search Operation

To enhance the directed search capability of genetic algorithms in path optimization, this study introduces the principles of “destroy” and “repair” from large-scale neighborhood search algorithms. Specifically, a “destroy” operator is used to move away a certain quantity of customers from the selected solution. Then, one repair operator is used to reinsert the removed customers into the destroyed solution.

The destroy operator removes several relevant customers from the solution based on Equations (27) and (28).

$$R(i,j)=1/(c{\prime }_{ij}+V_{ij})$$

(27)

$${c^{\prime }}_{ij}=\frac{c_{ij}}{\max c_{ij}}$$

(28)

where $c_{ij}$ represents the Euclidean distance between customers $i$ and $j$, and $c_{ij}^{\prime }$ denotes the normalized value of $c_{ij}$, ranging from 0 to 1. The variable $V_{ij}$ indicates whether customers $i$ and $j$ are on the same path. If $i$ and $j$ are on the same path, $V_{ij}$ is assigned 0; otherwise, it is assigned 1. The destroy operator is more likely to remove customers with a lower correlation.

The repair operator works based on the concept of minimum insertion cost. This concept refers to the increment in distance after inserting a customer into a path in a manner that minimizes the total traveled distance while still satisfying the constraints.

3.2.6. Population Repair

To ensure that the population size remains constant, the offspring population obtained after performing crossover, mutation, and local search operations on the parent individuals is combined with the parent population, with the aim of creating a temporary population. In the temporary population, individuals are sorted based on their fitness. Only the individuals that meet the maximum population size requirement are retained and considered to be the parent population for the next generation’s evolution.

3.2.7. Termination

If the predetermined number of iterations, which is 200 in this case, is reached, the iteration process concludes, and the best solution is outputted. Otherwise, the algorithm goes on to operate until the termination condition is met.

4. Experiment Procedure and Data Analysis

4.1. Data Description

In this study, a dataset consisting of 25 customers is selected from Solomon and modified, as presented in

Table 3. Experimental data.

Number	X Coordinate	Y Coordinate	Quantity Demanded	Left Window	Right Window	Service Time
0	35	35	0	0	1000	0
1	41	49	20	720	800	10
2	35	17	7	143	282	10
3	55	45	13	527	584	10
4	55	20	19	678	801	10
5	15	30	20	50	180	10
6	25	30	3	415	514	10
7	20	50	5	331	410	10
8	10	43	9	404	481	10
9	55	60	16	400	497	10
10	40	25	25	500	600	10
11	20	65	12	206	325	10
12	50	35	19	228	345	10
13	30	25	23	690	827	10
14	15	10	10	30	240	10
15	30	5	8	175	300	10
16	10	20	19	272	373	10
17	5	30	2	733	870	10
18	20	40	12	377	434	10
19	15	60	17	269	378	10
20	45	65	9	581	666	10
21	45	20	19	200	350	10
22	45	10	18	409	494	10
23	55	5	29	206	325	10
24	65	35	3	704	847	10
25	65	20	6	817	956	10

. The index 0 represents the distribution center, while the remaining points represent customer locations. It is assumed that the distribution center has an abundant number of vehicles available for centralized deployment, and all vehicles possess identical specifications. The vehicle parameters are shown in

Table 4. The vehicle parameters.

Parameter Name	Value	Parameter Name	Value
$q^{\ast }$	2 L/km	$R$	0.4 W/m∗K
$q^0$	1 L/km	$S_1-S_2$	35 m2
$v$	50 km/h	$\Delta T$	20 °C
$\alpha$	0.12	$r$	2.6 kg/L
$v_k$	13.9 m3	Fuel type	Diesel
The vehicle dimensions	5995∗2270∗2970	Engine power	100 kw
Interior dimensions	4015∗2100∗1800	Engine displacement	2900 mL

.

4.2. Data Solution

In this study, we implemented the algorithm using MATLAB 2021a as the programming language. The algorithm was executed on one PC according to these instructions: an Intel^® Core™ i5-11320H processor, 16GB RAM, and the Windows 10 64-bit operating system.

4.2.1. Static Solution Experiment Results

Based on the constructed model, we developed a genetic algorithm code in MATLAB and set the relevant parameters. The parameters for the genetic algorithm were configured as below: a population size of 100, a maximal iteration count of 200, a crossover ratio of 0.9, and a mutation ratio of 0.2. After 200 iterations, the total delivery cost obtained was 1207.01, with four vehicles used for delivery. The delivery routes are presented in

Table 5. Static delivery routes and cost.

Vehicles	Distribution Route	Transportation Costs	Carbon Costs	Cooling Costs	Total Costs
1	0 > 10 > 9 > 3 > 20 > 1 > 0	82.84	179.99	22.63	285.47
2	0 > 2 > 15 > 14 > 16 > 17 > 13 > 0	74.09	163.50	30.69	268.29
3	0 > 12 > 21 > 23 > 22 > 4 > 24 > 25 > 0	98.51	214.60	30.59	343.70
4	0 > 5 > 19 > 11 > 7 > 18 > 8 > 6 > 0	86.91	189.76	32.88	309.55

. To visually observe the entire delivery scenario, we used the FlexSim software 2023 simulation model to verify the feasibility of the delivery solution. The simulated delivery routes are illustrated in Figure 2.

4.2.2. Dynamic Optimization Solution Experiment Results

At time T = 100, the following dynamic events occurred: Customer points 1 and 2 experienced an increase in demand by 10 and 3 kg, respectively. Meanwhile, customer points 19 and 21 underwent a decrease in demand by 7 and 6 kg, respectively. Furthermore, customer points 1, 5, 10, and 21 had changes in their time windows. Additionally, four new customers requested delivery, namely, customer points 26, 27, 28, and 29, as shown in

Table 6. Information on changes in requirements.

Number	Type of Change	New Demands
1	increase in demand	increase of 10 kg
2	increase in demand	increase of 3 kg
19	decrease in demand	decrease of 7 kg
21	decrease in demand	decrease of 6 kg
1	time window adjustment	(720, 800)
5	time window adjustment	(50, 180)
10	time window adjustment	(500, 600)
21	time window adjustment	(200, 350)

and

Table 7. New customer information.

Number	X Coordinate	Y Coordinate	Quantity Demanded	Time Window	Service Time
26	64	42	19	(163,302)	10
27	12	24	9	(190,313)	10
28	63	23	13	(290,377)	10
29	35	58	2	(620,739)	10

.

(1)

Additional Vehicle Deployment Strategy Results

In real-life scenarios, when dynamic new orders arise during the vehicle delivery process, cold chain logistics companies often deploy additional vehicles to handle the new orders. This strategy is known as the additional vehicle deployment strategy. In the initial delivery process for the 25 customer points, in order to promptly respond to the new customer’s demand, the cold chain logistics company dispatched an emerging vehicle from the distribution center to consumer service points 26, 27, 28, and 29. By utilizing an improved genetic algorithm to solve the delivery routes, we obtained a total delivery cost of 1446.15, requiring a fleet of five vehicles. The simulated delivery routes for the vehicles are illustrated in Figure 3, and the specific delivery routes are listed in

Table 8. Route and cost table for the additional vehicle deployment strategy.

Vehicles	Distribution Route	Transportation Cost	Carbon Cost	Cooling Costs	Total Costs
1	0 > 10 > 3 > 9 > 20 > 1 > 0	65.86	124.28	22.63	212.77
2	0 > 2 > 15 > 14 > 16 > 17 > 13 > 0	74.09	142.99	30.69	247.77
3	0 > 12 > 21 > 23 > 22 > 4 > 24 > 25 > 0	98.51	185.84	30.59	314.94
4	0 > 5 > 19 > 11 > 7 > 18 > 8 > 6 > 0	86.91	162.48	32.88	282.27
5	0 > 26 > 29 > 27 > 28 > 0	129.83	230.05	28.51	388.39

.

(2)

Dynamic Optimization Strategy Results

Based on the updated delivery demand information, the vehicle routing problem was resolved using the presented dynamic optimization strategy in this research. The total delivery cost obtained was 1198.39, with four vehicles deployed. The simulated vehicle routing map is shown in Figure 4, and the specific delivery routes are presented in

Table 9. Dynamic optimization strategy route and cost table.

Vehicles	Distribution Route	Transportation Costs	Carbon Costs	Cooling Costs	Total Costs
1	0 > 10 > 3 > 26 > 9 > 20 > 1 > 0	76.09	145.61	26.96	248.66
2	0 > 2 > 15 > 14 > 16 > 27 > 13 > 17 > 0	95.48	181.06	35.55	312.09
3	0 > 12 > 21 > 23 > 22 > 4 > 28 > 24 > 25 > 0	100.39	189.73	34.83	324.95
4	0 > 5 > 19 > 11 > 29 > 7 > 8 > 18 > 6 > 0	95.37	184.52	32.79	312.69

.

4.3. Comparison of the Two Strategies’ Results

When implementing the additional vehicle deployment strategy, vehicles that have already departed for delivery only consider the dynamic events related to the changes in demand at the original customer points. For the newly added customer points 26, 37, 28, and 29 along the delivery route, a separate vehicle needs to be dispatched from the distribution center to handle their demands. As a result, the number of vehicles required for the additional vehicle deployment strategy exceeds that of the dynamic optimization strategy by one vehicle. From

Table 10. Comparison of distribution strategy results.

Distribution Strategy	Total Vehicle Movements	Transportation Cost	Carbon Cost	Cooling Costs	Total Costs
Additional vehicle deployment strategy	5	434.33	934.34	268.87	1637.54
Dynamic optimization strategy	4	396.16	759.05	268.87	1424.08

, it can be observed that the dynamic optimization strategy and the additional vehicle deployment strategy differ in total costs by 247.76 yuan, resulting in approximately 17.13% cost savings. Specifically, transportation costs, carbon emissions costs, and refrigeration costs are reduced by approximately 19.30%, 17.11%, and 10.43%, separately. It is demonstrated that the presented dynamic optimization strategy in this article holds advantages in handling dynamic customer demands, reducing delivery costs, improving responsiveness to customer needs, assisting cold chain distribution companies in achieving energy-saving and emission-reduction goals, as well as optimizing the utilization of delivery vehicles and conserving vehicle resources.

5. Conclusions

From a low-carbon perspective, in this study, the VRP is examined regarding cold chain logistics under dynamic demand. It explores three types of dynamic demand problems: the increase or decrease in existing customer demand, changes in existing customer time windows, and the emergence of new customer points. The study analyzes and solves these problems using a “static + dynamic” approach. Additionally, the study considers carbon emissions reduction during the delivery process to assist cold chain logistics companies in achieving their carbon reduction goals, thereby enhancing long-term business development and competitiveness. In the case study analysis, this study compares the dynamic optimization strategy proposed in this paper with the additional vehicle deployment strategy. It is found that the dynamic optimization strategy can save approximately 17.13% of the total cost. Specifically, in terms of carbon emissions costs, there is a difference of approximately 17.11% between the two strategies, thereby greatly promoting energy conservation and emission reduction targets in the companies of cold chain logistics. This demonstrates the effectiveness of the proposed strategy in addressing dynamic demand problems. Only the changes in consumer demand are considered in this article for the dynamic vehicle routing problem, but the driving speed of the delivery vehicle is also dynamically changed in real life, and the driving speed of the delivery vehicle can be further studied in the future.