Optimizing Distribution Routes for Chain Supermarket Considering Carbon Emission Cost

: The low-carbon economy and sustainable development have become a widespread consensus. Chain supermarkets should pay attention to path optimization in the process of distribution to reduce carbon emissions. This study takes chain supermarkets as the research object, focusing on the optimization of the vehicle routing problem (VRP) in supermarket store distribution. Firstly, based on the concept of cost-effectiveness, we constructed a green and low-carbon distribution route optimization model with the lowest cost. With cost minimization as the objective function, the total distribution cost in the vehicle delivery process includes ﬁxed cost, transportation cost, and carbon emission cost. The carbon emission cost is calculated using the carbon tax mechanism. Secondly, through integrating the Floyd algorithm, the nearest neighbor algorithm, and the insertion algorithm, a fusion heuristic algorithm was proposed for model solving, and an empirical study was conducted using the W chain supermarket in Wuhan as an example. The experimental results show that optimizing distribution routes considering carbon emission cost can effectively reduce carbon emissions. At the same time, it can also reduce the total costs of enterprises and society, thereby achieving greater social beneﬁts at lower costs. The research results provide effective suggestions for chain supermarkets to control carbon emissions during the distribution process.


Introduction
With the increasingly prominent effects of global warming caused by carbon emissions, low-carbon economy and sustainable development have become widely recognized, and more and more enterprises are realizing the importance of the green environmental protection.The development of low-carbon economy cannot be separated from the support of low-carbon logistics [1].As an emerging composite service industry, the logistics industry has become one of the most important driving forces for economic growth and an important source of carbon emissions [2,3].Low-carbon logistics is an emerging concept derived from the low-carbon economy, which is a low energy consumption and low pollution logistics that plays a crucial role in the development of the low-carbon economy.Its essence is to strive to achieve minimum energy consumption while achieving optimal efficiency under the premise of protecting the environment [4,5].Research on low-carbon logistics can, to some extent, solve the problems of resource and energy conservation and environmental pollution.Nowadays, low-carbon logistics has become an important foundation for the sustainable development of modern economy, and has also become an important field of discussion in the business and academic circles [6].
As an important part of modern enterprises, the logistics activities of chain retail enterprises include warehousing and distribution, circulation and processing, transportation, packaging, and the information processing of goods.Chain supermarkets have received high attention from domestic and foreign enterprises due to their standardized management mode, which achieves low-cost operation, efficient circulation, and low business risks [7].At present, many domestic and foreign chain retail enterprises have elevated their logistics operations to a strategic level.It is regarded by most enterprises as an important means to improve the overall performance of supply chain logistics, strengthen competitive advantages, and increase customer value [8].In recent years, with the rapid development of the economy, the scale of chain supermarkets has also been continuously expanding.Realizing logistics distribution between different stores is a critical business in the operation of chain supermarkets.Currently, there remains certain problems in the operation of chain supermarkets, such as unreasonable transportation, high distribution costs but low efficiency, and incomplete distribution systems.The root cause of these problems is the unreasonable arrangement of distribution routes, which in turn leads to issues such as energy consumption and environmental pollution [9,10].Therefore, the means with which to reasonably plan distribution routes, improve customer satisfaction, and reduce energy consumption and carbon emissions has become a serious problem that chain supermarkets must face in logistics operations [11].
The optimization of distribution routes for chain supermarkets can actually be attributed to the vehicle routing problem (VRP), which has been a hot topic of academic research since it was proposed [12].The optimization of distribution routes refers to the process in which enterprises plan vehicle distribution routes reasonably to achieve predetermined goals while meeting a series of constraints.These goals include the shortest distribution path, shortest transportation time, lowest distribution cost, and so on [13].With the in-depth research of scholars on VRP, variants such as capacitated vehicle routing problem (CVRP), vehicle routing problem with time windows (VRPTW), heterogeneous vehicle routing problem (HVRP), and green vehicle routing problem (GVRP) have emerged [14].In order to meet the requirements of low-carbon logistics development, we expanded the optimization objectives of traditional VRP when studying the optimization problem of chain supermarket distribution paths.We not only considered economic costs, but also carbon emission costs to achieve a comprehensive research on GVRP [15].The modeling and optimization of GVRP is much more complex than traditional VRP.At present, the methods for solving this problem include accurate algorithm, heuristic algorithm, metaheuristic algorithm, etc.However, GVRP belongs to the NP-hard problem and is too difficult for the accurate algorithm to solve.Accurate algorithm can only solve small-scale distribution problems and requires a significant amount of computational time.Therefore, the use of approximation algorithm, such as heuristic algorithm and metaheuristic algorithm, is a reliable alternative to solving such problems.However, the traditional heuristic algorithm is easy to fall into the local optimum and is difficult to achieve global optimization.The metaheuristic algorithm has problems such as difficulty in setting algorithm parameters, a strong dependence on initial solutions, and long computational time [16,17].Therefore, we considered using a fusion heuristic algorithm to study the optimization problem of chain supermarket distribution routes.
The rest of this paper is arranged as follows.Section 2 reviews and summarizes the previous research results on the path optimization problem of chain supermarkets.Section 3 introduces the research method of this paper and constructs a path optimization model.Section 4 presents the empirical research; taking the W chain supermarket in Wuhan as an example, we use the Floyd algorithm to solve the distance between any two points, divide the initial paths based on the nearest neighbor algorithm, and finally optimize the initial paths through insertion algorithm.Finally, Section 5 summarizes the conclusions of this study.

Related Literature Review
Chain supermarkets, as a form of retail industry, have the characteristics of high complexity, wide coverage, and large transportation volume in their logistics links.The rationality of logistics distribution routes in chain supermarkets directly affects the logistics cost and efficiency of enterprises.Therefore, conducting research on the optimization of distribution routes in chain supermarkets can help optimize the logistics network of chain supermarkets, reduce carbon emissions in the logistics system, and ultimately achieve lowcarbon development goals.This study reviews the existing literature from the perspectives of chain supermarket distribution and path optimization, and proposes reasonable solutions for the study of chain supermarket distribution path optimization problems.

Research on Chain Supermarket Distribution
Through research on the relevant literature, Liang and Lv found that the distribution system of chain supermarkets is still incomplete.There are still unreasonable transportation phenomena in logistics distribution, such as repeated transportation, detour transportation, convective transportation, and empty vehicle return, which lead to low distribution efficiency and high transportation costs in distribution centers.In response to the above issues, they proposed the quantum evolutionary algorithm (QEA), established a mathematical model for optimizing the distribution routes of chain supermarkets, and conducted a scientific and reasonable optimization design for the distribution routes [18].Liu et al. focused on cold chain logistics and analyzed the current situation of cold chain logistics distribution terminals in three specific industries: electronics commerce, supermarkets, and the food and beverage industry.The research results show that these industries have problems such as high cold chain transportation costs, low automation levels, and insufficient terminal logistics distribution capabilities in distribution centers.In order to solve the problem of insufficient terminal logistics' delivery capacity in distribution centers, they established a model and conducted research based on the idea of joint distribution [19].Ge and Yin found that the distribution process of large chain supermarkets has the characteristics of complex distribution networks, diverse product demands, and cumbersome distribution links, which can lead to high logistics distribution costs and delayed delivery.Therefore, they proposed a cross-warehouse delivery operation model to improve the operational efficiency of chain supermarkets [20].Guo and Wang, Hu, and Dong believed that chain supermarkets have various problems, such as a low loading rate of distribution vehicles, a high cost of distribution links, incomplete distribution systems, an unclear division of distribution centers, a low level of informatization, etc.Additionally, they proposed corresponding countermeasures and suggestions for optimizing the distribution path of chain supermarkets in response to these issues, which provide useful references for the optimization of distribution models and paths in the future development and transformation process of the industry [21][22][23].Li and Dai found that under the O2O model, the logistics distribution of community fresh food chain supermarkets has problems such as high distribution costs but low efficiency, an incomplete development of cold chain logistics, and difficulty in delivering fresh products.Additionally, they proposed to enhance the competitive advantage of chain supermarkets by improving distribution efficiency, expanding customer demand, and strengthening cold chain logistics capabilities [24].Liu et al. found that with the rapid growth of logistics business, traditional single transportation methods can no longer meet customers' needs for various aspects of chain supermarket distribution efficiency and service quality.Additionally, they explored the network optimization of logistics transportation under multimodal logistics distribution methods to solve this problem [25].

Research on Distribution Routes Optimization
Xia and Fu, and Yu et al. explored a vehicle routing problem with time windows (VRPTW) based on the timeliness requirements of the distribution process.The former designed the adaptive tabu search (ATS) algorithm to solve the corresponding double objective mathematical model.The latter proposed the adaptive large neighborhood search (ALNS) algorithm to solve large-scale GVRP instances.They all tested the effectiveness of the algorithm based on corresponding examples to optimize the distribution vehicles and paths of chain supermarkets, thereby achieving the goal of reducing the total cost of the distribution system [16,26].Xiong, Zhao et al., Xie, and Bao et al. solved the VRP issue in a multi-objective optimization model based on the improved ant colony optimization (ACO) algorithm, and developed a solution for cold chain logistics distribution path optimization [12,[27][28][29].Dewi and Utama developed a hybrid whale optimization algorithm (HWOA) to solve GVRP in order to minimize distribution costs, including fuel costs, carbon emissions costs, and vehicle usage costs [30].Han et al. and Tan constructed an emergency logistics vehicle path optimization model to address the problems in the emergency material distribution process.The former combined genetic algorithm with saving algorithm and large-scale neighborhood search algorithm, and designed a hybrid genetic algorithm (HGA) to solve the model.The latter introduced an improved particle swarm optimization (PSO) algorithm to solve global optimization problems [31,32].Liu proposed to apply the recursive fuzzy neural network algorithm to the selection of e-commerce logistics distribution path schemes in response to issues such as single optimization methods for logistics distribution path systems and inconsistent data evaluation rules.The results show that this method can achieve an optimization of e-commerce logistics distribution paths, and the optimized distribution accuracy can reach more than 97% [33].Li et al. established a hybrid programming model to conduct in-depth research on the optimal urban distribution route problem that meets both electric vehicle and customer time window constraints.Additionally, they used a hybrid heuristic algorithm to solve the model.The results show that the Tabu search mode with insertion or exchange can effectively improve the calculation speed and accuracy of the algorithm [34].
The above research results on chain supermarket distribution and route optimization have certain guiding significance for this paper.Through the literature review, we found that there remains problems with regard to the development of chain supermarkets, such as high distribution costs, low distribution efficiency, unreasonable transportation, etc.However, these problems ultimately stem from the unreasonable arrangement of distribution routes.At present, research on distribution path optimization is generally focused on either ordinary logistics vehicle path optimization without considering carbon emissions, or ordinary logistics path optimization considering carbon emissions.However, there are relatively few research results on optimizing the distribution routes of chain supermarkets that take into account carbon emission factors.In addition, there is almost no research considering the path optimization problem of chain supermarkets based on the carbon tax price calculation.The means to optimize the route of distribution vehicles while meeting the needs of stores, and the way to reduce energy consumption and carbon emissions are both the focus of research for logistics and transportation enterprises.Therefore, this study distinguishes itself from traditional path optimization research by exploring the GVRP that takes chain supermarkets as the research object, while considering carbon emission costs.

Mathematical Model
This paper focused on exploring the optimization of logistics distribution paths for chain supermarkets in a low-carbon economy.In terms of constructing the objective function, we started from the perspective of logistics distribution costs and constructed a logistics distribution path optimization model for chain supermarkets at the lowest possible cost.Meanwhile, we considered the fixed costs, transportation costs, and carbon emission costs, which were generated during the vehicle distribution process, and conducted a detailed analysis of the factors affecting these three costs.For the cost of carbon emissions, we introduced a carbon tax mechanism for calculation.In addition, during the transportation and distribution process, limitations on meeting store needs and vehicle capacity were taken into account.The purpose of our research is to meet the vehicle distribution plan with as little carbon emissions as possible while ensuring the completion of distribution services.

Problem Assumptions and Basic Parameters
Chain supermarket distribution refers to the use of scientific methods by distribution centers to plan distribution routes reasonably with the goal of minimizing distribution costs under the comprehensive consideration of store demand.During the delivery process, all delivery vehicles depart from the distribution center, efficiently deliver products to their destinations on time according to the stores' needs, and finally return to the distribution center.To ensure the scientificity of assumptions and the completeness of model construction, we referred to the relevant literature and proposed the following assumptions and basic parameter settings for the VRP model of chain supermarkets [2,35,36]: (1) The location and number of distribution centers and stores are determined, and the goods are distributed from a single distribution center to multiple stores; (2) The demand for goods in each store is known; (3) The types of vehicles in the distribution center and their capacity are known; (4) All vehicles depart from the distribution center and must return to the distribution center when their distribution tasks are completed, and each supermarket store is only visited once; (5) The distribution center is interconnected with various stores, and the roads between stores are also bidirectional; (6) Regardless of road conditions and time costs, the vehicle travels at a uniform speed; (7) The carbon emissions of the vehicle are positively correlated with fuel consumption.
According to the needs of model construction, our study set the following basic parameters and decision variables, as shown in Table 1.

O
The distribution center i, j The number of the node N The total number of nodes v The vehicle number The distance between the i-th node and the j-th node q i The demand of i-th node Q v The maximum load capacity of a v-type truck.
The load capacity of a v-type truck from the i-th node to the j-th node c vk The fixed cost of the k-th vehicle of the v-type truck c ij The unit distance cost of vehicle from the i-th node to the j-th node E The carbon emission coefficient per unit of fuel ∂ The carbon tax per unit of carbon emissions a 0 The fuel consumption per unit distance when the vehicle is unloaded a 1 The influence factor of vehicle under extra load on unit mileage fuel consumption Binary variable, if the k-th vehicle of type v completes the delivery task from the i-th node to the j-th node, x vk ij = 1, otherwise, x vk ij = 0 y iv Binary variable, if the demand for the i-th node is delivered by the v-type vehicle, y iv = 1, otherwise, y iv = 0

Cost Function Analysis
The GVRP model of chain supermarkets explored in this study belongs to a type of VRP.We proposed a chain supermarket VRP model that considered carbon emission costs to achieve the selection of low-carbon distribution routes.The carbon emissions during the distribution process of chain supermarkets are mainly from the fuel consumption of vehicles.However, focusing only on low-carbon emissions as the optimization goal is fruitless for chain enterprise distribution.Therefore, the objective function we construct is not to minimize the carbon emissions or fuel consumption, but to use the minimum comprehensive cost as the objective function when establishing the mathematical models.In the VRP model of chain supermarkets in this paper, the optimized costs mainly include three parts: fixed costs, transportation costs, and carbon emission costs.
(1) Fixed costs When dispatching vehicles to carry out distribution tasks, some fixed fees need to be paid, including wages paid to truck drivers, depreciation fees required during vehicle operation, vehicle protection fees, etc.The fixed fees vary for different types of vehicles.In general, the fixed cost of using vehicles is constant, mainly referring to the fixed cost of vehicles with distribution tasks, excluding idle vehicles.Moreover, the fixed cost of vehicles is independent of distribution mileage and the number of distribution stores.We assumed that the distribution center has V types of vehicles (v = 1, 2, 3), with a total of M vehicles, and the fixed cost of the k-th vehicle of type v is c vk .f vk is a 0-1 variable, where f vk = 1 indicates that the k-th vehicle of the v-type vehicle is performing a distribution task, and f vk = 0 indicates that the vehicle is idle.The total fixed costs C 1 of the vehicle during the distribution process can be formulated as: (2) Transportation costs The transportation costs of the delivery vehicles in the execution of a task are determined by the fuel consumption costs incurred via the normal running of the vehicles during a distribution process.Therefore, the total transportation cost during vehicle distribution mainly includes the fuel cost of all vehicles, which is positively correlated with the vehicles' mileage.It is now known that the distance from store i to store j is d ij , and the unit transportation cost of vehicles from store i to store j is c ij .x vk ij is a 0-1 variable, where x vk ij = 1 indicates that the the k-th vehicle of type v completes the delivery task from store i to store j, and x vk ij = 0 indicates that the task is not completed by the vehicle.Therefore, the transportation costs C 2 of vehicles during the distribution process can be formulated as: According to the requirements of green logistics, the carbon emissions generated by vehicles during the distribution process are mainly caused by the fuel consumed by vehicles during transportation.Carbon emissions are the most direct criterion reflecting the cost of carbon emissions, and calculating vehicle fuel consumption can obtain the cost of carbon emissions.Through a review of the relevant literature, we found that fuel consumption is not only related to transportation distance, but is also influenced by factors such as vehicle load capacity [37,38].a 0 is the fuel consumption per unit distance of the vehicle when unloaded and a 1 is the influence factor of vehicle under extra load on unit mileage fuel consumption.Q v ij represents the vehicle load of the v-type truck when completing the delivery task from the i-th node to the j-th node.
This paper calculated the carbon emission costs of vehicles through carbon tax prices.Assuming ε is the carbon emission coefficient per unit of fuel (kg/L), ∂ is the carbon tax (RMB/kg), representing the cost of carbon emissions per unit.It refers to the environmental tax that needs to be paid due to CO 2 emissions.Therefore, the carbon emission costs C 3 of vehicles during the distribution process can be formulated as: Through the comprehensive analysis of the optimization objectives of fixed costs, transportation costs, and carbon emission costs mentioned above, we proposed an optimization model for the distribution path of chain supermarkets under low-carbon logistics: Equation ( 4) represents the total cost of distribution, including fixed costs, transportation costs, and carbon emission costs.It indicates that the objective of our problem is to minimize the overall distribution costs.Formulas ( 5)-( 9) serve as constraints.Among them, constraint (5) indicates that during the route distribution process, the total demand of all stores on each route cannot exceed the rated load capacity of the v-type vehicle.Constraint (6) restricts the vehicles upon departure from the distribution center so as to only distribute goods to the stores one by one, and return to the distribution center after the distribution is completed.Equation ( 7) is an integer value constraint of 0 or 1, with a value of 1 indicating that the k-th vehicle with type v has departed from the distribution center and is executing a distribution task; otherwise, the value is 0. Equation ( 8) is an integer value constraint of 0 or 1, with a value of 1 indicating that the k-th vehicle with type v is completing the distribution task from store i to store j; otherwise, the value is 0. Equation ( 9) is an integer value constraint of 0 or 1, with a value of 1 indicating that the goods in store i are distributed by v-type vehicles; otherwise it is 0.

Algorithm Design
The distribution route optimization problem of chain supermarkets belongs to the NP-hard problem, which is generally solved by an approximation algorithm.Our study considered using a fusion heuristic algorithm to solve the problem of optimizing the distribution paths of chain supermarkets.Firstly, the Floyd algorithm was used to calculate the shortest paths between the distribution center of a chain supermarket and each store, as well as between stores.Secondly, based on the shortest distance matrix, the nearest neighbor algorithm was used to divide the distribution network paths, and then the initial path partitioning results were obtained.Finally, the insertion algorithm was used to optimize the initial solution to obtain the optimal distribution paths for chain supermarkets.

Floyd Algorithm
Floyd algorithm is a dynamic path planning algorithm that can solve the problem of the shortest path between any two nodes, and is suitable for solving the shortest path of all sources [39].The core idea of Floyd algorithm is to solve the shortest path matrix [40].There are only two possibilities for the shortest path from any node i to node j.The first possibility is the Euclidean distance between two nodes, which is the direct distance from node i to node j.Another possibility is to start from node i and pass through several intermediate nodes to node j [41].Assuming Dist ij is the Euclidean distance from node i to node j, for all nodes k outside of these two nodes, the Floyd algorithm will check whether the inequality Dist ik + Dist kj < Dist ij holds.If the inequality holds, it is proven that the path from node i to node k and then to node j is shorter than the path directly from node i to node j; therefore, let Dist ij = Dist ik + Dist kj .After traversing node k, the shortest distance from node i to node j is recorded in Dist ij [39,42].The shortest distance between any two nodes obtained by the Floyd algorithm is saved as basic data for direct use during path partitioning.
The implementation of the Floyd algorithm is as follows [43]: • Number all nodes of the specified graph theory model, where Dist ij is the path length from i-th node to j-th node, defined as follows:

•
The adjacency matrix Dist is constructed with Dist ij as the element, and it is recursively updated n times from the initial adjacency matrix Dist.Assuming k is a node located between node i and node j, Dist k ij represents the shortest path between node i and node j.If Dist k ij does not pass through node k, then Dist k ij = Dist ij .If Dist k ij passes through node k, then Dist k ij = Dist ik + Dist kj .The calculation formula for Dist k ij is as follows:

Nearest Neighbor Algorithm
The nearest neighbor algorithm was first proposed by Rosenkrantz and Stearns et al. in 1977.The algorithm adopts a breadth-first shortest first-search idea, which is used to solve the shortest path problem and generate the initial paths [44].The advantage of the nearest neighbor algorithm is to solve the problem of one supply point corresponding to multiple demand points.
The basic principle of this algorithm is as follows [45].Starting from the distribution center, search for the node closest to the distribution center that has not been visited as the first node, and set that node as visited.Take this node as the center and search for adjacent nodes that have not been visited, and check if the constraint conditions are met.If the addition of this node does not exceed the capacity limit, then add the node to the line and set it as visited.Otherwise, end the line.Then, continue the search with the newly added node as the center until no adjacent nodes that have not been visited are found, ending the route.Repeat the above steps to find the nearest node that has not been visited from the distribution center as the first node of the new route and generate a new route.Until all nodes are visited, the algorithm ends.
In order to make the distance between each distribution node closer, this paper improved on the traditional nearest neighbor algorithm by using the node with the shortest second-order distance from the center node as the center of the next node.We assumed that the logistics distribution network G = (V, E) has n nodes, forming m paths, where V is the set of nodes in the network and G is the set of paths formed by nodes.The distance from node v i to node v j is D ij , v i , v j ∈ V (i, j = 1, 2, . . ., n).
The implementation steps of the improved nearest neighbor algorithm are as follows [46]: Step 1: Determine the distribution center, calculate the distance from any node to the center and the distance between nodes, and then generate a distance matrix.

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Step 2: The first node v 0 in path L p is the distribution center itself.Among them, L p is the initial path formed, and L p ∈ G (p = 1, 2, . . ., m).

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Step 3: From the distance matrix, take the node v k that is closest to the first-order distance of distribution center v 0 and has not been visited as the next node of path L p , and set this node as visited, forming a round-trip subloop.The formula for calculating the first-order distance of node v k is: Step 4: Continue the search with node v k as the center, and find the node with the smallest second-order distance from the current node in the set of nodes that have not been visited.If the node meets the constraint conditions, it will be considered as the next node in path L p .If it does not meet the constraint conditions, it will be returned to Step 2. The calculation formula for the second-order distance of node v k is: Step 5: Check the status of all nodes until all nodes have been traversed.
The distance matrix in Step 1 of the nearest neighbor algorithm can be directly obtained by solving the shortest distance between any two nodes through Floyd algorithm.In addition, the results obtained by dividing the distribution paths using the nearest neighbor algorithm may not necessarily be the optimal solution.Therefore, it is necessary to further verify and optimize the initial paths through the insertion algorithm.The implementation process of the nearest neighbor algorithm is shown in Figure 1.

Insertion Algorithm
The insertion algorithm is a heuristic algorithm used to solve VRP.The basic principle of this algorithm is to sequentially select the most suitable unassigned nodes and insert them at the optimal position in the route to optimize the delivery route [47,48].Assuming that there are two initial paths L p and L q , where the original path length of path L p is D k , insert node v k on path L q into different positions on path L p , and calculate the path D k after node v k is inserted into different positions.The calculation of the path is shown in Formula (12).If the path after inserting a node satisfies D k < 0 under vehicle constraints, then node v k on path L q is inserted into path L p .Additionally, the position of the inserted node should be such that min D k is achieved.On the contrary, if the path after inserting a node satisfies the inequality D k ≥ 0, then the node is not inserted.
where D k represents the path length of L p after inserting node v k ; D ik represents the distance between node v i and node v k ; D kj represents the distance between node v k and node v j ; and D ij represents the distance between node v i and node v j .The steps to optimize the distribution paths using the insertion algorithm are as shown in Figure 2.

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Step 1: Select an initial path L A and determine if there is node v on that path that can be removed and inserted into other paths.If present, select the node for insertion optimization.If all paths have been determined, the algorithm ends.

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Step 2: Select another initial path that has not been judged yet, and insert node v in Step 1 into different positions on this path.If inserting node v into any path cannot reduce the total distance, then step 1 is repeated.

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Step 3: If inserting node v in path L B reduces the total distribution distance, then select the location where the total distribution distance decreases the most to insert.If node v is inserted at any position and cannot reduce the total distribution distance, then return to Step 2.

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Step 4: Determine whether node v has exceeded the maximum capacity of the vehicle after being inserted into this position.If not exceeded, select the best position to insert.
If the maximum capacity is exceeded, return to Step 2.
Step 5: Repeat the above steps until all paths have been determined, and the algorithm ends.

Empirical Study
This study took Wuhan W chain supermarket as the research object to study the optimization problem of distribution routes.W chain supermarket is a large chain supermarket in Wuhan, with stores throughout Hubei.The supermarket has a distribution center in Wuhan, from which it can complete the delivery of goods to various store outlets within the city.It was required to reasonably divide and optimize the distribution routes throughout the entire distribution process without exceeding the vehicle capacity and to obtain the minimum distribution costs.

Data Source
By consulting relevant materials, we obtained the demand for goods from 38 stores of W chain supermarket, as shown in Table 2. From the table, it can be seen that there are significant differences in demand among different stores of W chain supermarket.The relevant parameters of the vehicles in the distribution center are shown in Table 3.The distribution center uses road transportation to deliver goods and uses three different types of vehicles to provide services to different stores.Different types of vehicles have different deadweight, payload, and fixed costs, and the larger the payload, the higher the fixed cost of a vehicle performing a distribution task.In addition, different types of vehicles have varying fuel consumption per unit distance when unloaded, as well as the influence factor of vehicle under extra load on unit mileage fuel consumption.According to the needs of the research content, this case calculates the actual distribution distance from the distribution center to each store and between stores based on the actual geographical location of each node in the map.Since the 39 39 matrix involved an extensive amount of data, only the distance matrix between the first 12 stores was given as an example, as shown in Table 4.The actual distance from the distribution center to each store and between stores is now known.The known issue was that a single distribution center delivered goods to 38 stores, and we considered the distribution center and stores as a total of 39 nodes.We first used the Floyd algorithm to calculate the shortest distance between any two nodes, that is, the shortest distribution distance between any two stores.The solution results were kept as basic data for backup.The shortest distance matrix from the distribution center to each store and between stores optimized by Floyd algorithm was shown in Table 5.Since the 39 × 39 matrix involved an extensive amount of data, only the distance matrix between the first 12 stores was given as an example.Then, we used the nearest neighbor algorithm to preliminarily partition the distribution paths.We took the distribution center O as the initial node, and found the adjacent second-order short distances as the next node, with that node as the center.We continued to search for the next node centered around the newly added node.By analogy, we can divide the distribution routes into different paths in order, without exceeding the vehicle capacity.According to the vehicle data of the distribution center in Table 3, the load capacities of the three types of vehicles are 5 t, 8 t, and 12 t, respectively.The preliminary path partitioning results obtained based on the nearest neighbor algorithm are shown in Table 6.The preliminary path division results in Table 6 showed that the total distribution route of W chain supermarket can be preliminarily divided into 12 paths.Among them, the shortest delivery path 1 was: distribution center-Miaoshan store-Jinxiu Longcheng store-Zhuobao store-Luoyu store, with a driving distance of 18.84 km.The longest delivery path 12 was: Distribution center-Longting store-Huangpi store-Yangluo store-Hannan store, with a delivery distance of 192.41 km.In addition, among the 12 routes, route 4 required a vehicle with a load of 5 t for delivery, route 1 required a vehicle with a load of 12 t for delivery, and the other 10 routes required a vehicle with a load of 8 t for transportation.The total driving distance obtained through initial path partitioning was 628.64 km.However, this path partitioning may not necessarily result in the optimal path results.Therefore, the insertion algorithm was needed to verify and optimize the initial paths.The path allocation before optimization using the insertion algorithm is shown in Figure 3.

Optimizing the Initial Paths through the Insertion Algorithm
We chose two initial paths for partitioning and selected one store from one path to insert into different locations in the other path.If the insertion reduces the maximum delivery distance, the store is inserted at that location until it cannot be further optimized.The premise for selecting a certain path as an example for insertion algorithm optimization is that the newly formed path cannot exceed the maximum carrying capacity of the vehicle of 12 t.When the nearest neighbor algorithm was used for initial path division, the distance matrix the optimal value obtained by Floyd algorithm, so the distance of adjacent nodes on each path reached the optimal value.Therefore, under the limit of vehicle capacity, we only needed to consider the top and end nodes to determine the stores that needed to be inserted.
According to the initial path division in Table 6, the total demand for path 2 is 7.5 t.We selected the last store in the path, Nanhu Store, as the end node.Then, we continued to search around the store and find the nearest front-end node in path 4, the Baishazhou store, with a distance of 9.73 km between the two stores.The total demand for the Baishazhou store on path 4 was 4.5 t.If the Baishazhou store on path 4 was inserted into the Nanhu store on path 2, the total demand for the two paths was 12 t, which did not exceed the maximum vehicle load.Before insertion, the total distribution distance for paths 2 and 4 was 60.67 km.The distribution distance of the new path formed by inserting the Baishazhou store and Bandung Square store on path 4 into the Nanhu store was 49.74 km.Choosing this insertion method can reduce the delivery distance by 10.93 km.
Similarly, the total demand for path 4 was 7 t, and we chose the last store in path 4, Bandung Plaza, as the end node.Searching around this store, it was found that the nearest front-end node adjacent to it is the Yanzhi road store in path 5, and the distance between the two store points was 4.93 km.When the Yanzhi road store in Path 5 was inserted into the Bandung Square store, the total demand for both paths was 11.5 t, which did not exceed the maximum vehicle load.Before insertion, the total delivery distance for paths 4 and 5 was 63.39 km.After inserting the store on path 5 into path 4, the delivery distance of the new path was 45.96 km.Choosing this insertion method can reduce the delivery distance by 17.43 km.Comparing the two insertion methods mentioned above, we found that inserting path 5 into path 4 would result in a greater optimization of the delivery path.Therefore, we chose this method to insert and form a new path.
The optimization process of the insertion method was shown in Figure 4.By continuously inserting stores from one path into another, conducting repeated tests, comparing results, and continuously optimizing, we ultimately obtained a new path partition until no further optimization can be achieved by inserting any stores.The final path optimization results obtained through the insertion algorithm were shown in Table 7.The optimization steps through insertion algorithm were as follows: (1) Insert the four stores on initial path 5 into initial path 4, and the total driving distance of the two paths is 63.39 km.After merging, the total driving distance of the paths is The optimized delivery routes of W chain supermarket can be divided into nine paths, with a total driving distance of 480.47 km.The path with the longest delivery distance optimized through the insertion algorithm was: distribution center-Xingguang store-Baisheng store-Longting store-Huangpi store-Yangluo store, with a delivery distance of 125.01 km.In addition, out of the optimized nine paths, one path required a vehicle with a load of 5 t for delivery, three paths required a vehicle with a load of 8 t for delivery, and the other paths required a vehicle with a load of 12 t for transportation.The optimized total distribution distance was reduced by 148.17 km.

Calculation of Distribution Costs
After initial path partitioning and path optimization, we calculated the distribution costs of W chain supermarkets before and after optimization based on the partitioning results.At the same time, we also analyzed the comparison of distribution costs before and after considering carbon emission costs.After consulting the relevant literature [38,49], we used a carbon trading price of 0.125 RMB/kg to levy a carbon tax on each kilogram of carbon emissions.In this study, the carbon emission coefficient per unit of fuel is 2.9 kg/L [50], and the unit distance transportation cost for vehicles from store i to store j is 3 RMB/km [37].
Based on the relevant parameters in Table 2, we calculated the fixed cost and transportation cost of vehicle delivery before and after optimization.When we did not consider the cost of carbon emissions, we substituted the data into the objective function to obtain the cost analysis before and after optimization, as shown in Table 8.When not considering the cost of carbon emissions, we found that after optimization, the fixed cost was reduced by 250 RMB and the transportation cost was reduced by 444.51 RMB.The total distribution cost has been reduced by 694.51 RMB.When we comprehensively considered fixed cost, transportation cost, and carbon emission cost, we substituted these data into the objective function to obtain the costs of the initial distribution path and the optimized distribution path, as shown in Table 9.When considering various costs comprehensively, the total distribution cost decreased by 698.76 RMB.The initial path partitioning results obtained based on the nearest neighbor algorithm and the results optimized using the insertion algorithm are shown in Tables 6 and 7. Through comparison, we found that a total of 12 initial paths were divided using the nearest neighbor algorithm, with a total delivery distance of 628.64 km.A total of one type 1 vehicle, ten type 2 vehicles, and one type 3 vehicle were required for delivery.After optimization through insertion algorithm, a total of nine paths were divided, with a total delivery distance of 480.47 km.A total of one type 1 vehicle, three type 2 vehicles, and five type 3 vehicles were required for delivery.Therefore, the total delivery mileage has been optimized by 148.17 km.
The fixed cost of the vehicles was optimized from 1800 RMB to 1550 RMB, reducing it by 250 RMB.The transportation cost of the vehicles was optimized from 1885.92 RMB to 1441.41 RMB, reducing by 444.51 RMB.The carbon emission cost of the vehicles was optimized from 117.28 RMB to 113.03 RMB, reducing by 4.25 RMB.When we did not consider the carbon emission costs during the delivery process, the total delivery costs before and after optimization were 3685.92RMB and 2991.41RMB, respectively, resulting in a total reduction of 694.51 RMB, as shown in Table 8.When we considered the carbon emission cost during the delivery process, the total delivery cost was optimized from 3803.20 RMB to 3104.44 RMB, resulting in a total reduction of 698.76 RMB, as shown in Table 9.
In previous studies, Lin et al. considered the improved algorithm combining genetic algorithm and Tabu search algorithm to study the urban distribution route optimization problem of perishable food.After optimization, the total delivery cost was reduced by 63.29 RMB and the carbon emissions were reduced by 239.92 kg [38].Deng et al. studied the distribution path optimization problem of cold chain logistics for fresh agricultural products, considering carbon emissions based on genetic algorithms.Through example solving, it was found that the scheme considering carbon emissions reduces carbon emission costs by 30.0% and total costs by 3.1%, compared to the scheme without considering carbon emissions [50].Their research results all show that path optimization considering low-carbon factors can reduce the total delivery cost, which is consistent with our research.On the contrary, the results of Yao et al. differ from our research.They designed an improved ant colony optimization to study the green vehicle routing problem for fresh agricultural products considering carbon emissions.The experimental results show that after implementing the carbon tax policy, the carbon emissions of enterprises are significantly reduced, but the carbon emission cost and total delivery cost increase.This is because the continuous increase in carbon tax value will to some extent reduce the economic benefits of enterprises [51].
After comparing the results of optimizing the distribution path of W chain supermarket in Wuhan before and after, we found that chain supermarkets can reduce losses through the reasonable planning of vehicle arrangements in the distribution center.That is to say, enterprises can choose the vehicle type corresponding to the demand on a delivery path for distribution, thereby avoiding resource waste.On the other hand, enterprises can reduce distribution costs by reasonably planning distribution routes.For chain retail enterprises, in the fierce market competition and low-carbon economic demand, how to meet delivery needs and achieve low-carbon development is the key issue they must face.Based on the concept of low-carbon logistics, enterprises should pay more attention to the issue of carbon dioxide emissions in distribution to reduce pollutant emissions and protect the environment.

Conclusions
After analyzing the various cost components and constraints of chain supermarket distribution, this study constructed a low-carbon distribution path optimization model.We proposed a fusion heuristic algorithm for solving the GVRP model of chain supermarket.Firstly, we used the Floyd algorithm to calculate the shortest distance between any two nodes.Then, the shortest distance matrix was used in the nearest neighbor algorithm to divide the initial distribution paths of chain supermarket.Additionally, the insertion algorithm was used to optimize the initial delivery path, forming the optimal distribution paths.Finally, an empirical study was conducted using the W chain supermarket in Wuhan as an example.The results showed that after using the fusion heuristic algorithm for optimization, the carbon emission of a single distribution was reduced by 11.73 L, and the total distribution cost was reduced by 698.76 RMB.
In dealing with the distance between nodes, traditional calculation methods only considered the spatial straight-line distance between two nodes, which can cause some deviation from reality.The research on distribution path optimization in this study was based on the actual road network distribution and the distance between stores.On this basis, we further used the shortest path calculation method to calculate the shortest distance between any two nodes, and thus determined the shortest path partition.In addition, in terms of vehicle configuration in the distribution center, we explored the ways in which to arrange different types of vehicles for transportation to effectively reduce carbon emissions.In the calculation of distribution costs, we comprehensively considered fixed cost, transportation cost, and carbon emission cost in distribution, and considered the method of using carbon tax prices to calculate carbon emission cost.
The research on the optimization of distribution routes for chain supermarkets in a lowcarbon economy is very meaningful.For enterprises, the carbon dioxide generated during the business process will be converted into economic costs.How to develop a reasonable distribution route is not only beneficial for enterprises to achieve more comprehensive social benefits, but also beneficial for enterprises and society to jointly achieve sustainable development.In a low-carbon economy, we suggest that government departments provide appropriate carbon tax subsidies or tax incentives to enterprises implementing low-carbon distribution.These measures can enhance the enthusiasm of enterprises to reduce emissions, promote the development of low-carbon logistics in cities, and achieve a win-win situation between enterprises and society.Therefore, research on the optimization of distribution routes for chain supermarkets is beneficial for enterprises to choose better distribution routes and reduce the total costs of enterprises and society.On the other hand, it is a positive response to the implementation of low-carbon policies by the country and the realization of carbon emissions reduction by chain retail enterprises.
This study provided relevant reference for the path optimization problem of chain retail enterprises.However, in the actual distribution process, more complex environments may arise, such as road traffic conditions, multiple distribution centers, and other factors.The practical application of this problem should be further expanded and improved.Therefore, additional constraints can be introduced in future research.For example, it is

Figure 1 .
Figure 1.Nearest neighbor algorithm implementation process.Schemes follow the same formatting.

Figure 2 .
Figure 2. Implementation process of insertion algorithm.

Figure 3 .
Figure 3. Path allocation before optimization of insertion algorithm.

Figure 4 .
Figure 4. Optimization process of insertion algorithm.

Table 2 .
Demand information for each store of W chain supermarket.

Table 3 .
Vehicle information of distribution center.

Table 4 .
Actual distance matrix between some stores of W chain supermarket.

Table 5 .
The shortest distance matrix between some stores of W chain supermarket.

Table 6 .
Initial path partitioning results.

Table 7 .
Final path partitioning result.
45.96 km, optimized by 17.43 km.The distribution vehicles have been changed from two vehicles with a capacity of 5 t and 8 t, respectively, to one vehicle with a capacity of 12 t.(2) Insert the two stores on initial path 6 into initial path 7. The total driving distance of the two paths is 63.6 km, and the combined total driving distance is 51.4 km, optimized by 12.2 km.The distribution vehicle has been changed from two vehicles with a capacity of 8 t to one vehicle with a capacity of 12 t.(3) Insert three stores on initial path 12 into initial path 8, three stores on initial path 11 into initial path 10, and one store on initial path 12 into initial path 11.The total driving distance of the original path is 375.38 km, and after insertion optimization, three new paths are synthesized.The optimized total driving distance is 256.84 km, with a total of 118.54 km optimized.The distribution vehicles have been changed from four vehicles with a capacity of 8 t to two vehicles with a capacity of 12 t and one vehicle with a capacity of 5 t.

Table 8 .
Cost analysis without considering carbon emission cost.

Table 9 .
Cost analysis when considering carbon emission costs.