Sustainable Urban Logistics Distribution Network Planning with Carbon Tax

Abstract

Global warming caused by excessive carbon dioxide emissions is threatening the sustainable development of human society. Considering the upcoming carbon tax policy in China, this paper studies the planning of dual-level urban logistics distribution network in the context of carbon emissions. Based on reasonable assumptions, a bi-objective mixed-integer programming model considering logistics operating costs and carbon emission costs is constructed. Given the problem size, an improved genetic algorithm is designed. Based on a numerical example, the optimization results of the improved genetic algorithm and the GLPK optimization suite are compared to verify the effectiveness of the proposed model and algorithm. Under different carbon tax rates, by adjusting the logistics distribution network along, the logistics operators can achieve a maximum cost savings of 19.4%, while carbon emissions can be reduced by up to 47.8%. The major conclusions include: carbon tax will bring about huge cost burdens for urban logistics operators; the reconfiguration of urban logistics network is a powerful measure to reduce carbon emission with the least extra costs; with problem size rises quickly, the intelligent algorithm as proposed in this article can always find near optimal solutions with acceptable time costs.

1. Introduction

Global warming has brought severe challenges to the sustainable development of human society. Various countries are exploring more low-carbon and sustainable economic development paths. As the world’s largest emitter of carbon dioxide, the Chinese government has announced in 2020 that China’s carbon emissions will peak in 2030 and achieve carbon neutrality in 2060 [1]. On 16 July 2021, China’s national unified carbon trading market was officially launched. The first batch of 2162 key thermal power plants stepped into the market for trading, covering an annual carbon dioxide emission of about 4.5 billion tons. It became the largest carbon trading market in the world [2]. At the same time, the Chinese government is studying tax policies related to carbon emission reduction, among which carbon tax has received widespread attention. It is difficult for a pure carbon trading market to cover all market players, but the price formed by the carbon market can provide an important reference for determining carbon tax rates [3].

Since the beginning of the 21st century, especially with the increasing prosperity of the Internet and e-commerce in China, China’s urban logistics distribution industry has developed rapidly. On the one hand, the urban logistics industry plays a key basic role in optimizing the distribution of resources and enhancing the comprehensive competitiveness of the city [4]. On the other hand, under the new low-carbon economic development mode, the external diseconomy of urban logistics has been criticized, such as its considerable energy consumption and significant pollutant emissions. Statistics show that residential life, industrial production, and logistics are the top three sources of carbon emissions in China [5].

There is a large body of research literature on the low-carbon, green, and sustainable development of urban logistics, most of which focus on the macro low-carbon economic policies. Policies to reduce carbon emissions are divided into two categories, namely price-based policy tools and quantity-based policy tools [6], including the carbon tax, carbon cap-and-trade policy, and carbon emission cap policy. The carbon tax is considered to be one of the most market-efficient policies to reduce carbon emissions [7]. Up to now, it has been implemented in the Netherlands, Norway, Finland, and other countries around the globe. There is also some literature discussing the carbon reduction of enterprises at the micro-level. Two ways can help enterprises reduce their carbon emissions. One is to invest in low-carbon technologies, including investment in new energy, new production processes, or new emission reduction equipment or technologies. For enterprises, technology investment costs are very high, which has a greater impact on the sustainable development and expanded reproduction of enterprises. Another way is to optimize the logistics operation network of enterprises, including logistics network planning, warehouse location, transportation route optimization, etc. For example, Tesco [8], Walmart [9], etc. had launched carbon footprint management initiatives on the above two paths at the same time to reduce emissions. Benjaarfar et al. were the first to introduce the concept of carbon footprint into the supply chain optimization model, analyzing how supply chain companies can make pricing decisions by adjusting their order quantity and output under different carbon emission reduction policies to maximize overall supply chain performance [10]. Generally, logistics activities such as warehousing, transportation, distribution, online processing, storage, and information processing will generate carbon emission, which is hard to measure, especially in the optimization of urban logistics network operations. Therefore, it is often necessary to simplify the carbon emission assessment process in modeling or optimizing a logistics network. The most common method is to assume a linear proportional relationship between carbon emissions and decision variables [11,12,13,14]. Under the carbon tax policy, it is also necessary to consider converting carbon emissions into the cost of urban logistics operators, so that the goals of logistics cost and carbon emission reduction can be combined into one [15]. Based on the traditional models, Hoen et al. [16] added carbon emission factors to conduct in-depth discussions on the choice of transportation methods. Taking the logistics network of French retail enterprises as an example, Ballot et al. [17] utilized real data to demonstrate that the shared supply network can achieve a 25% carbon dioxide emission reduction. The study by Pan et al. [18] found that combined transportation by road and rail can achieve a 5.2% emission reduction. Agatz et al. [19] draw lessons from the method of revenue management. In the express business of home delivery, through the design of the pricing mechanism, customers are encouraged to choose the delivery time similar to their neighbor’s order, thereby reducing the total delivery mileage. The result showed the efficient sales mechanism design indirectly reduces the carbon emissions caused by logistics. Based on the fact that in urban logistics, the transportation link is an important cause of traffic congestion, low economic efficiency, and high carbon emissions, more literature focuses on the optimization of urban logistics transportation links, namely the transportation route optimization problem, such as the literature [20,21,22,23]. Among the above literature on the sustainable operation of urban logistics, the size of the distribution network is not large, and the empirical cases are very limited. Moreover, their analysis of the network characteristics and results under different carbon taxes is scarce or too simple, making it hard to propose effective policy recommendations or business operation measures.

A sustainable carbon tax-constrained two-tiered urban logistics distribution network, including logistics hubs, candidate distribution centers, and retail terminals is studied in this article. The structure is as follows. In Section 2, a mixed-integer programming model about the urban logistics distribution network is established based on reasonable assumptions, simplifications, and notational conventions. Section 3 introduces an improved heuristic genetic algorithm to solve the above formulation. In Section 4, firstly, the performance of the proposed genetic algorithm is evaluated on different problems of various scales, and secondly, a numerical case is provided to study the strategic measures that the network shall take under different carbon tax rates, and we analyze the strategy adjustment together with the operational performance changes of these strategies. In Section 5, we discuss the research result. Meanwhile, the explicit theoretical and practical value of the research is also shown in this section. The last section offers some advice to the government to formulate industry or carbon policies and to enterprises to take carbon management measures.

2. Problem Description and Modeling

The research object of this article is an urban logistics enterprise, which is responsible for collecting materials from large logistics hubs normally located on the periphery of cities, selecting and assembling the goods through several alternative distribution centers, and then distributing them to the sales terminals located in all corners of the city. The business process is shown in Figure 1. In the logistics network, the location of the logistics hubs and the maximum quantity of goods supplied are known, the location and maximum distribution capacity of all alternative distribution centers are also known, and the demand of the sales terminal is independent and determined. Taking into account the government’s new carbon tax regulations, the city’s logistics enterprise needs to replan its distribution network, to minimize the total operating cost, including the cost of logistics itself and carbon emissions.

Before establishing the mathematical model of the above problem, it is necessary to make the following assumptions and give mathematical notations for variables and parameters.

Hypothesis 1 (H1).

Multiple logistics hubs can serve one distribution center at the same time;

Hypothesis 2 (H2).

Multiple distribution centers can serve one sales terminal at the same time;

Hypothesis 3 (H3).

In any distribution center, the distribution cost and carbon emissions are linearly proportional to the quantity of goods handled;

Hypothesis 4 (H4).

During the distribution process, the distribution cost and carbon emissions are linearly proportional to the product of the transportation distance and the quantity of the distributed goods.

The notation conventions of this model are shown in

Table 1. Symbolic conventions for the proposed model.

Symbol	Connotation and Unit
$M$	Number of logistics hubs
$N$	Number of alternative distribution centers
$K$	Number of sales terminals
$I$	Set of subscripts for $M$ logistics hubs, |$I$| = $M$
$J$	Set of subscripts for $N$ alternate distribution centers, |$J$| = $N$
$L$	Set of subscripts for $K$ sales terminal, |K| = L
$i$	The logistics hub $i$, $i$∈$I$
$j$	The alternative distribution center $j$, $j$∈$J$
$l$	The sales terminal $l$, $l$∈$L$
$P_i$	The maximum amount of goods that can be supplied by the logistics hub $i$, $mt$
$C_j$	The maximum goods handling capacity of the alternative distribution center $j$,$mt$
$D_l$	Demand for the sales terminal $l$,$mt$
$d_{ij}$	Distance from the logistics hub $i$ to the alternative distribution center $j$,$km$
$d_{jl}$	Distance from the alternative distribution center $j$ to the sales terminal $l$,$km$
$F_j$	Fixed cost for setting up the alternative distribution center $j$, $RMB yuan/mt$
$V_j$	Variable cost per unit of goods handled in the alternative distribution center $j$, RMB $RMB yuan/mt$
$T_i$	Freight per unit of goods transported from the logistics hub $i$ to the alternative distribution center $j$,$RMB yuan/(mt\cdot km)$
$T_j$	Freight per unit of goods transported from the alternative distribution center $j$ to any sales terminal, $RMB yuan/(mt\cdot km)$
$v_j$	The variable carbon emissions per unit of goods handled in the alternative distribution center $j$,$kg C{O}_{2eq}/mt$
$t_i$	The variable carbon emissions per unit of goods transported from the logistics hub $i$ to any alternative distribution center,$kg C{O}_{2eq}/(mt\cdot km)$
$t_j$	The variable carbon emissions per unit of goods transported from the alternative distribution center $j$ to any sales terminal, $kg C{O}_{2eq}/(mt\cdot km)$
$Z_{ij}$	Shipment quantity from the logistics hub $i$ to the alternate distribution center $j$, $mt$
$X_{jl}=\{\begin{array}{c}0\\ 1\end{array}$	The sales terminal $l$ is not assigned to the distribution center $j$ The sales terminal $l$ is assigned to the distribution center $j$
$Y_j=\{\begin{array}{c}0\\ 1\end{array}$	The alternative distribution center $j$ was not selected The alternative distribution center $j$ is selected

below.

According to the above assumptions and notation conventions, we can establish the following bi-objective logistics distribution network planning problem model considering carbon emissions, abbreviated as model $M_0$ hereafter.

$$\begin{array}{cc}Min& TC\end{array}={\displaystyle \sum _i{\displaystyle \sum _j{T}_i{d}_{ij}{Z}_{ij}+{\displaystyle \sum _j{F}_j{Y}_j}}}+{\displaystyle \sum _j{\displaystyle \sum _l{V}_j{X}_{jl}{D}_l+{\displaystyle \sum _j{\displaystyle \sum _l{T}_j{d}_{jl}{X}_{jl}{D}_l}}}}$$

(1)

$$\begin{array}{cc}Min& CE\end{array}={\displaystyle \sum _i{\displaystyle \sum _j{t}_i{d}_{ij}{Z}_{ij}+}}{\displaystyle \sum _j{\displaystyle \sum _l{t}_j{d}_{jl}{X}_{jl}{D}_l+{\displaystyle \sum _j{\displaystyle \sum _l{v}_j{X}_{jl}{D}_l}}}}$$

(2)

Subject to

$$Z_{ij}\le P_i{Y}_j$$

(3)

$${\displaystyle \sum _j{Z}_{ij}\le P_i}$$

(4)

$${\displaystyle \sum _l{X}_{jl}{D}_l}\le C_j{Y}_j$$

(5)

$${\displaystyle \sum _i{\displaystyle \sum _j{Z}_{ij}}}\ge {\displaystyle \sum _l{D}_l}$$

(6)

$${\displaystyle \sum _i{Z}_{ij}}={\displaystyle \sum _l{X}_{jl}{D}_l}$$

(7)

$${\displaystyle \sum _j{C}_j{Y}_j}\ge {\displaystyle \sum _l{D}_l}$$

(8)

$${\displaystyle \sum _j{X}_{jl}}=1$$

(9)

$$X_{jl}\le Y_j$$

(10)

$$Z\ge 0$$

(11)

$$0\le X\le 1$$

(12)

$$Y\in B$$

(13)

In the above model, there are two objective functions. Objective (1) is the minimum total operating cost ($TC$) requirement of the enterprise, which is composed of four parts, namely, the freight from the logistics hubs to the selected distribution centers, the fixed operating expenses for the selected distribution centers, possibly in the form of rent or construction cost, variable expenses such as picking, assembling, reprocessing, and loading and unloading within the selected distribution centers, as well as the freight from the selected distribution centers to the sales terminals. Objective (2) is the environmental constraints ($CE$) that the urban logistics distribution system needs to meet, that is, the requirements for carbon emissions. It includes the carbon emissions in the transportation links between different network levels and the variable carbon emissions in the internal processing of the selected distribution centers.

Constraint (3) is the capacity constraint of the logistics hubs to supply each selected distribution center. Constraint (4) covers constraint (3), and the former is to make the constraint more compact, indicating the supply capacity for each logistics hub. Constraint (5) is the capacity constraint of the alternative distribution centers. Constraint (6) is the constraint that the overall shipping volume of the logistics hubs is greater than the overall demand of the sales terminals. Constraint (7) is the logistic balance constraint between the two network levels. Constraint (8) is the constraint that the total storage and processing capacity of the alternative distribution center is greater than the demand of the served sales terminals. Constraint (9) ensures that the needs of all sales terminals must be just met. Constraint (10) states that the distribution center can only form an effective supply to the sales terminals if it is selected. Constraint (11) gives that the delivery volume from the logistics hubs to the alternative distribution centers can only be nonnegative. Constraint (12) shows the multisource nature of the problem. Constraints (13) define the binary decision variables of whether the distribution center is selected.

Under the background of carbon tax regulation in this paper, the carbon emission cost must be internalized as the operating cost of the enterprise. Therefore, the objective function can be combined into one to obtain a new model objective function as shown in the following Formula (14), and the new objective function together with all the constraints for $M_0$ could be abbreviated as the model $M_1$.

$$\begin{array}{l}\begin{array}{cc}Min& TC\end{array}+CE={\displaystyle \sum _i{\displaystyle \sum _j{T}_i{d}_{ij}{Z}_{ij}+{\displaystyle \sum _j{F}_j{Y}_j}}}+{\displaystyle \sum _j{\displaystyle \sum _l{V}_j{X}_{jl}{D}_l+{\displaystyle \sum _j{\displaystyle \sum _l{T}_j{d}_{jl}{X}_{jl}{D}_l}}}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\displaystyle \sum _i{\displaystyle \sum _j{t}_i{d}_{ij}{Z}_{ij}+}}{\displaystyle \sum _j{\displaystyle \sum _l{t}_j{d}_{jl}{X}_{jl}{D}_l+{\displaystyle \sum _j{\displaystyle \sum _l{v}_j{X}_{jl}{D}_l}}}}\end{array}$$

(14)

3. Intelligent Solution Algorithm Design

For solving the model $M_1$, a kind of mixed-integer programming, there are generally two types of techniques. One is based on the cutting plane method or the branch and bound method, which are often embedded in the commercial optimization kits, such as GLPK, CPLEX, Gurobi, etc. Another way is a type of technology called intelligent algorithms, such as genetic algorithm, particle swarm algorithm, or tabu search algorithm. The genetic algorithm is the earliest and most popular intelligent algorithm. Considering the possibly large size of the problem $M_1$, this research will develop a heuristic genetic algorithm based on GLPK [24], and it will also be compared to the exact algorithm in terms of solution efficiency and solution accuracy.

The genetic algorithm is one of the most popular intelligent algorithms for solving combinatorial optimization problems in the operational research field. It realizes the evolution of the population to a higher level of fitness by simulating the process of natural selection, gene recombination, and gene mutation in the evolution process of organisms for the whole population. The basic process of the algorithm is to first randomly generate an initial population of a certain size. Based on the results of the fitness evaluation of all individuals in the population, which can also be called chromosomes or genes, individuals with larger fitness shall be selected. The selection process can be based on the probability decided by individual fitness, which is called the selection operator. After that, the genetic crossover operator is used to carry out the gene recombination operation, which is the most important step to generate new individuals. Then, the genetic mutation operator is used to perform gene mutation operations on some loci of some individuals, to ensure the diversity of the population and avoid premature local convergence of the algorithm. After the whole population is handled with these operators, the newly generated population can replace the original population, and so forth, and finally realize the evolution of the population.

According to the nature of the problem $M_1$, we have compiled the following heuristic intelligent genetic algorithm, which could be referred to as HGA. The specific process for HGA is as follows.

3.1. Data Preprocessing

From the observation of the problem model $M_1$, it is known that the most memory-consuming part of the operation of HGA is the evaluation of the fitness of all individuals in a population. Each individual represents a group of selected alternative distribution centers. To avoid repeating computation, two distance matrices for distances among different logistics levels and a variable cost matrix for variable cost per unit of goods within various distribution centers could be built before the algorithm starts. Of course, another factor has also been considered that the algorithm will run on the MATLAB platform, whose most obvious advantage lies in the processing of large-scale matrix data. In this way, when executing the genetic algorithm, it is not necessary to calculate the transportation cost between each level and the operation cost within the alternative distribution centers many times, but it could directly read from these two matrices.

3.2. Genetic Coding

Considering the number of the candidate distribution centers and the loose constraints on the number of the finally selected distribution centers in the problem model $M_1$, to save computer memory, the encoding of genetic individuals adopts the natural number encoding method. Assuming that under a certain carbon tax price, the number of selected distribution centers for the genetic population continues to increase, the length of the individual natural encoding string will also increase sequentially. For example, when the number of candidate distribution centers is equal to 5, the coding of individuals in the population could be like [12, 5, 37, 53, 6], which means that the 12th, 5th, 37th, 53rd, and 6th candidate distribution centers are selected into the solution. It has to be pointed out that the individual loci only represent the selected distribution center serial number, and there is no priority in any order, but the natural numbers on all loci obviously must be different from each other. Since the capacity of the distribution center is assumed to be infinite, that is, it can always meet the needs of all customers assigned to it, so each individual is always a feasible solution.

3.3. Fitness Evaluation

Each individual in a population represents a feasible solution. First, the fixed cost of all selected alternative distribution centers in an individual can be obtained easily. The variable cost shall be calculated based on the above-mentioned variable cost matrix in Section 3.1, including goods handling cost and carbon emission cost. Second, a heuristic method is used here. According to the variable cost matrix, the sales terminals that minimize the increase in comprehensive costs are allocated first, and this process continues until all sales terminals are allocated. At this time, the designed capacity of each distribution center can also be determined, that is, it is equal to the cumulative demands of all sales terminals allocated to the distribution center. Then, according to the cost of transit transportation from each logistics hub to each distribution center, the lowest transit transportation cost determines the delivery volume from the logistics hub to the distribution center, but the designed capacity of the distribution centers should be considered. According to the above two costs, the overall logistics cost is just the fitness value of individuals, and then all individuals are sorted according to their fitness.

3.4. Selection Operator Design

After an initial population is generated in a random uniform distribution space, genetic selection, crossover, and mutation operations should be conducted. The highly effective tournament selection method is used here, and the scale is set to 4; that is, 4 individuals are randomly selected from the population each time, and the first two with the best fitness are selected for subsequent operations.

The strategy of population evolution adopts the steady-state substitution strategy, which means that two parent individuals will generate one offspring through the operation of the genetic operators. If this offspring is better than the parent with poorer fitness in the two parent individuals, then the offspring will enter the population and replace the poorer parent individual. Meanwhile, in HGA, the optimal individual retention strategy is taken in all iterative processes. The individual with the lowest cost does not participate in the operation of all subsequent genetic operators.

3.5. Crossover Operator Design

In the design of the crossover operator, we did not adopt the most common probability-based crossover. When the two parents perform traditional crossover operations, since the individual codes are out of order, the traditional single-point or double-point crossover operator will likely result in the same sequence numbers in the children. Therefore, we adopt a shared loci-based intersection algorithm here.

The so-called shared loci refer to loci composed of the sequence numbers shared by the two parent individuals, and then a random single-point crossover operation is performed on the two unshared loci after removing the shared loci from the two parents to generate a new individual. It is guaranteed that the same sequence numbers will not appear at the same time in the children. The process is shown in Figure 2 below.

3.6. Mutation Operator Design

The traditional mutation operator is used with a specified probability, $p_m=0.01$ and a random number [0, 1] is continuously generated according to the length of an individual. If the random number is lower than $p_m$, the sequence number in the corresponding gene locus will be replaced by another random number representing the sequence number of any distribution center that is not in the individual. After evaluating the fitness of the new individuals, according to the steady-state replacement strategy, replace the poorer individual in the two parents to form a new population.

3.7. Rules to Stop Iterating

The method combining the maximum number of iterations and the number of iterations no longer evolution for the optimal individual is used. The entire population failing to find a better individual within designated generations is a priority principle, and the maximum number of iterations is set large enough, which is also characteristic of the steady-state replacement strategy.

For the parameter design of the genetic algorithm, in principle, we set the size of the population as 50, the mutation probability as $p_m=0.01$, and the maximum number of iterations as $T=10,000$. When the number of iterations exceeds 1000, the evolution of the optimal solution in the population is monitored. If there is no longer any evolution for 1000 consecutive generations, the iteration will be terminated at once. Just as with any intelligent algorithms, the above parameters will be continuously fine-tuned in the process of algorithm evolution to find the optimal parameters.

In addition, to obtain an accurate solution to the problem for comparisons with the proposed HGA, we also express the model $M_1$ in Matlab, based on the modeling rules of the YALMIP toolbox in Matlab, and call the GLPK optimization suite to solve it.

4. Numerical Experiment and Result Analysis

4.1. Algorithm Comparisons

The heuristic genetic algorithm proposed in this paper is compared to the GLPK optimization suite to solve the problem $M_1$ with different scales for their optimization efficiency and effect. The results are shown in

Table 2. Comparison of efficiency and effect of HGA and GLPK.

Problem Size			Time Elapse/Seconds		Proportion to Find the Optimal Solutions for HGA in 10,000 Runs/%
LC	DC	ST	GLPK	HGA
5	50	100	0.2702	0.3271	99.6%
5	500	1000	3.5743	3.4586	99.2%
50	5000	1000	51.7922	23.1539	98.2%
500	5000	10,000	>5 h (e)	91.2264	N/A

LC—Number of logistics hubs; DC—Number of candidate distribution centers; ST—Number of sales terminals; (e)—Time cost estimated by the GLPK optimization kit.

below. It is assumed that the carbon tax is set at 0.1 yuan/kg CO_2e.

Since the maximum number of iterations of the genetic algorithm is set to be relatively large, we observe that the results given by the HGA and GLPK are the same on the small-scale problems, and its efficiency is slightly lower than that of GLPK. However, when the problem size is increased, it could be seen that the HGA can always give the best or good reference solutions, whose efficiency also outperforms the GLPK kit. From the view of algorithm reliability, most of the time HGA can find the best solutions. More importantly, the biggest advantage of the proposed algorithm is that for the solution of large-scale problems, especially when general commercial optimization software, such as GLPK, fails to give the optimal solutions, HGA can always give an approximate optimal solution within the acceptable time cost, which is essential for solving large-scale engineering and management optimization problems.

4.2. Numerical Experiment

A real numerical case is used to verify the effectiveness of the proposed model. In a megacity within China, there is a professional third-party logistics firm responsible for providing logistics and distribution services for 126 chain sales terminals in the city. Its operation process is as follows. First, it collects and distributes the required goods from five logistics hubs located in the suburbs of the city, and then transfers them to 28 self-operated alternative distribution centers. After loading, unloading, packing, assembling, and processing within these distribution centers, the goods are then distributed to 126 sales terminals scattered all over the city. The distribution network has now achieved the optimal configuration based on the principle of the lowest cost but without considering the upcoming cost of the carbon tax. Now the logistics distribution network shall be reconfigured by taking the carbon tax cost into account.

The values of part key parameters in the model are given according to the actual situation of the enterprise in

Table 3. Partial model parameters’ value range.

Parameter	${\mathit{D}}_{\mathit{l}}$	${\mathit{P}}_{\mathit{i}}$	${\mathit{C}}_{\mathit{j}}$	${\mathit{F}}_{\mathit{j}}$	${\mathit{V}}_{\mathit{j}}$	${\mathit{T}}_{\mathit{i}}$	${\mathit{T}}_{\mathit{j}}$	${\mathit{v}}_{\mathit{j}}$	${\mathit{t}}_{\mathit{i}}$	${\mathit{t}}_{\mathit{j}}$
Scope	60–180	5000–10,000	1800–3000	10,000–11,000	20–22	2–2.2	4–4.5	100–600	0.4–1.6	0.4–2.0

below, and the parameter values are all within a range. At the same time, the range of carbon tax rate is varying between 0.01 to 0.10 yuan/kg carbon dioxide equivalent according to the carbon tax range currently being studied by the Chinese government. The carbon tax rate in this study is also set in the range of 0.01 to 0.10 yuan/kg carbon dioxide equivalent. Optimization results are shown in Figure 3.

It could be seen from Figure 3 that, if the government implements the steadily increasing carbon tax policy, the logistics operator does not continuously adjust the distribution network layout and implement active carbon management according to the different carbon tax rates, but simply digests the costs caused by the carbon tax, it could be seen that its overall operating costs will undoubtedly skyrocket. That is to say, every time the carbon tax rate increases by 0.01 yuan/kg of carbon dioxide, the overall operating cost of the logistics distribution firm will increase by 61,512 RMB yuan, while the carbon emission will always remain unchanged. Conversely, if it implements an active carbon management strategy and continuously optimizes its distribution network, it will offset some of the increased cost pressure due to the carbon tax imposed, and at the same time, its carbon emissions will drop significantly. For example, when the carbon tax was changed from 0 to 0.01 yuan/kg CO_2e, by optimizing the network configuration, its overall operating cost increased by about 6.50% only, or 58,470 yuan, rather than 61,512 yuan without optimization. That is to say, the cost of 3042 yuan can be saved by simply optimizing the network configuration, and the carbon dioxide emission in the same period has dropped by 16.5% or about 1010 tons. As the carbon tax rate increases, so does the benefits of operational optimization. When the carbon tax rate is increased to 0.10 yuan/kg of carbon dioxide, the cost reduction effect brought by optimizing the network configuration can reach 179,780 yuan, and the carbon emission is about 48% lower than before the carbon tax was imposed.

Through the analysis of output results, it could also be observed where carbon emission comes from and what the operating cost structure is in detail when carbon tax rates vary, as is shown in Figure 4 and Figure 5 below. During the optimization process, the fixed cost remained unchanged or even decreased slightly. For the transportation cost, which accounted for the largest proportion of the total cost, it remained unchanged during the optimization process, but its proportion continued to decrease. The internal variable cost of distribution centers has shown a slow-growth trend. It can be seen from Figure 5 that the variable carbon emissions of distribution centers, which account for a large proportion of carbon emissions, are the main optimization objects of the HGA algorithm, and they drop rapidly during the entire optimization process.

In addition, by processing and analyzing the output results of the network configuration, it can be seen that the use of this model can achieve good economic and environmental benefits for the urban logistics distribution network at the same time. Furthermore, such network configuration optimization is achieved through local network fine-tuning gradually, as has a limited impact on the overall structure of the operating network. For example, in Figure 6 below, as the carbon tax rate continues to increase, the number of distribution centers that need to be selected remains between 9 to 11, and when the tax rate gradually increases steadily, the distribution center that needs to be adjusted in the distribution network is 0 or 2 at most.

The binary variable $Y$, which represents whether the distribution center is selected, remains unchanged or changes slightly with the increasing carbon tax rate. It means that the logistics flow of the overall logistics distribution network also changes slightly to reduce carbon emissions and operating costs. For example, when the carbon tax is increased from 0 to 0.01 yuan/kg CO₂, it can be seen in Figure 6 that only distribution center #19 is abandoned and replaced by distribution centers 12 and 15 simply.

Through the analysis of the output results, it can be found that when the carbon tax starts from zero and then gradually increases, the third-party logistics firm needs to constantly make appropriate adjustments to its logistics network. However, such adjustments are local, slight, and continuous, and would not have a great impact on the network structure, which means such changes to the logistics network could easily be made. Meanwhile, the firm has achieved some cost savings in this fine-tuning process, and significantly reduces carbon emissions during the process of logistics and distribution services.

5. Discussions

In this study, an urban logistics network model under the carbon tax policy was constructed, and a corresponding intelligent genetic algorithm was designed. Finally, the algorithm and model were verified in a specific numerical example. The results of the study are exciting.

First, at the micro level, after analyzing the research results, we found that the proposed model can help urban logistics operators effectively reduce overall operating costs, while reducing carbon emissions, that is, the model can simultaneously help achieve better economic and environmental benefits of the urban logistics sector.

Secondly, as the carbon tax increases year by year, the model can help urban logistics operators to continuously adjust the network structure, specifically, adjust the shipment volume from logistics centers to distribution centers, as well as the service relationship between logistics centers and distribution centers, and between distribution centers and sales terminals to offset some of the carbon tax costs. This kind of network adjustment is not for the whole logistics network to be demolished and rebuilt, but a slight fine tune, sometimes only the shipment volume is adjusted, or only a certain distribution center is added or adjusted. This adjustment will not cause huge disturbance to the entire logistics network, which not only brings cost savings, but also makes the management of the logistics network easier, making urban logistics operations more sustainable and maintaining good consistency and continuity.

The theoretical significance of this model lies in the following two points.

First, the proposed urban logistics network optimization model under the carbon tax policy can perfectly achieve the balance between the operating cost and the carbon emission cost. If the carbon tax is set to 0, the proposed problem formulation degenerates into a traditional two-layer network operation optimization location–allocation problem. The results of model optimization give the selection of distribution centers, the paired service relationship between the two network layers, and the logistics flow on the network. Lots of existing literature studies the low carbon supply chain either from the perspective of macroeconomics or from the perspective of game theory. This paper is one of the few using a mathematical programming model to study the operation optimization problem of carbon emission reduction from the micro-operation level of urban logistics operators. In this sense, it is a contribution of this study in terms of theoretical formulation.

Secondly, the results of this study also verify many theories in economics and management, including that the initial values of the carbon tax rates must be set as low as possible, that is to say, the implementation of the carbon tax has a symbolic meaning and cannot be reckoned as a new government taxation source. Carbon tax will definitely lead to the migration of social investment to low-carbon technology or management. If the magnitude is too large, it will affect regional economic development; in addition, carbon tax is indeed an effective market-based means, which can help the whole society to effectively reduce emissions; in addition, network operation optimization is a cost-effective and controllable factor for urban logistics operators, which enables them to largely offset the adverse impact of carbon tax on the operating costs through purely managerial optimization means.

The research results are also of great significance for guiding the practice of government and enterprises. First of all, the government should realize that, unlike other carbon emission reduction mechanisms, carbon tax only increases the cost of enterprises and cannot be fully absorbed by enterprises. Therefore, carbon tax will reduce the competitiveness of enterprise products and services. The timing of implementation should be carefully evaluated. The carbon tax rates should not be very high, and can start from a minimum of 0.01 yuan/kg CO₂; secondly, in view of the high proportion of carbon emissions in the distribution center, in order to reduce the overall carbon emission level of social logistics, it is recommended that the government build a number of low-carbon distribution centers for the society enterprise to rent; thirdly, for enterprises, negative response to carbon taxes will lead to a skyrocketing cost, and active carbon management measures must be adopted when caron taxes come true. As in our numerical case, as the carbon tax changes, the network configuration is continuously adjusted to partially offset extra costs due to new carbon taxes.

6. Conclusions

To achieve the sustainable development of the urban logistics sector, this paper studies the planning problem of an urban logistics distribution network consisting of logistics hubs, distribution centers, and sales terminals under the regulation of carbon tax policy. We studied the design and strategy changes of urban logistics distribution networks under the condition of a gradual increase in the carbon tax rate, which is of great significance for urban authorities to formulate carbon tax policy and the logistics industry to take active countermeasures. The main conclusions of this paper are as follows.

First, if the carbon tax is imposed, it will bring about huge cost to the urban logistics operators. As one of the most market-efficient policies for reducing carbon emissions, the implementation of the carbon tax policy in China should be cautious, and the initial carbon tax rate shall be set at a lower level. It could only be increased gradually to leave time and space for logistics firms to accumulate funds for low-carbon technology upgrades.

Second, the adjustment of urban logistics network structure, including selection of distribution centers, service relations adjustment for different network layers, and dynamic shipment changes, is proved to be an effective way to offset the adverse effects of carbon taxes. Regardless of the implementation of any carbon emission reduction policy, a lot of research has shown that it will increase the additional investment of the whole society, thereby affecting the growth of the macro economy. As Benjaafar et al. [10] believe, although the technological transformation is the most effective, it is often costly and brings difficulties to sustainable business growth. This study shows that operational optimization can partially offset the new carbon cost at a small price. At the same time, it should be seen that for the urban logistics and distribution industry, operation optimization is the most cost-effective way. However, when the cost rises beyond the ability of the enterprise, the investment in more carbon-efficient facilities and technologies will be an inevitable choice.

Third, the mixed-integer programming model and the proposed large-scale intelligent optimization genetic algorithm, HGA, is also proved to be very effective. When the problem size is limited, HGA performs as well as the commercial optimization package tools such as GLPK. When the problem size increases dramatically, HGA is far more efficient than GLPK.

The above conclusions are also the main contributions of this study. In addition, the model proposed in this paper can also be used by urban logistics operators to optimize their existing logistics network. After the implementation of the carbon tax policy in the future, according to the changes of carbon tax rates, the model can be used to continuously change the urban logistics network configuration to achieve the goal of the lowest overall operating cost. This research further proves both theoretically and practically that, in addition to new energy, energy-saving and emission-reduction technologies and equipment, industrial structure adjustment and other means, urban logistics network reconfiguration is another powerful alternative means, in an economically feasible way, to greatly reduce the carbon emissions of the urban logistics network.

The study has the following deficiencies. First of all, this study assumes that the logistics center locations are fixed, but in reality, many urban logistics operators need to choose to build or rent logistics centers of different scales. Secondly, this paper assumes that demand for various sales terminals is constant, which is inconsistent with the random and fuzzy characteristics of customer demand in reality. Furthermore, it is known that even when the distribution center is idling, there will be fixed carbon emissions, but this study does not take them into account. As for the future research avenues, we believe that research on the optimal configuration of urban logistics networks under the background of other carbon emission reduction policies other than carbon tax, including carbon cap, carbon cap-and-trading, carbon offsets, carbon subsidies, and other policies, will be fruitful. It will be the same fruitful to study the random network optimization configuration problem under the fuzzy, or random or even multiple uncertainties for demand of sales terminals. These are very promising research directions.