Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method

Shenghua Yan; Lei Huang

Dettagli rivista e numero

Applied Mathematics and Nonlinear Sciences

Dettagli della rivista

Formato: Rivista
eISSN: 2444-8656
Prima pubblicazione: 01 Jan 2016
Frequenza di pubblicazione: 2 volte all'anno
Lingue: Inglese

As a complex industrial chain, logistics covers a wide range of areas and rises with the rapid rise of e-commerce. The timeliness of logistics is crucial for the circulation of e-commerce items. In the logistics industry chain, the distribution centre can reduce the transaction links of goods, improve industrial efficiency, reduce the inventory of merchants, and at the same time can quickly get feedback on demand. The specific process is shown in Figure 1, including five links of express delivery, such as stocks, storage, sorting, shipment and despatch [1–3]. Among these five links, the sorting of express delivery is the most important, and the time and labour costs are also the highest, which has a great impact on the efficiency of the entire logistics system.

In the entire distribution centre, the logistics storage warehouse with strong liquidity has the characteristics of high inflow and outflow frequency of goods and a short inventory cycle. A complete distribution centre first needs to purchase the customer’s goods according to the order information, and then store the purchased goods for a short period of time, which can effectively handle the supply of goods according to customer needs, and properly adjust the stability of the goods in the circulation process to avoid the presence too many or too few products on the market. Second, it has the function of quick sorting, which can sort the goods according to the customer’s order information, and sort according to the customer’s delivery location, the number of goods, the weight of the goods, the specifications of the goods, the customer information, and the order number. After the basic sorting is completed, the sorted goods are effectively combined, and the goods at the same location are uniformly packaged to form an effective, reasonable, low-cost, and high-efficiency logistics channel. The whole process of sorting can be simply described as sorting the goods according to the order information with a certain sorting optimisation method, sorting the delivered goods according to the order of shipment, division, serial number of distribution equipment, customer priority, etc. and finally distribute to specific locations according to logistics vehicles [4, 5]. In the entire logistics sorting chain, the sorting efficiency of orders has a huge impact on the efficiency of the entire operation. Compared with other links, the logistics sorting process accounts for a large proportion of time and consumes high costs [6]. For the rapid sorting of commodities, it can be divided into sorting unit division, sorting method division, sorting operation area division, etc. according to different division principles. The sorting unit partition is classified according to the categories of goods to be sorted, such as large objects, small objects, and special commodities. Here, the two unrelated processes of sorting and transportation are independent, making the sorting professional and modular. Sorting method partition, for different sorting unit partitions, according to the different sorting methods and equipment, sorting is divided into multiple areas, and the purpose is to improve the efficiency of sorting operations and reduce the cost of sorting time [7]. In the case of keeping the sorting method unchanged, the sorting operation area is partitioned, and picking personnel is assigned to carry out the next sorting in a fixed place.

At present, in the logistics transmission chain, the development of the sorting system is not optimistic, and the cost and capital consumed by it still account for a large proportion of the entire logistics system. For the logistics industry, commodity materials are dense, and the optimisation and improvement of automatic sorting are crucial to the improvement of the efficiency of the entire logistics distribution. In modern logistics transportation, there are various commodities, and the market’s demand for commodities has become diverse. As the basis of logistics distribution, logistics distribution needs to improve distribution efficiency while providing basic liquidity guarantees. In the entire logistics sorting process, in this paper, we will discover the modus operandi to improve the express sorting speed, optimise the sorting efficiency of the intelligent transmission chain without purchasing new automation, and optimise the sorting algorithm and model, as well as the key research directions of related research. Boysen et al. [8] conducted a comprehensive review of automated sorting conveyors from the perspective of operations research. Their review focuses on research on the layout design and system operation of conveyor-based systems. The research problems are divided into four categories, namely layout design, inbound problems, outbound problems and short-term scheduling decisions. Schenk and Klabjan [9] models the processes of express classification and transportation strategy through dynamic programmes. The ensemble model solves dynamic programming by approximation, where the value function is approximated as a linear function. Further strategies were developed to speed up the algorithm and reduce the time required to find a viable solution. The method is tested on several instances of express package carriers. The dynamic programming solution is much better than the current best practice and the best solution obtained from the integer programming formulation of the problem. In the process of warehouse vertical sorting optimisation, Tan et al. [10] achieved a higher level of automated sorting by applying conveyor sorters and AGVs and studied parcel sorting in e-commerce warehouses waiting for sorting and delivery Optimisation. The allocation between parcels, picking stations and AGVs was determined to minimise the completion time of processing the last parcel. A mixed integer linear programming model was established based on this problem, and a particle swarm optimisation (PSO) algorithm was used to solve the problem. Numerical experiments show that the proposed PSO algorithm can solve the model efficiently, and the sensitivity analysis makes suggestions for the arrangement of trailer positions. Leung et al. [11] proposed a picking and sorting order batch method as a system-based solution, by combining cloud database management, fuzzy logic and genetic algorithm methods. IOHS development and application of the concept of ‘warehouse delay’ was used to effectively generate a B2B order grouping solution. The solution facilitates order processing under FTWB and VTWB setups and results show a significant increase in order throughput. He and Meng et al. [12] developed an approximate solution to study the throughput capability of the system by using aggregation techniques and matrix geometry methods. This model is suitable for supporting the rapid design of complex zone picking systems, including zone number and length, input and output buffer capacity, and storage allocation of products to zones to meet pre-specified performance targets. A comparison of approximate results with simulations shows that the average relative error in system throughput is typically less than 5% for a wide range of parameters. The model accurately predicts throughput loss due to congestion and blocking at the merge and can be used to allocate input and output buffer space to maximise the throughput capability of the system.

Through the analysis of related sorting and the optimisation research of related scholars in sorting and transmission, it shows the importance of sorting in the overall logistics transmission chain, and improving the sorting efficiency of the logistics transmission chain is very important for the entire logistics system. Therefore, in this paper, we use the data mining clustering method to sort related items, classify and merge variables according to aggregation and decentralised clustering methods, and optimise the intelligent transmission of the entire logistics chain combined with effectiveness experiments, improve the efficiency of sorting operations, and at the same time improve the efficiency and stability of the entire logistics level, providing a strong guarantee for the development of the society and the logistics industry.

Overview of variable clustering

In the logistics intelligent sorting and conveying chain, there are often several variables, and the variables have a group structure. Cluster analysis is an analysis process that divides samples or variables with high similarity into one class, and its main goal is to classify the collected data based on similarity. Cluster analysis is widely used in many disciplines, such as mathematics, statistics and so on. Under the influence of artificial intelligence, data mining, as an important tool for data analysis, has become more and more common in applications from academic research to market analysis. Sisman and Aydinoglu [13] improves the performance of large national real estate valuation by applying dataset optimisation and spatially constrained multivariate clustering analysis, which defines geographic value clusters to improve valuation accuracy. Park et al. [14] improved the PMF model through cluster analysis, and the improved source coordination process allowed for more sources, clearly specified ambiguous sources, and the identification of secondary sources for specific sites. For variable clustering, it is necessary to define the degree of intimacy between variables, give a measure of the similarity between variables, and then define the variable distance, and then select a clustering technique to cluster the variables. Commonly used clustering algorithms are mainly divided into structural and decentralised. General clustering algorithms are mainly divided into five categories [15–18], as shown in Table 1.

Table 1

Different clustering algorithms and their feature tables

Types	Characteristic
Partition-based clustering Algorithms	Heuristic algorithm, difficult to deal with complex data
Hierarchical class	Sensitive to data entry order
Density based	Very sensitive to custom user parameters
Grid based	Grid granularity is not easy to control
Based on neural network	Grid fixed structure, long training time

The partition-based clustering algorithm first defines the indicator function, but most of its algorithms are heuristic algorithms, which are difficult to deal with large-scale data types, easy to fall into a local minimum, and weak in noise processing [19,20]; In clustering algorithms, the segmentation between levels is highly dependent, and as long as the aggregation is performed, the results cannot be modified [21–23]; density-based clustering algorithms use the density function for clustering, and the nodes are continuously expanded according to the clustering, which can handle any data type, but is sensitive to custom user parameters [24–26]; the grid-based clustering algorithm is a discretised method to process spatial data, but the grid particles are not easy to control, and the parameter sensitivity is high [27, 28]; the clustering algorithm based on neural network has some shortcomings, mainly due to the long training time [29, 30].

Optimal design of the sorting system model of the logistics distribution centre

3.1

Data Mining Clustering Algorithms

At present, all walks of life are using cluster analysis to divide objects with the same or similar attributes into one or more subsets through a mathematical algorithm. At present, it is widely used in machine learning, data mining, image analysis and other fields. Clustering algorithms can be divided into two types: structural type and decentralised type according to the form of clustering. The former is reclassified by successful clusters, and the initial N samples are regarded as independent N clusters, which are continuously aggregated through a certain clustering algorithm or an iterative algorithm. The method is mainly divided into partition-based, hierarchical-based, density-based, grid-based, and neural network-based clustering algorithms. The selection of the clustering algorithm is shown in Figure 2.

Algorithm classification and characteristics

The latter is to determine the classification at one time and perform the division of the set or the merge operation of the set according to the given set of elements. The method is mainly divided into clustering hierarchical clustering method and decentralised hierarchical clustering method. The specific hierarchical clustering effect is shown in Figure 3. This paper adopts the clustering hierarchical clustering algorithm.

Aggregation and Decomposition Hierarchical Clustering Operation Flow

3.2

Variable Clustering

3.2.1

Determination of variable affinity

Variable cluster analysis is classified according to the degree of closeness and similarity of variables in features. To express it intuitively, this section gives two variables. $X_{i} = {(x_{1 i}, x_{2 i}, \dots, x_{n i})}^{T}$ , $X_{j} = {(x_{1 j}, x_{2 j}, \dots, x_{n j})}^{T}$ , $x_{t i} (t = 1, \dots n)$ is the t observation of the variable, $x_{t j} (t = 1, \dots n)$ is the t-th observation of the variable. Let C_ij X_i and X_j be the similarity coefficient, $| C_{i j} |$ . The closer to 1 the closer the two variables are, and vice versa.

3.2.2

Similarity coefficient between variables

Common types of variables are qualitative and quantitative variables. In this paper, quantitative variables are mainly used, and the commonly used similarity coefficients are the cosine of the included angle and the correlation coefficient. The specific definition expression is as follows: 1 $\begin{aligned} C_{i j} = \cos θ_{i j} = \frac{\sum_{i = 1}^{n} x_{t i} x_{t j}}{\sqrt{\sum_{i = 1}^{n} x_{t i}^{2}} \sqrt{\sum_{i = 1}^{n} x_{t j}^{2}}} (i, j = 1, \dots, q) \end{aligned}$ $$\matrix{ {{C_{ij}} = \cos {\theta _{ij}} = {{\mathop \sum \limits_{i = 1}^n {x_{ti}}{x_{tj}}} \over {\sqrt {\mathop \sum \limits_{i = 1}^n x_{ti}^2} \sqrt {\mathop \sum \limits_{i = 1}^n x_{tj}^2} }}\quad (i,j = 1, \ldots ,q)} \cr } $$ 2 $\begin{aligned} C_{i j} = r_{i j} = \frac{\sum_{i = 1}^{n} (x_{t i} - {\bar{x}}_{i}) (x_{t i} - {\bar{x}}_{j})}{\sqrt{\sum_{i = 1}^{n} {(x_{t i} - {\bar{x}}_{i})}^{2}} \sqrt{\sum_{i = 1}^{n} {(x_{t j} - {\bar{x}}_{j})}^{2}}} (i, j = 1, \dots, q) \end{aligned}$ $$\matrix{ {{C_{ij}} = {r_{ij}} = {{\mathop \sum \limits_{i = 1}^n ({x_{ti}} - {{\bar x}_i})({x_{ti}} - {{\bar x}_j})} \over {\sqrt {\mathop \sum \limits_{i = 1}^n {{({x_{ti}} - {{\bar x}_i})}^2}} \sqrt {\mathop \sum \limits_{i = 1}^n {{({x_{tj}} - {{\bar x}_j})}^2}} }}\quad (i,j = 1, \ldots ,q)} \cr } $$

In formula (1–2), the distance method for measuring samples needs to be given. There are single linkage, full linkage, group average, and median algorithms, in addition to the gravity centre method and square sum of deviations for calculating the similarity distance between classes.

3.2.2.1

Single chain method

The two classes with the closest distance between classes are merged, and the specific distance formula is as follows: 3 $\begin{aligned} D_{p q} = min_{i \in C_{p} j \in C_{q}} {d_{i j}}, p \neq q \end{aligned}$ $$\matrix{ {{D_{pq}} = \mathop {\min }\limits_{i \in {C_p}\;j \in {C_q}} \{ {d_{ij}}\} ,\quad p \ne q} \cr } $$

3.2.2.2

Full connection method

Refers to the aggregation of classes according to the longest distance between clusters. The specific distance formula is as follows: 4 $\begin{aligned} D_{p q} = max_{i \in C_{p} j \in C_{q}} {d_{i j}} \end{aligned}$ $$\matrix{ {{D_{pq}} = \mathop {\max }\limits_{i \in {C_p}\;j \in {C_q}} \{ {d_{ij}}\} } \cr } $$

3.2.2.3

Group averaging

The distance between clusters is equal to the average distance between two cluster objects. The specific distance formula is as follows: 5 $\begin{aligned} D_{p q}^{2} = \frac{1}{N_{p} \cdot N_{q}} \cdot \sum i \in C_{p} \sum i \in C_{q} d_{i j}^{2} \end{aligned}$

3.2.2.4

Centre of gravity method

The distance between clusters is represented by the centroid distance of the clusters. The specific distance formula is as follows: 6 $\begin{aligned} D_{p q} = ({\bar{X}}^{(p)} - {\bar{X}}^{(q)}) \cdot ({\bar{X}}^{(p)} - {\bar{X}}^{(q)}) \end{aligned}$ $$\matrix{ {{D_{pq}} = \left( {{{\bar X}^{(p)}} - {{\bar X}^{(q)}}} \right) \cdot \left( {{{\bar X}^{(p)}} - {{\bar X}^{(q)}}} \right)} \cr } $$

Among them, c_p and c_q. The centrer of gravity area ${\bar{X}}^{(p)}$ and ${\bar{X}}^{(q)}$ .

3.2.2.5

Median method

The distance between clusters is based on the single linkage and the full linkage method, and the median value is expressed by the single linkage and the full linkage. The specific distance formula is as follows: 7 $\begin{aligned} D_{k r}^{2} = \frac{1}{2} \cdot D_{k p}^{2} + \frac{1}{2} \cdot D_{k q}^{2} + \frac{1}{2} \cdot D_{p q}^{2} \end{aligned}$

Among them, c_r is the aggregation of c_p and c_q; c_k is any other cluster.

3.2.2.6

The sum of the squared deviation method

According to the mathematical method, the specific distance formula is as follows: 8 $\begin{aligned} S = \sum_{t = 1}^{k} \sum_{α = 1}^{N_{t}} (X_{(t)}^{(α)} - {\bar{X}}_{(t)}) \cdot (X_{(t)}^{(α)} - {\bar{X}}_{(t)}) \end{aligned}$ $$\matrix{ {S = \mathop \sum \limits_{t = 1}^k \mathop \sum \limits_{\alpha = 1}^{{N_t}} \left( {X_{(t)}^{(\alpha )} - {{\bar X}_{(t)}}} \right) \cdot \left( {X_{(t)}^{(\alpha )} - {{\bar X}_{(t)}}} \right)} \cr } $$

This paper uses the Fisher distance to verify the optimal solution for hierarchical clustering, where the distance F_jk between the j cluster and the k cluster is: 9 $\begin{aligned} V_{j} = \frac{1}{n_{j}} \cdot \sum_{h = 1}^{n_{j}} x_{h} \end{aligned}$ 10 $\begin{aligned} D_{i j} = ‖ V_{i} - V_{j} ‖ \end{aligned}$ 11 $\begin{aligned} σ_{j}^{2} = \frac{1}{n_{j}} \cdot \sum_{h = 1}^{n_{j}} {| x_{h} - V_{j} |}^{2} \end{aligned}$ 12 $\begin{aligned} F_{i j} = \frac{D_{j k}}{\sqrt{σ_{j}^{2} + σ_{k}^{2}}} \end{aligned}$

Among them, V_i and V_j are the cluster centroids of the i class and the j class, respectively; n_j indicates the number of elements of the j class; $σ_{j}^{2}$ and $σ_{k}^{2}$ are the variances of the j class and the k class, respectively.

3.3

Group Structure Recognition Algorithm

The variable group structure identification algorithm designed in this paper uses the hierarchical clustering method to cluster variables, and uses sampling to obtain the Rand index for multiple adjustments so that the number of clusters when the average value of the Rand index reaches the maximum is used as the final number of groups. Specific steps are as follows:

3.3.1

Self-help method

To extract the complex sample useful information without omission, it is necessary to process the sample data. Suppose a given dataset contains m samples, and then sample the dataset m times with replacement to generate a training set of m samples. During the whole process: the probability of being selected is $\frac{1}{m}$ . The probability of not being selected is $1 - \frac{1}{m}$ . When m tends to infinity, the probability of not being selected tends to be 0.368, and the samples left in the training set are 63.2% of the original ones. This method enables efficient estimation. Adjust the Rand coefficient. In this paper, the maximum value of the average value of the adjusted Rand coefficients under different clusters is used to determine the number of clusters. The definition expression is: 13 $\begin{aligned} R I = \frac{e + h}{e + f + g + h} \end{aligned}$

Among them, e, h, f and g are the set of n objects, respectively, and divide U and V into the same class and the same class; different classes and different classes; the same class and different classes; different classes and the same class.

In addition, the specific calculation process of adjusting the Rand coefficient is as follows: 14 $\begin{aligned} A R I = \frac{R I - E (R I)}{max (R I) - E (R I)} \end{aligned}$ $$\matrix{ {ARI = {{RI - E(RI)} \over {\max (RI) - E(RI)}}} \cr } $$

Among them 15 $\begin{aligned} R I = \sum_{i, j} (\begin{matrix} n_{i j} \\ 2 \end{matrix}) \end{aligned}$ $$\matrix{ {RI = \mathop \sum \limits_{i,j} \left( {\matrix{ {{n_{ij}}} \cr 2 \cr } } \right)} \cr } $$ 16 $\begin{aligned} E (R I) = \frac{\sum_{i} (\begin{matrix} n_{i} \\ 2 \end{matrix}) \sum_{j} (\begin{matrix} n_{j} \\ 2 \end{matrix})}{(\begin{matrix} n \\ 2 \end{matrix})} \end{aligned}$ $$\matrix{ {E(RI) = {{\mathop \sum \limits_i \left( {\matrix{ {{n_i}} \cr 2 \cr } } \right)\mathop \sum \limits_j \left( {\matrix{ {{n_j}} \cr 2 \cr } } \right)} \over {\left( {\matrix{ n \cr 2 \cr } } \right)}}} \cr } $$ 17 $\begin{aligned} max (R I) = \frac{1}{2} [\sum_{i} (\begin{matrix} n_{i} \\ 2 \end{matrix}) \sum_{j} (\begin{matrix} n_{j} \\ 2 \end{matrix})] \end{aligned}$ $$\matrix{ {\max (RI) = {1 \over 2}\left[ {\mathop \sum \limits_i \left( {\matrix{ {{n_i}} \cr 2 \cr } } \right)\mathop \sum \limits_j \left( {\matrix{ {{n_j}} \cr 2 \cr } } \right)} \right]} \cr } $$

3.3.2

Group structure algorithm steps

Assuming that there are n samples in the data set and the number of variables is q, the steps of the variable group structure identification algorithm are as follows: (a)

Use the bootstrap method to extract n samples from the original data set to obtain the data set S.

(b)

Normalise the q variables of dataset S.

(c)

Calculate the q variable distances D for the dataset S.

(d)

Clustering the q variables using hierarchical clustering and adjusting for ARI.

(e)

Repeat (a)–(d) to calculate the average of the Rand index.

(f)

Determine the optimal number of variable categories.

(g)

Normalise the original dataset to calculate the distance D for the q variables.

(h)

Use hierarchical clustering to cluster q variables into k categories, and record the category labels of each variable.

Model establishment and analysis of logistics parcel intelligent sorting system

The data source of this paper and the manual sorting system in operation include customer order, inventory status, product variety, product specification, product weight and other information. We run simulations under two conditions: one assumes that the variables assigned to each group are uniformly grouped, and the other assumes that the variables per group are not uniformly grouped. In addition, according to the use of six inter-cluster distance calculation methods and the clustering effect, this paper uses the median method and the single connection method for clustering and combines the needs of practical work to reasonably divide the number of clusters. The validity of its classification results is verified. Finally, the results of this paper select an optimal item allocation method based on the user-defined range of the number of partitions.

The verification of the classification results needs to use the Fisher distance. According to the actual needs, the classification range is set to 2–5 partitions, that is, 2≤ Z≤ 5, and a red line is used as the benchmark for segmentation, and the ordinate D is the distance between the clusters. The horizontal axis G represents the item information. Based on different colours, the clustering situation under different segmentation conditions is distinguished. For the segmentation of the clustering results of the single connection method, two results are finally divided into two partitions and three partitions.

As can be seen from the Figures 4 and 5, it can be determined that when the number of points is 3 by the single connection method, the corresponding segmentation value is F3 = 5.8; when the number of points is 4, the corresponding segmentation value is F4 = 4.66. When using this classification method, the item allocation distance is more advantageous. When using the single connection method, the number of points is 3, and the corresponding value of segmentation is F3 = 2.94; when the number of points is 4, the corresponding value of segmentation is F4 = 2.35. When using this classification method, the results of item distribution are relatively uniform.

Single-connection method for clustering segmentation

Conclusion

By comparing the clustering and segmentation results of the two distance calculation methods, it is concluded that each calculation method has its advantages and disadvantages, logistics distribution time cost and logistics package distribution accuracy. Combining the characteristics of the data, conclusions can be drawn about the median method and the single connection method, which are summarised as follows:

Analysis of the internal compactness of clusters, the distance between clusters, and the distribution of samples, the single-connection clustering results are more in line with the needs of real data than the median method, and the allocation time is faster, but at the same time the sample distribution The results show that the sample distribution of the median method is more accurate.

From the analysis of the compactness of the clustering, the median method and the sample data in practical applications are more densely clustered, but there are obvious differences in the compactness within each cluster, and it also supports more partition ways.

From the analysis of the distance between clusters, the distance between clusters of the single connection method is better, the cluster assignment will be better and clearer, and the distance between clusters of the median method is less prominent.

From the analysis of the distribution results of item distribution, the median method makes the distribution of items more evenly distributed under the partition.

Figure e tabelle

Different clustering algorithms and their feature tables

Types	Characteristic
Partition-based clustering Algorithms	Heuristic algorithm, difficult to deal with complex data
Hierarchical class	Sensitive to data entry order
Density based	Very sensitive to custom user parameters
Grid based	Grid granularity is not easy to control
Based on neural network	Grid fixed structure, long training time

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Applied Mathematics and Nonlinear Sciences

Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method

Shenghua Yan e
Shenghua Yan e
Lei Huang
Lei Huang

Pubblicato online: 15 Dec 2022

Volume & Edizione: AHEAD OF PRINT

Pagine: -

Ricevuto: 02 Jun 2022

Accettato: 16 Jun 2022

Dettagli rivista e numero

Applied Mathematics and Nonlinear Sciences

Anteprima PDF

Articolo

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Figure e tabelle

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Different clustering algorithms and their feature tables

Riferimenti

Articoli recenti

Pianifica la tua conferenza remota con Sciendo

Applied Mathematics and Nonlinear Sciences

Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method

Shenghua Yan eShenghua Yan eLei HuangLei Huang

Pubblicato online: 15 Dec 2022

Volume & Edizione: AHEAD OF PRINT

Pagine: -

Ricevuto: 02 Jun 2022

Accettato: 16 Jun 2022

Dettagli rivista e numero

Applied Mathematics and Nonlinear Sciences

Anteprima PDF

Articolo

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Figure e tabelle

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Different clustering algorithms and their feature tables

Riferimenti

Articoli recenti

Pianifica la tua conferenza remota con Sciendo

Shenghua Yan e
Shenghua Yan e
Lei Huang
Lei Huang