## Qiang Xiao , Shuangshuang Yao and Mengjun Qiang## |

The total goal | First level index | The two level index |
---|---|---|

Evaluation of supply chain collaboration A | Capital flow [TeX:] $$\mathrm{B}_{1}$$ | Net assets income rate [TeX:] $$\mathrm{C}_{1}$$ |

Sales profit rate [TeX:] $$\mathrm{C}_{2}$$ | ||

Sales growth rate [TeX:] $$\mathrm{C}_{3}$$ | ||

Receivable turnover rate [TeX:] $$\mathrm{C}_{4}$$ | ||

Inventory turnover rate [TeX:] $$\mathrm{C}_{5}$$ | ||

Current ratio [TeX:] $$\mathrm{C}_{6}$$ | ||

Cash flow liability ratio [TeX:] $$\mathrm{C}_{7}$$ | ||

Interest guarantee multiples [TeX:] $$\mathrm{C}_{8}$$ | ||

Asset-liability ratio [TeX:] $$\mathrm{C}_{9}$$ | ||

Operating Cost Ratio [TeX:] $$\mathrm{C}_{10}$$ | ||

Business flows [TeX:] $$\mathrm{B}_{2}$$ | Product qualified rate [TeX:] $$\mathrm{C}_{11}$$ | |

Timely delivery rate [TeX:] $$\mathrm{C}_{12}$$ | ||

Delivery accuracy rate [TeX:] $$\mathrm{C}_{13}$$ | ||

The core of enterprise production and marketing rate [TeX:] $$\mathrm{C}_{14}$$ | ||

Warehouse utilization rate [TeX:] $$\mathrm{C}_{15}$$ | ||

Supplier return rate [TeX:] $$\mathrm{C}_{16}$$ | ||

The supplier’s timely delivery rate [TeX:] $$\mathrm{C}_{17}$$ | ||

Supplier order satisfaction rate [TeX:] $$\mathrm{C}_{18}$$ | ||

Information flow[TeX:] $$\mathrm{B}_{3}$$ | Supply chain information sharing rate [TeX:] $$\mathrm{C}_{19}$$ | |

Timeliness of information transmission [TeX:] $$\mathrm{C}_{20}$$ | ||

Accuracy of information transmission [TeX:] $$\mathrm{C}_{21}$$ |

In matter–element analysis, the object M and its feature C and magnitude X constitute the matter element R. Then according to the matter-element analysis method combined with the characteristics and value of objects, the functional relationship between objects can be established, as follows:

If the magnitude X in the matter-element model is ambiguous, then it is a fuzzy matter element. If the object M has n features [TeX:] $$C_{1} C_{2} \ldots C_{n}$$ and corresponding magnitudes [TeX:] $$X_{1} X_{2} \ldots X_{n},$$ then R is an n-dimensional fuzzy matter element, expressed as:

**Step 1.** The classical domain matrix is a matter-element matrix composed of the standard range of things and their characteristics, denoted as R.

In Formula (3), [TeX:] $$N_{j}$$ Nj represents the jth evaluation grade, [TeX:] $$C_{i}$$ represents the ith evaluation index, and [TeX:] $$X_{j i}=\left(a_{j i}, b_{j i}\right)$$ represents the range of the evaluation parameter [TeX:] $$C_{i}$$ in evaluation grade [TeX:] $$N_{j},$$ which becomes the classical domain.

**Step 2.** The nodal domain matrix is composed of describing objects, their features and corresponding ranges of magnitude, denoted as [TeX:] $$R_{p}.$$

Among them, NP denotes the totality of the evaluation grade, [TeX:] $$C_{i}$$ Ci represents the ith evaluation index, [TeX:] $$X_{p i}=\left(A_{P I}, B_{P I}\right)$$ represents all values of [TeX:] $$C_{i},$$ that is, section field of p.

**Step 3.** Determine the matter-element matrix to be tested.

Among them, [TeX:] $$R_{d}$$ represents the matter element to be evaluated, [TeX:] $$N_{i}$$ is the ith thing, and [TeX:] $$C_{i}$$ is the ith eigenvalue.

**Step 1.** Fuzzy matter-element with preferential membership

The corresponding fuzzy value of each individual index is subordinate to the corresponding fuzzy value that is, in turn, subordinate to the corresponding evaluation index of the standard scheme, which is called subordinate–superior–subordinate degree. Large eigenvalues of each evaluation index are suitable for scheme evaluation, whereas small and different formulas are used for calculating different membership degrees. The relativity of each synergistic index is reflected in the following form:

(1) Bigger is better

(2) The smaller the better

In formula (7), [TeX:] $$U_{i j}$$ denotes optimal membership degree, while max [TeX:] $$X_{i j}$$ and min [TeX:] $$X_{i j}$$ denote the maximum and minimum values of each evaluation index in each scheme respectively.

**Step 2.** Standard deviation fuzzy matter-element [TeX:] $$R_{0 n}$$ refers to the maximum or minimum values of the optimal membership degree of each evaluation index in the fuzzy matter-element [TeX:] $$R_{m n} \text {. If } \Delta_{i j}$$ represents the square of each difference in the standard fuzzy matter-element [TeX:] $$R_{m n},$$ then the difference square composite fuzzy matter-element [TeX:] $$R_{\Delta}$$ is established [30-32]. That is [TeX:] $$\Delta_{i j}=\left(U_{Q j}-U_{i j}\right)^{2},$$ which can be expressed as:

**Step 3.** Determination of entropy weight

(1) The judgment matrix of M evaluation indexes and N things [TeX:] $$R_{\Delta}\left(\Delta_{i j}\right)_{m n}$$ is constructed.

2) The judgment matrix is normalized as [TeX:] $$b_{i j}=\frac{\Delta_{i j}-\Delta_{\min }}{\Delta_{\max }-\Delta_{\min }} \text { or } b_{i j}=\frac{\Delta_{\max }-\Delta_{i j}}{\Delta_{\max }-\Delta_{\min }}$$ or [TeX:] $$b_{i j}=\frac{\Delta_{\max }-\Delta_{i j}}{\Delta_{\max }-\Delta_{\min }}$$ to obtain [TeX:] $$B\left(b_{i j}\right)_{m n}.$$

In formula (11), [TeX:] $$b_{i j}=\frac{b i j}{\sum b i j}.$$

(3) Determine the entropy of evaluation index

This study determines the meaning of [TeX:] $$\ln f_{i l}$$ as follows. When [TeX:] $$f_{i j}=0,$$ according to the practical significance of supply chain coordination evaluation, [TeX:] $$\ln f_{i l}$$ can be understood as a large number. When multiplied with [TeX:] $$f_{i j} \text { to } 0, f_{i j} \cdot \ln f_{i j}=0.$$ However, [TeX:] $$f_{i j}=1, f_{i j} \cdot \ln f_{i j}=0,$$ which are clearly contrary to the degree of information disorder reflected by entropy, which is not practical. Therefore, [TeX:] $$f_{i j}$$ needs to be modified as:

(4) Calculation evaluation index w

where [TeX:] $$\sum_{i=1}^{m} W_{j}=1.0 \leq W_{j} \leq 1.$$

**Step 4.** The closeness of the matter-element to be evaluated is calculated to judge the grade of the object of study. The closeness refers to the correlation between the matter-element samples and the standard ones. The large value indicates high correlation and the small value indicates low correlation between the two samples. The calculation of the closeness reflects the merits and demerits of the matter element to be evaluated.

In this study, the Euclidean distance is chosen as the basis for calculating the degree of closeness, which is expressed as:

In formula (15), [TeX:] $$P H_{j}=1-\sqrt{\sum_{i=1}^{m} w_{i} \Delta_{i j} \quad(j=1,2, \cdots n)}.$$

In this study, Gree Electric Appliances Inc. of Zhuhai, is selected as the representative company to study the degree of synergy between upstream and downstream enterprises. Gree Electric Appliances Inc. of Zhuhai is established in 1991 as a collection of research and development, production, sales, and service in one of the international home appliances manufacturing companies. Their main home appli¬ances are refrigerators, washing machines, and air conditioners. Its products are sold all over the world and have a high reputation. This enterprise is thus representative of the industry and is suitable to study the change trends of its upstream and downstream coordination. By investigating the production, sales, and R&D departments, and analyzing the annual report, the original order parameter data representing the development level of the company’s synergy from 2011 to 2017 is obtained (Table 2).

Table 2.

Index | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |
---|---|---|---|---|---|---|---|

[TeX:] $$\mathrm{C}_{1}$$ | 0.3316 | 0.3138 | 0.3577 | 0.3523 | 0.2731 | 0.3041 | 0.3744 |

[TeX:] $$\mathrm{C}_{2}$$ | 0.0761 | 0.0882 | 0.1087 | 0.1216 | 0.1525 | 0.1711 | 0.1518 |

[TeX:] $$\mathrm{C}_{3}$$ | 0.0211 | 0.0293 | 0.0416 | 0.0325 | 0.01316 | 0.03705 | 0.3692 |

[TeX:] $$\mathrm{C}_{4}$$ | 17.1404 | 18.3805 | 17.8434 | 41.99 | 8.8209 | 12.1805 | 25.0291 |

[TeX:] $$\mathrm{C}_{5}$$ | 4.7509 | 5.7625 | 9.0399 | 20.7824 | 10.3173 | 13.8012 | 6.0092 |

[TeX:] $$\mathrm{C}_{6}$$ | 1.1178 | 1.0794 | 1.075 | 1.1085 | 1.0739 | 1.0337 | 1.163 |

[TeX:] $$\mathrm{C}_{7}$$ | 0.0589 | 0.2335 | 0.1344 | 0.1719 | 0.394 | 0.1171 | 0.1109 |

[TeX:] $$\mathrm{C}_{8}$$ | 14.9794 | 19.9937 | 16.6154 | 18.7793 | 8.7299 | 4.8244 | 62.716 |

[TeX:] $$\mathrm{C}_{9}$$ | 0.816 | 0.7899 | 0.7362 | 0.639 | 0.6754 | 0.673 | 0.6714 |

[TeX:] $$\mathrm{C}_{10}$$ | 0.7843 | 0.7436 | 0.7347 | 0.8284 | 0.6996 | 0.6988 | 0.6891 |

[TeX:] $$\mathrm{C}_{11}$$ | 0.89 | 0.9 | 0.91 | 0.92 | 0.93 | 0.95 | 0.997 |

[TeX:] $$\mathrm{C}_{12}$$ | 0.98 | 0.99 | 0.992 | 0.995 | 0.995 | 0.999 | 0.999 |

[TeX:] $$\mathrm{C}_{13}$$ | 0.98 | 0.98 | 0.99 | 0.992 | 0.993 | 0.999 | 0.999 |

[TeX:] $$\mathrm{C}_{14}$$ | 0.96 | 0.97 | 0.95 | 0.99 | 0.99 | 0.996 | 0.996 |

[TeX:] $$\mathrm{C}_{15}$$ | 0.94 | 0.95 | 0.97 | 0.98 | 0.94 | 0.99 | 0.98 |

[TeX:] $$\mathrm{C}_{16}$$ | 0.025 | 0.026 | 0.01 | 0.02 | 0.015 | 0.015 | 0.01 |

[TeX:] $$\mathrm{C}_{17}$$ | 0.86 | 0.89 | 0.895 | 0.90 | 0.91 | 0.99 | 0.98 |

[TeX:] $$\mathrm{C}_{18}$$ | 0.87 | 0.85 | 0.90 | 0.91 | 0.925 | 0.93 | 0.95 |

[TeX:] $$\mathrm{C}_{19}$$ | 0.90 | 0.95 | 0.96 | 0.98 | 0.97 | 0.99 | 0.95 |

[TeX:] $$\mathrm{C}_{20}$$ | 0.85 | 0.87 | 0.89 | 0.90 | 0.89 | 0.90 | 0.98 |

[TeX:] $$\mathrm{C}_{21}$$ | 0.89 | 0.88 | 0.90 | 0.93 | 0.90 | 0.96 | 0.97 |

Construct the compound fuzzy matter-element according to Eq. (5).

The optimal membership matrix [TeX:] $$R_{21 \times 7}$$ is calculated from Eq. (8).

Construct a difference squared fuzzy complex element matrix [TeX:] $$R_{\Delta}\left(\Delta_{i j}\right)_{21 \times 7}$$ according to the standard fuzzy matter element and the preferred membership degree matrix [TeX:] $$R_{m n}.$$

Using the entropy method to determine the weight

(a) Matrix [TeX:] $$B\left(b_{i j}\right)_{m n}$$ can be obtained from formula (11). [TeX:] $$b_{i j}=\frac{b i j}{\sum b i j}$$

(b) [TeX:] $$F_{i j}$$ matrix obtained from formula (13).

(c) Entropy [TeX:] $$H_{i}$$ can be obtained from formula (12).

[TeX:] $$\begin{aligned} &H_{i}=(0.0498,0.0488,0.0422,0.0469,0.0457,0.0485,0.0462,0.0447,0.0458,0.0469,0.0463, \\ &0.0514,0.0490,0.0501,0.0480,0.0475,0.0476,0.0497,0.05111,0.0475,0.0463) \end{aligned}$$

(d) Weight [TeX:] $$W_{i}$$ of Indicators Obtained from formula (14).

[TeX:] $$\begin{aligned} &W_{i}=(0.0498,0.0488,0.0422,0.0469,0.0457,0.0485,0.0462,0.0447,0.0458,0.0469,0.0463 \\ &0.0514,0.0490,0.0501,0.0480,0.0475,0.0476,0.0497,0.0511,0.0475,0.0463) \end{aligned}$$

Calculating evaluation grade.

According to (15), the European proximity degree [TeX:] $$R_{P H}$$ can be obtained.

[TeX:] $$R_{P H}=[0.1740,0.2730,0.3298,0.4299,0.3201,0.4117,0.5407]$$

First, the weights of 21 order parameters are obtained using the entropy weight method. The calculation results are as follows. The indicators for capital flow subsystem are the net asset income rate [TeX:] $$C_{1},$$ sales profit rate [TeX:] $$C_{2},$$ and current ratio [TeX:] $$C_{6};$$ the indicators for business flow subsystem are delivery time rate [TeX:] $$C_{12},$$ delivery accuracy rate [TeX:] $$C_{13},$$ core enterprise production and sales rate [TeX:] $$C_{14},$$ warehouse utilization rate [TeX:] $$C_{15},$$ and supply business order fulfillment rate [TeX:] $$C_{18} ;$$ and the indicator for information flow subsystem is the supply chain information sharing rate [TeX:] $$C_{19 .}$$ The weights of these indicators account for a relatively large average of 0.048. Therefore, Gree Electric Appliances Inc. of Zhuhai should focus on improving the aforementioned order parameters to enhance their collaboration with upstream and downstream enter¬prises.

Fig. 2 illustrates the data of the Euclid approach degree; RPH. Fig. 1 shows that the synergistic degree has increased annually from 2011 to 2014, and the synergistic development is stable. However, the collaboration in 2015 is lower than that in 2014. Table 2 shows that the raw data (i.e., accounts receivable turnover rate, inventory turnover rate, interest guarantee multiple, warehouse utilization rate and information transmission timely rate) in 2015 decreased compared with those of 2014. This phenomenon directly led to the decrease of synergy in 2015. Among the raw data, the turnover rate of accounts receivable in 2015 decreased by 33.1691 units compared with that in 2014. This finding indicates that the working capital in 2015 was lax in accounts receivables, which affected the normal capital turnover and solvency. The inventory turnover rate in 2015 decreased by 10.465 units compared with that in 2014. This occurrence indicates a slow inventory turnover in 2015, and no balance was observed between sales and inventory. The interest coverage ratio decreased by 10.0114 units, which indicates that the enterprise solvency declined in 2015. The utilization of warehouses in 2015 is slightly lower than that in 2014. Each order parameter controls the collaboration among subsystems in the composite system, which in turn affects the overall collaboration. Therefore, Gree Electric Appliances Inc. of Zhuhai should improve the low-level order parameters to achieve enhanced collaboration.

With the intensification of competition in the global market, the collaboration between the upstream and downstream enterprises in the supply chain to form mutual dependence, mutual cooperation, and common growth is an inevitable trend. On the basis of previous research, the present study focuses on the supply chain of manufacturing enterprises. Moreover, this work explores the collaboration and synergistic development of upstream and downstream enterprises on the basis of synergistic theory. An improved matter-element algorithm is used to calculate the order parameter weights by using the entropy weight method. The degree of enterprise cooperation is calculated by the European closeness algorithm. Thus, better accuracy can be obtained given that this algorithm avoids the disadvantages of subjectively determining the feature value and the correlation degree in the traditional matter-element algorithm. This method can also provide suggestions for companies to improve collaboration.

The collaboration model of Gree Electric Appliances Inc. of Zhuhai is established on the basis of synergistic theory and matter-element algorithm. The three subsystems and 21 order parameters of the company and the upstream and downstream enterprises are selected. Their development status is measured according to actual data from 2011 to 2017. Overall, Gree Electric Appliances Inc. of Zhuhai has a good synergistic development trend. However, the synergistic effect is still unstable and needs further improvement. In practice, the cooperation between upstream and downstream enterprises has formed a new type of coordinated development model in a continuous improvement. Enterprises are mutually integrated and promoted for the common benefit. Follow-up research can focus on how to establish the response mechanism under the influence of internal and external environmental factors of manufacturing enterprises, improve the ability of supply chain collaboration to resist sudden problems, and strengthen the construction of soft collaboration ability such as supply chain cost, comprehensive quality of labor force, industrial chain supporting, and logistics cost service system and infrastructure.

He received M.S. degrees in School of electronic information and electrical engineering from Lanzhou Jiaotong University in 2007, and Ph.D. degree in School of Traffic and Transportation from Lanzhou Jiaotong University in 2017. He is currently a professor in School of Economics and Management, Lanzhou Jiaotong University, Gansu, China. His research interests include data mining and data analysis.

She received M.S. degrees in School of Economics and Management from Lanzhou Jiaotong University in 2020. Since September 2020, she is with Business School of Tianjin University of Finance and Economics, Tianjin, China as a Ph.D. candidate. His current research interests include social network analysis and network organization governance

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