Selection of Logistics Service Provider for port enterprises: Combination of the weighting-grey synthetic decision-making method

Abstract

The purpose of this paper is to explore how port enterprises can scientifically select a better logistic service provider (LSP) to achieve a high efficiency. An empirical study is conducted to verify the effectiveness of the combination weighting-grey synthetic decision-making method by helping the LSP selection of a port enterprise in China. Data are collected from questionnaires administered to port logistics’ industry professionals. The method is proposed, which associates the analysis network process method with the entropy method to determine the combined weights of the evaluation indexes. The improved centre-point triangular whitenization weight function is introduced to cluster the alternative port LSPs and judge the corresponding grey classes. Subsequently, the synthetic weighted decision-making vectors are used to determine the grey synthetic decision-making coefficient vectors. The grey synthetic clustering decision-making coefficients are calculated to establish a synthetic decision-making rank of the alternative plans. The combined method can help the port enterprises realize the selection of better LSPs in a scientific manner.

Keywords

Combination weighting grey synthetic decision-making logistics service provider selection

1 Introduction

With the globalization of the economic market, logistics is now seen as a key area in which industries can cut costs and improve their customer service quality [1]. Each outsourcing company has its unique needs for the logistics support from a provider [2]. The reasonable selection of logistics service providers (hereinafter referred to as LSPs) is one of the key issues that enterprises need to address. Generally, the decisions of the enterprises are often unclear and cannot be estimated as an exact numerical value. Thus, realizing a better selection of LSPs is difficult and challenging. Due to the uncertainty of the evaluation process, the problem exhibits a grey character, thereby becoming a complex multiple attribute decision-making problem [3]. Currently, the LSPs of the port enterprises in China are mainly small and medium sized. The overall strength and operation standardization degree of these LSPs is not sufficiently high. In addition, in some cases, the quality of the logistics services provided cannot satisfy the requirements of the port enterprises. Therefore, studying the selection strategy of the LSPs of port enterprises has a certain practical significance to improve the operation efficiency and operation level of the port enterprises.

Many scholars have performed relevant studies in this domain and attempted to solve this problem. Different types of methods have been applied or developed to evaluate the selection of the LSPs considering different aspects. Such methods include analysis network process method (ANP), entropy method, fuzzy Delphi method, grey clustering method, double-layer planning model, combination of the grey relational analysis and the technique for order preference by similarity to ideal solution (TOPSIS) method, combination of the entropy method and the G1 method, and empirical studies. The methods that have been applied in the literature to evaluate and select the LSPs are summarized in Table 1, and further details can be found in [4]. This table also presents the most recently conducted studies. Some scholars used methods other than those mentioned above to study the LSP selections. For example, [5] applied structural equation modelling to test the conceptual model based on the survey data from 245 Chinese third-party logistics (3PL) providers. [6] introduced a fairness entropy function to establish a new game model for determining the optimal number of multifunctional LSPs. Asian et al. [7] used a new method based on the Kano model for evaluating and indexing 3PL providers. Goker [8] introduced an integrated cognitive map-based intuitionistic fuzzy multiple criteria decision aid to rank agile outsourcing provider alternatives and then determine the best performing one. Ilgin [9] proposed a novel third party reverse logistics providers (3PRLPs) evaluation methodology combining linear physical programming (LPP) and fuzzy programming (FP), which considers the uncertainty of budget allocation and capacity, and the determination of 3PRLP order quantity. These authors found that the uncertainty, order frequency, and transaction size, but not the asset specificity, were significantly associated with the third-party purchasing.

Table 1
A summary of methods for LSP selection

Method References

ANP Jharkharia and Shankar [10]; Meade and Sarkis [11]; Yang et al. [12]

ANP and ISM Thakkar et al. [13]

ANN Efendigil et al. [14]

CBR Yan et al. [1]

CBR and RBR and CP Isiklar et al. [15]

AHP Göl and Çatay [16]; Hong and Lee [17]; Singh [18]; So et al. [19]

DEA Azadi and Saen [4]; Haas et al. [20]; Min and Joo [21]; Momeni et al. [22]; Saen [23, 24]; Venkatesh et al. [25]

DEA and AHP Zhang et al. [26]

TOPSIS Gupta et al. [27]

AHP and TOPSIS Min and Perçin [28]

AHP and DEA and LP Falsini et al. [29]

DEMATEL and ANP and VIKOR Liou and Chuang [30]

Fuzzy AHP and fuzzy TOPSIS Singh et al. [31]; Yayla et al. [32]

Fuzzy TOPSIS Bottani and Rizzi [33]; Rashidi and Cullinane [34]

ISM and fuzzy TOPSIS Kannan [35]

Fuzzy AHP Ecer [36]; Qureshi et al. [37]

Intuitionistic fuzzy LP and TOPSIS Li [38]; Wan et al. [39]

Fuzzy LP Li and Wan [40]; Liu and Wang [2]

Fuzzy modelling Bansal et al. [41]; Li et al. [42]

Interval-valued fuzzy-based method Sahu et al. [43]

Method	References
ANP	Jharkharia and Shankar [10]; Meade and Sarkis [11]; Yang et al. [12]
ANP and ISM	Thakkar et al. [13]
ANN	Efendigil et al. [14]
CBR	Yan et al. [1]
CBR and RBR and CP	Isiklar et al. [15]
AHP	Göl and Çatay [16]; Hong and Lee [17]; Singh [18]; So et al. [19]
DEA	Azadi and Saen [4]; Haas et al. [20]; Min and Joo [21]; Momeni et al. [22]; Saen [23, 24]; Venkatesh et al. [25]
DEA and AHP	Zhang et al. [26]
TOPSIS	Gupta et al. [27]
AHP and TOPSIS	Min and Perçin [28]
AHP and DEA and LP	Falsini et al. [29]
DEMATEL and ANP and VIKOR	Liou and Chuang [30]
Fuzzy AHP and fuzzy TOPSIS	Singh et al. [31]; Yayla et al. [32]
Fuzzy TOPSIS	Bottani and Rizzi [33]; Rashidi and Cullinane [34]
ISM and fuzzy TOPSIS	Kannan [35]
Fuzzy AHP	Ecer [36]; Qureshi et al. [37]
Intuitionistic fuzzy LP and TOPSIS	Li [38]; Wan et al. [39]
Fuzzy LP	Li and Wan [40]; Liu and Wang [2]
Fuzzy modelling	Bansal et al. [41]; Li et al. [42]
Interval-valued fuzzy-based method	Sahu et al. [43]

Grey systems theory initiated by Deng [44] is suitable for uncertain and small systems that include many decision makers [45]. This theory has made several contributions to numerous economic applications from various fields such as supply chain management, decision-making processes, and financial performance evaluations [46]. In recent years, grey systems theory has been applied by many researchers to solve the LSP selection problem. Chen et al. [47] combined grey relational analysis and TOPSIS methods and proposed a combination weighting GI-TOPSIS method to realize the selection of the logistics providers. Zhou [48] proposed a multiple objective decision-making model based on grey clustering and entropy weight methods to select the best provider. Rajesh and Ravi [49] used the grey relational analysis method to choose providers and considered the change in the weights to study the sensitivity of the change in the selection results. Pitchipoo et al. [50] combined the entropy method with principal component analysis to solve weights; subsequently, the grey relational analysis method was used to select the providers. Parkouhi et al. [51] proposed Grey Simple Additive Weighting technique (GSAW) to determine the score of each supplier. In general, there is a tendency to combine gray system theory with other decision-making methods for selecting LSP.

However, several shortcomings remain in the selection of the LSPs. For example, the index system cannot accurately reflect the interdependence relationship among the indexes; the manner of solving the index weights relies excessively on expert judgement and other subjective factors, and the degree of attention to objective factors is not sufficiently high; and the manner of handling the grey character of the problem is not appropriate. In this paper, LSP evaluation index system is determined by service quality, business ability, logistics cost, enterprise soft power and cooperation. ANP is used to determine the subjective weight, which is beneficial for the index weight value to fully consider the experts’ professional judgments. Besides, the entropy method is used to determine the objective weight, which reflects the significance of objective factors of evaluation index data. In addition, the calculation of the grey clustering coefficients is determined by using the improved center-point triangle whitenization weight function, which reflects properly handling the grey characteristics of this problem. Accordingly, a combined weighting-grey synthetic decision-making method is proposed, which can help enterprises solve the problem of selecting LSPs, and the effectiveness of the decision-making method is verified through empirical research.

The paper is structured as follows: In Section 2, we constructed and analyzed the LSP suppliers’ evaluation index. In Section 3, combination weighting-grey synthetic decision-making method is proposed to solve the problem of selection of LSP suppliers. In Section 4, a practical example is shown to the effectiveness and the sensitivity analysis on the objects is carried out also. Finally, a conclusion is given in Section 5.

2 Evaluation index system

2.1 Preliminary creation of the evaluation index system

Supplier selection is mainly composed of two aspects: development the index system and researching the selection method. The index system should be systematic, simple, comparable, flexible, independent, dynamic, scientific, efficient, general, and a combination of qualitative and quantitative principles. Li et al. [52] evaluated and chose procurement logistics service providers in the IT industry using the C2 R DEA model and they examined the index system of these providers from five perspectives: business level, resource level, service level, cooperation level, and information level. To assess and choose third-party logistics service providers for medical equipment, Zhang et al. [53] built an evaluation index system based on four factors: basic resources, business operation, monitoring management, and human resources. The five factors of commitment, competence, communication, creativity, and customization, as well as coordination and collaboration, were part of the 5 C framework that Gupta and colleagues [54] proposed. This framework further clarified how the best LSP should be chosen based on the ongoing quality of service. For an enterprise to grow, its soft power is crucial, which also holds for LSP. This paper divides the evaluation factors influencing the choice of LSP for port enterprises into five first-level factors based on a literature review: service quality, business ability, logistics cost, enterprise soft power, and cooperation. This paper further differentiates the first-level indicators into certain second-level indices by the literature of Li et al. [55], Senthil et al. [56], Asian et al. [57], and Huang et al. [58]. To further define the indicators, this paper specifically selected the qualitative or quantitative indicators, as indicated in Table 2.

Table 2
Preliminary evaluation index system and evaluation data for the LSP

First -level indexes Second-level indexes Background of the optimality

Service quality Customer satisfaction rate Quantitative index

Order completion rate Quantitative index

On-time delivery rate Quantitative index

Product integrity rate Quantitative index

Problem handling rate Quantitative index

Service innovation capability Qualitative index

Value-added services Qualitative index

Service flexibility Qualitative index

Business ability Business diversity Qualitative index

Logistics network Qualitative index

Operation management ability Qualitative index

Risk coping ability Qualitative index

Demand analysis ability Qualitative index

Scheme design ability Qualitative index

Working experience Qualitative index

Logistics cost Transportation cost Quantitative index

Storage cost Quantitative index

Circulation processing cost Quantitative index

Handling and carrying costs Quantitative index

Packaging cost Quantitative index

Logistics information and management costs Quantitative index

Enterprise soft power Market share Quantitative index

Enterprise qualification Qualitative index

Enterprise reputation Qualitative index

Professional talent ratio Quantitative index

Corporate culture Qualitative index

Cultural compatibility Qualitative index

Cooperation Cooperation success rate Quantitative index

Informatization degree Qualitative index

Communication level Qualitative index

First -level indexes	Second-level indexes	Background of the optimality
Service quality	Customer satisfaction rate	Quantitative index
	Order completion rate	Quantitative index
	On-time delivery rate	Quantitative index
	Product integrity rate	Quantitative index
	Problem handling rate	Quantitative index
	Service innovation capability	Qualitative index
	Value-added services	Qualitative index
	Service flexibility	Qualitative index
Business ability	Business diversity	Qualitative index
	Logistics network	Qualitative index
	Operation management ability	Qualitative index
	Risk coping ability	Qualitative index
	Demand analysis ability	Qualitative index
	Scheme design ability	Qualitative index
	Working experience	Qualitative index
Logistics cost	Transportation cost	Quantitative index
	Storage cost	Quantitative index
	Circulation processing cost	Quantitative index
	Handling and carrying costs	Quantitative index
	Packaging cost	Quantitative index
	Logistics information and management costs	Quantitative index
Enterprise soft power	Market share	Quantitative index
	Enterprise qualification	Qualitative index
	Enterprise reputation	Qualitative index
	Professional talent ratio	Quantitative index
	Corporate culture	Qualitative index
	Cultural compatibility	Qualitative index
Cooperation	Cooperation success rate	Quantitative index
	Informatization degree	Qualitative index
	Communication level	Qualitative index

2.2 Release and recovery of the questionnaire

According to the preliminary construction of the index system, a survey related to the importance of the evaluation index was designed. A total of 140 copies were delivered to the professionals of the port logistics industry. Subsequently, 132 copies were recovered, of which 120 were valid questionnaires; 12 questionnaires were removed, as some of the questionnaires were not completed, and the others had the same answers. The valid return rate was 85.71%.

The effective SPSS 22.0 software was used to collect the data for the statistical analysis. The main statistical scores of minimum and maximum values and the average and standard deviation of each index are listed in Table 3. A higher index score means that it is more important in the selection of the port enterprise LSP.

Table 3
Statistical summary of the questionnaire for the importance of the evaluation indexes

Evaluation index Minimum Maximum Average Standard

deviation

Business diversity 5 9 7.31 0.88

Logistics network 5 9 7.28 0.86

Customer satisfaction rate 5 9 7.29 1.04

Order completion rate 5 9 7.46 0.89

On-time delivery rate 5 9 7.30 0.87

Product integrity rate 5 9 7.39 0.86

Problem handling rate 6 9 7.27 0.82

Cooperation success rate 5 8 7.14 0.72

Value-added services 3 8 5.51 1.44

Service flexibility 3 8 5.88 1.41

Transportation cost 4 9 7.34 1.04

Storage cost 4 9 7.40 0.94

Circulation processing cost 5 9 7.35 1.02

Packaging cost 3 8 5.73 1.60

Logistics information and management costs 3 8 5.37 1.45

Handling and carrying costs 4 9 7.33 1.02

Demand analysis ability 3 9 5.38 1.55

Scheme design ability 3 9 5.92 1.45

Operation management ability 5 9 7.28 0.86

Risk coping ability 4 9 7.35 0.86

Service innovation capability 3 9 6.29 1.37

Working experience 3 9 5.88 1.42

Market share 4 9 7.19 1.06

Enterprise qualification 4 9 7.19 0.91

Enterprise reputation 4 9 7.19 1.08

Corporate culture 3 9 5.84 1.43

Cultural compatibility 3 8 5.94 1.45

Professional talent ratio 4 9 7.11 1.10

Informatization degree 4 9 7.22 0.89

Communication level 5 9 7.17 0.81

Evaluation index	Minimum	Maximum	Average	Standard
Business diversity	5	9	7.31	0.88
Logistics network	5	9	7.28	0.86
Customer satisfaction rate	5	9	7.29	1.04
Order completion rate	5	9	7.46	0.89
On-time delivery rate	5	9	7.30	0.87
Product integrity rate	5	9	7.39	0.86
Problem handling rate	6	9	7.27	0.82
Cooperation success rate	5	8	7.14	0.72
Value-added services	3	8	5.51	1.44
Service flexibility	3	8	5.88	1.41
Transportation cost	4	9	7.34	1.04
Storage cost	4	9	7.40	0.94
Circulation processing cost	5	9	7.35	1.02
Packaging cost	3	8	5.73	1.60
Logistics information and management costs	3	8	5.37	1.45
Handling and carrying costs	4	9	7.33	1.02
Demand analysis ability	3	9	5.38	1.55
Scheme design ability	3	9	5.92	1.45
Operation management ability	5	9	7.28	0.86
Risk coping ability	4	9	7.35	0.86
Service innovation capability	3	9	6.29	1.37
Working experience	3	9	5.88	1.42
Market share	4	9	7.19	1.06
Enterprise qualification	4	9	7.19	0.91
Enterprise reputation	4	9	7.19	1.08
Corporate culture	3	9	5.84	1.43
Cultural compatibility	3	8	5.94	1.45
Professional talent ratio	4	9	7.11	1.10
Informatization degree	4	9	7.22	0.89
Communication level	5	9	7.17	0.81

Most of the indicators have more than 7 points, and the standard deviation of these values is approximately 1. The following indexes with relatively low scores and relatively large standard deviation values were removed: value-added services, service flexibility, packaging cost, logistics information and management costs, demand analysis ability, scheme design ability, service innovation capability, working experience, corporate culture, and cultural compatibility.

Next, the reliability and validity of the remaining 20 indexes were analysed.

2.3 Analysis of reliability and validity of the evaluation index system

2.3.1 Reliability analysis

The reliability is used to represent the stability and consistency of the test results when the measurement is repeated. This aspect has a decisive influence on the reliability of the contents of the questionnaire to ensure the reliability and stability of the questionnaire content and the accuracy of the results of the questionnaire analysis. Under ordinary circumstances, the internal reliability of the scale, that is, the internal consistency between the items of the questionnaire, is mainly investigated to test the correctness of the obtained conclusions.

In this paper, we consider the comparison of the internal consistency reliability by using the commonly used Cronbach coefficient (Cronbach’s α) method that initiated by Cronbach & Gleser [59] to analyse the reliability of the questionnaire. The alpha coefficient is between 0–1. A larger alpha coefficient corresponds to a greater credibility of the questionnaire. It is generally believed that a reliability coefficient of 0.7 or above is acceptable.

The reliability analysis indicated that the overall reliability coefficient of the questionnaire was 0.738. Consequently, the internal consistency and reliability of the questionnaire are satisfactory.

2.3.2 Validity analysis

The validity corresponds to the correctness of the results measured using measurement tools or means to reflect the degree of the tested objects. A higher validity indicates a higher consistency with the test results. In this paper, the structural validity of the questionnaire was analysed.

As shown in Table 4, the eigenvalues of 5 factors are greater than 1; these factors together account for 66.947% of the total variance, and further analysis of the factor square load after rotation indicates that the 5 main factors contributed considerably to the interpretation of the overall sample. Consequently, the questionnaire can be considered reasonable.

The factor load matrix, which is rotated using the orthogonal rotation method, is presented in Table 5.

Table 4
Results of total variance

Factor Initial Extracting square Rotating square

eigenvalue and loading and loading

Total Variance% Cumulative% Total Variance% Cumulative% Total Variance% Cumulative%

1 3.721 18.603 18.603 3.721 18.603 18.603 3.335 16.673 16.673

2 2.919 14.595 33.198 2.919 14.595 33.198 2.681 13.406 30.079

3 2.638 13.191 46.389 2.638 13.191 46.389 2.676 13.382 43.461

4 2.378 11.889 58.278 2.378 11.889 58.278 2.605 13.023 56.484

5 1.734 8.669 66.947 1.734 8.669 66.947 2.093 10.463 66.947

6 .801 4.007 70.954

7 .649 3.245 74.200

.... .... .... ....

19 .251 1.256 99.002

20 .200 0.998 100.00

Factor	Initial	Extracting square	Rotating square
1	3.721	18.603	18.603	3.721	18.603	18.603	3.335	16.673	16.673
2	2.919	14.595	33.198	2.919	14.595	33.198	2.681	13.406	30.079
3	2.638	13.191	46.389	2.638	13.191	46.389	2.676	13.382	43.461
4	2.378	11.889	58.278	2.378	11.889	58.278	2.605	13.023	56.484
5	1.734	8.669	66.947	1.734	8.669	66.947	2.093	10.463	66.947
6	.801	4.007	70.954
7	.649	3.245	74.200
....	....	....	....
19	.251	1.256	99.002
20	.200	0.998	100.00

Table 5

Factor load matrix after rotation

Evaluation index	Principal component
	1	2	3	4	5
Business diversity		.786
Logistics network		.822
Customer satisfaction rate	.817
Order completion rate	.775
On-time delivery rate	.809
Product integrity rate	.802
Problem handling rate	.818
Cooperation success rate					.783
Transportation cost			.818
Storage cost			.814
Circulation processing cost			.812
Handling and carrying costs			.785
Operation management ability		.809
Risk coping ability		.821
Market share				.790
Enterprise qualification				.797
Enterprise reputation				.800
Professional talent ratio				.797
Informatization degree					.829
Communication level					.835

According to the validity analysis results, the evaluation indexes were grouped into the following five first-level index groups: service quality, business ability, logistics cost, enterprise soft power, and cooperation. Thus, the index system for the selection of the logistics service providers of the port enterprises is established, as given in Table 6.

Table 6

Index system for selection of logistics service providers of port enterprises

First -level indexes	Second-level indexes	Background of the optimality
Service quality A	Customer satisfaction rate A₁ (%)	Quantitative index
	Order completion rate A₂ (%)	Quantitative index
	On-time delivery rate A₃ (%)	Quantitative index
	Product integrity rate A₄ (%)	Quantitative index
	Problem handling rate A₅ (%)	Quantitative index
Business ability B	Business diversity B₁ (Hundred mark)	Qualitative index
	Logistics network B₂ (Hundred mark)	Qualitative index
	Operation management ability B₃ (Hundred mark)	Qualitative index
	Risk coping ability B₄ (Hundred mark)	Qualitative index
Logistics cost C	Transportation cost C₁ (Vehicle 16M)	Quantitative index
	Storage cost C₂ (Yuan/(m²*day))	Quantitative index
	Circulation processing cost C₃ (Yuan/m³)	Quantitative index
	Handling and carrying costs C₄ (Yuan/t*1)	Quantitative index
Enterprise soft power D	Market share D₁ (%)	Quantitative index
	Enterprise qualification D₂ (Hundred mark)	Qualitative index
	Enterprise reputation D₃ (Hundred mark)	Qualitative index
	Professional talent ratio D₄ (%)	Quantitative index
Cooperation E	Cooperation success rate E₁ (%)	Quantitative index
	Informatization degree E₂ (Hundred mark)	Qualitative index
	Communication level E₃ (Hundred mark)	Qualitative index

2.4 Content description of the evaluation index system

2.4.1 Service quality

The core product of the port LSP in the supply chain operation is the port logistics service; therefore, the quality of the logistics service is an evaluation index that must be considered.

Furthermore, it should be noted that because the port enterprise has not yet established a strategic partnership with the port LSP, only a preliminary knowledge of the former service quality of the LSP is taken as a reference.

(1) Customer satisfaction rate

In the present buyers’ market, customer satisfaction is one connotation of the supply chain management in the 21st century. In the selection process of the LSP, the customers refer to the core enterprises served by the port logistics service providers. Customer satisfaction is a subjective index, which represents the differences between the expected and actual levels of the LSP. In actual evaluation, we selected the port enterprises that are being served currently or have been served previously by the port LSP as the investigation objects and designed the questionnaire for customer satisfaction. The customer satisfaction is calculated using formula (1) with the data from the returned questionnaires.

$CS = \sum_{i = 1}^{N} s_{i} / - (N \times S)$ (1)

In formula (1), CS denotes the customer satisfaction, N denotes the number of the returned valid questionnaires, Si denotes the marks of the valid questionnaire i, and S denotes the full marks of the questionnaire for the customer satisfaction.

(2) Order completion rate

The order completion rate reflects the ability of the LSP to complete the order and directly reflects the reliability of the supply chain. The characteristic of the order completion rate is that the service provided by the supplier is consistent with the customer’s requirement. The rate can be calculated using formula (2).

$\begin{matrix} Order completion rate \\ = \frac{Order completion quantity}{Total number of orders received by enterprises} \end{matrix}$ (2)

(3) On-time delivery rate

The on-time delivery rate refers to the timeliness of the LSP to provide logistics services. This rate corresponds to not only the real capacity of the logistics enterprise to meet the customer demand but also to the integrated scheduling management capabilities of the logistics service provider. Therefore, a higher index corresponds to a higher level of enterprise management.

$On - time delivery rate = \frac{On time delivery number}{Total delivery number}$ (3)

(4) Product integrity rate

The product integrity rate refers to the product in the logistics process and its maintenance of the overall integrity of the ratio, reflecting the implementation of service control by the logistics enterprises. Improving the product integrity rate plays a key role in improving customer satisfaction.

$Product integrity rate = \frac{Product integrity number}{Total number}$ (4)

(5) Problem handling rate

The core enterprise attaches considerable importance to the problem handling rate of the port logistics service provider. This rate reflects the supplier’s ability to solve problems in time when encountering problems in the provision of the logistics services. Therefore, it is of significance to establish a suitable corporate image of dealing with problems in the logistics service. The calculation formula for the problem handling rate is given in formula (5).

$\begin{matrix} Problem handling rate \\ = \frac{Average number of problems handled per unit time}{Average number of problems occurring per unit time} \end{matrix}$ (5)

2.4.2 Business ability

In the choice of an LSP, from the point of view of the port enterprise or the customer, a satisfactory business service capability is the premise to judge whether the supplier is eligible. In the complex logistics environment, satisfactory logistics business ability enables enterprises to promptly meet customers’ needs and effectively address challenges and risks.

(1) Business diversity

The business diversity refers to the diversity of services provided by the logistics services suppliers. A more extensive business scope and more service types offered correspond to a more comprehensive business ability of the supplier. With a stronger ability to meet customer demands, the supplier can provide better services for the enterprises.

(2) Logistics network

The logistics network reflects the logistics hierarchy of the suppliers. The business level of a port LSP is not only reflected in port logistics but also in the required cooperation with aviation, road and railway transportation, etc. Therefore, the corresponding multimodal transport capacity and logistics network structure also reflect the business level of the suppliers. The logistics network is a qualitative indicator that can be obtained by the method of grading.

(3) Operation management ability

The operation management ability refers to the ability of the LSP to handle various operational activities during service provision, such as human resource planning, the coordination of resource allocation, and controlling equipment and facilities. The core aspect of the operation management ability is to design the service process with a high performance, turning a limited resource input into an efficient output. Providers with excellent operation management ability can considerably save resources, reduce costs and improve efficiency.

(4) Risk coping ability

The risk response ability refers to the ability of the logistics enterprise to deal with strain when facing unexpected situations. An LSP may be affected by the internal and external environment, such as typhoons, tsunamis, earthquakes and the enterprise’s internal problems and other factors, resulting in the disruption of the logistics services supply. Therefore, the logistics enterprises must have a suitable risk response capacity. This ability is a qualitative indicator, which can be obtained by the method of grading.

2.4.3 Logistics cost

The logistics cost is an important index when an enterprise selects a logistics service provider. If the logistics cost is reduced, the total cost of the enterprise is also reduced, which makes the product more competitive, and the main reason enterprises choose an LSP is to reduce the cost of logistics in addition to risk transfer.

(1) Transportation cost

The transportation cost constitutes an important part of the enterprise logistics cost, including the energy consumption, transportation vehicles, transport personnel and other related costs. The transportation costs can reflect the market competitiveness of a logistics enterprise. This indicator is the dominant cost, which is relatively easy to measure. Further, the transportation cost is a quantitative indicator, which needs to be measured according to the characteristics of the enterprise product, and one can obtain the corresponding data through the logistics enterprise.

(2) Storage cost

The storage cost refers to the cost incurred by the LSP to provide warehousing services for the enterprises. The storage cost is an important part of the logistics cost and has a direct impact on the level of the logistics costs. Most storage costs vary not with inventory levels, but with the number of storage locations. The storage cost mainly refers to the cost of an enterprise leasing the warehouse space of the logistics service provider and the cost of the various types of storage operations.

(3) Circulation processing cost

The circulation processing cost refers to the cost of processing products to improve the logistics efficiency when an LSP provides logistics services for the enterprises. This cost mainly includes the circulation processing packaging, materials and labour costs.

(4) Handling and carrying costs

The handling and carrying costs refer to the costs incurred by the LSP in helping the enterprises in the logistics work and handling the sum of expenses generated by the direct and indirect costs of handling. These costs mainly include the labour costs, cost of machinery use, energy consumption and other related costs.

2.4.4 Enterprise soft power

(1) Market share

The market share is the proportion of the logistics enterprises in the market, that is, the market share reflects the existing market share and development potential of an LSP. A greater market share corresponds to a greater ability of the logistics service provider to control the market. This share is a sign of the soft strength of the logistics enterprises.

$\begin{matrix} Market share \\ = \frac{Sales volume of logistics services}{Total market sales volume of logistics services} \end{matrix}$ (6)

(2) Enterprise qualification

To distinguish the situation of the logistics enterprises and allow the customers to obtain a comprehensive understanding of the domestic logistics enterprises, China performed a grade evaluation to assess the domestic logistics enterprises. The rating of the domestic logistics enterprises are divided into five grades: A, AA, AAA, AAAA, AAAAA, of which the 5A level is the highest level of qualification. The enterprises with a higher qualification ranking have a stronger comprehensive competitiveness.

(3) Enterprise reputation

The enterprise reputation of an LSP represents the society’s and customer’s recognition towards the enterprise. The reputation of an enterprise can more intuitively reflect the strength of a business level in its industry. Port enterprises tend to value the enterprise’s reputation more when choosing an LSP. The reputation is a qualitative indicator, which can be obtained by the method of grading.

(4) Professional talent ratio

The professional ratio of the port logistics of a port LSP reflects its level of human resources in the area of port logistics. This ratio can be calculated using formula (7).

$\begin{matrix} Professional ratio \\ = \frac{The number of port logistics professionals}{The total number of staffs} \end{matrix}$ (7)

2.4.5 Cooperation

(1) Cooperation success rate

The cooperation success rate refers to the number of successful instances of cooperation between the port LSP and the core enterprises of other ports in the past. This element shows the ability of the supplier in terms of cooperation, the cooperation performance and the level of cooperation. The calculation formula is as follows.

$\begin{matrix} Cooperation success rate \\ = \frac{Number of successful collaboration with partners}{The total number of collaboration with all partners} \end{matrix}$ (8)

(2) Informatization degree

The enterprise informatization degree is the basis for realizing a prompt response of the supply chain, and it is also the basic premise to realize information sharing. Logistics enterprises apply advanced management information systems and the human, financial, material and other integrated information management systems of the enterprise to realize internal and external information sharing. A high or low level of informatization degree is a crucial factor to be considered when selecting the LSP for the port enterprises.

(3) Communication level

Effective communication is the precondition and guarantee for cooperation. Therefore, a port LSP should possess excellent communication skills and maintain close communication with the commissioned enterprises. Furthermore, the LSP should ensure that both sides can receive feedback in a timely and effective manner.

3 Combination weighting-grey synthetic decision-making method

The pronounced advantages of the combination weighting-grey synthetic decision-making method includes: 1) using ANP to determine the subjective weight is beneficial to fully consider the expert’s professional judgments, 2) using entropy method to determine the objective weight, which reflects the significance of objective factors of evaluation index data, 3) using the calculation of grey clustering coefficient to determine the improved central-point triangle whitenization weight function, which reflects properly handling the grey characteristics of this problem.

There exist m alternative plans in the logistics service market, and n evaluation indexes for the evaluation of the alternative plans. The evaluation data for the alternative plans i (i = 1, 2, . . . , m) pertaining to the evaluation indexes j (j = 1, 2, . . . , n) are represented as x_ij (i = 1, 2, . . . , m ; j = 1, 2, . . . , n). This paper contains a total of s grey classes. w_j = (w₁, w₂, . . . , w_n) represents the combined weight of each evaluation index. The decision steps of the combination weighting-grey synthetic decision-making method are as follows.

3.1 Combination weighting

We consider the combination weight composed of the subjective weights by using the ANP method and the objective weights by using the entropy method to comprehensively reflect the importance of the evaluation indexes.

3.1.1 Determination of subjective weights based on the ANP method

(1) ANP network structure

According to the size of the controlling force, the system elements in the ANP network structure are divided into the control layer and the network layer. The control layer has a decision-making objective. According to the various decision-making problems, the control layer can also contain a number of decision-making criteria, which are assumed to be independent from each other. The network layer is composed of the elements and influence relationships controlled by the control layer. Depending on whether the interactional elements belong to the same cluster or if the influence is bidirectional, the influence relationships are divided into the inner dependence, outer dependence and feedback. A typical ANP network structure is shown in Fig. 1.

Fig. 1

ANP network structure.

(2) Construction of the unweighted supermatrix

To reflect the complex and multiple influence relationships among the elements in the network layer, the ANP approach uses various supermatrices as the modelling tools for determining the influence relationships, in which the construction of the unweighted supermatrix is the operational basis.

We assume that the control layer of the ANP network structure has a total of M decision-making criteria (P₁, P₂, ⋯ , P_M). The decision-making criteria of ANP are determined by the objective of the decision problem. All the decision-making criteria are independent of each other, from which sub-criterion elements under its decision criterion layer can be established. The network layer has N clusters that have interactions, denoted by C₁, C₂, ⋯ , C_N, and the elements in cluster C_j are denoted by e_j1, e_j2, ⋯ , e_jn. Among these elements, some may be influenced by not only the elements from the same cluster, namely, the inner dependence, but also the elements from other clusters, namely, the outer dependence. For example, if the element e_jk (k = 1, 2, ⋯ , n_j)in cluster C_j is influenced by the elements in cluster C_i, according to the size of the local influence of the elements in cluster C_i on e_jk, we can use the 9-scale method to construct a pair-wise judgement matrix with respect to a certain criterion and sub-criterion e_jk and derive a normalized weight vector, denoted by $w_{i}^{jk} = {(w_{i 1}^{jk}, w_{i 2}^{jk}, \dots, w_{{in}_{i}}^{jk})}^{T}$ . $w_{i}^{jk}$ reflects the local influence priority of the elements in cluster C_i on e_jk. It should be noted that when an element in cluster C_i has no influence on e_jk, its influence priority in $w_{i}^{jk}$ is directly assigned (not derived) as zero. If the other elements in cluster C_j are also influenced by the elements in cluster C_i, accordingly, the normalized weight vector can be derived in a similar manner. Furthermore, if all the elements in cluster C_i have no influence on e_jp, $w_{i}^{jp}$ is directly assigned (not derived) as a zero vector. After arranging all the normalized weight vectors according to the relevant order, we can obtain the following matrix $w_{i}^{j}$ : $\begin{matrix} W_{i}^{j} = (w_{i}^{j 1}, w_{i}^{j 2}, . . . . . ., w_{i}^{{jn}_{j}}) \\ = [\begin{matrix} w_{i 1}^{j 1} & w_{i 1}^{j 2} & . . . & w_{i 1}^{{jn}_{j}} \\ w_{i 2}^{j 1} & w_{i 2}^{j 2} & . . . & w_{i 2}^{{jn}_{j}} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ w_{{in}_{i}}^{j 1} & w_{{in}_{i}}^{j 2} & . . . & w_{{in}_{i}}^{{jn}_{j}} \end{matrix}] \end{matrix}$

$W_{i}^{j}$ is a block matrix of the unweighted supermatrix and represents the local influence priority that the elements in cluster C_i have on the elements in cluster C_j. If all the elements in cluster C_i have no influence on all the elements in cluster C_j, cluster C_i has no influence on cluster C_j; therefore, $W_{i}^{j} = 0$ . After finishing the other block matrices in accordance with the abovementioned manner, we can obtain the unweighted supermatrix W as follows: $W = [\begin{matrix} W_{1}^{1} & W_{1}^{2} & \dots & W_{1}^{N} \\ W_{2}^{1} & W_{2}^{2} & \dots & W_{2}^{N} \\ ⋮ & ⋮ & ⋮ \\ W_{N}^{1} & W_{N}^{2} & \dots & W_{N}^{N} \end{matrix}]$

(3) Construction of the weighted supermatrix

The block matrix $W_{i}^{j}$ of the unweighted supermatrix is a column normalized matrix; however, the unweighted supermatrix W is not column normalized. Therefore, from the overall perspective, the weights in W cannot represent the total influence priority of an element on the left to the element on the top. This aspect is the reason we consider the normalized weight vector derived in the construction of the unweighted supermatrix as the local influence priority. Consequently, we must compare the clusters and construct a weighting matrix to weight the block matrices in the unweighted supermatrix.

Let the clusters that have one or more elements influencing e_jk in C_j be denoted by set g_jk. Consequently, the clusters in set G_j = g_j1 ∪ g_j2 ⋯ ∪ g_jk ⋯ ∪ g_{jn_j} are the clusters that influence C_j. Thus, with respect to the sub-criterion C_j, we need to construct a pair-wise judgement matrix to compare the clusters in G_j and obtain the normalized weight vector, which relates the influence priority of these clusters, denoted by $z^{j} = (z_{1}^{j}, z_{2}^{j}, \dots \dots, z_{N}^{j})^{T}$ . Here, the weights of the clusters that have no influence on C_j in z^j are directly assigned (not derived) as zero. After finishing all the other clusters in accordance with the abovementioned approach, we can obtain the weighted matrix A as follows: $Z = (z^{1}, z^{2}, \dots \dots, z^{N})$ $= [\begin{matrix} z_{1}^{1} & z_{1}^{2} & \dots & z_{1}^{N} \\ z_{2}^{1} & z_{2}^{2} & \dots & z_{2}^{N} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ z_{N}^{1} & z_{N}^{2} & \dots & z_{N}^{N} \end{matrix}]$

After weighting the unweighted supermatrix W by using the weighted matrix A, we can obtain the weighted supermatrix $\bar{W}$ , which is column normalized.

(4) Limit processing of the weighted supermatrix

The complex and multiple influence relationships between the elements in the network layer, including the direct and indirect influences, complicate the comparison of the global influence priority of these elements. Thus, the ANP approach derives the limit matrix through the limit processing of the weighted supermatrix. The limit processing of the weighted supermatrix is equivalent to a Markov process, in which the influence relationships are transmitted and overlaid through constant iterations. Therefore, the steady global weight vector is obtained when a steady state is attained. It can be proved that the limit matrix exists in a network structure that simultaneously possesses an inner dependence and feedback, and any column of the limit matrix is a steady global weight vector.

3.1.2 Determination of the objective weights based on the entropy method

Entropy method has the important characteristic of reflecting the degree of information uncertainty. Entropy method is used by many scholars to determine attribute weights. Garg [60] proposed a new strategy which uses different entropy values and unknown attribute weights to solve multi-attribute decision-making problems. Garg [61] used entropy functions to calculate the attribute weight vectors exploited to aggregate the preferences of decision makers. Wang, Gar and Li [62] defined a Pythagorean fuzzy entropy measure, established a method to determine the attribute weights and explored a novel approach to manage multiple attribute decision making problems. In this paper, the objective weights of the evaluation indexes are determined by using the entropy method. As this method depends only on the information of the objective evaluation data of the alternatives, the weight determined by the entropy method is termed as the objective weight. The basic steps of the objective weight determination by the entropy method can be described as follows:

(1) Construction of the original evaluation data matrix

Suppose that there exist m alternatives, and the evaluation index system has n evaluation indexes. The original evaluation data matrix is labelled X (x_ij represents the original evaluation data of the ith alternative pertaining to the jth evaluation index). $X = [\begin{matrix} x_{11} & x_{12} & \dots & x_{1 n} \\ x_{21} & x_{22} & \dots & x_{2 n} \\ ⋮ & ⋮ & \dots & ⋮ \\ x_{m 1} & x_{m 2} & \dots & x_{mn} \end{matrix}]$

(2) Construction of the standardized evaluation data matrix

Considering the evaluation indexes that are different in dimension and the assessment criteria, the original evaluation data matrix cannot be directly used in the multiple attribute decision-making process. Based on formulas (9) and (10), the original evaluation data matrix is transformed into the dimensionless standardized evaluation data matrix R. $R = [\begin{matrix} r_{11} & r_{12} & \dots & r_{1 n} \\ r_{21} & r_{22} & \dots & r_{2 n} \\ ⋮ & ⋮ & \dots & ⋮ \\ r_{m 1} & r_{m 2} & \dots & r_{mn} \end{matrix}]$ If the index is positive, the standardization formula would be as follows:

$r_{ij} = \frac{x_{ij} - min_{i} x_{ij}}{max_{i} x_{ij} - min_{i} x_{ij}} j = 1, 2, \dots, n$ (9)

If the index is negative, the standardization formula would be as follows:

$r_{ij} = \frac{max_{i} x_{ij} - x_{ij}}{max_{i} x_{ij} - min_{i} x_{ij}} j = 1, 2, \dots, n$ (10)

(3) Calculation of the entropy value

The formula for calculating the entropy value is as follows:

$E_{j} = - K \sum_{i = 1}^{m} f_{ij} ln f_{ij} j = 1, 2, \dots, n$ (11)

$f_{ij} = r_{ij} / - \sum_{i = 1}^{m} r_{ij} j = 1, 2, \dots, n$ (12)

$E_{j} = - K \sum_{i = 1}^{m} f_{ij} ln f_{ij} j = 1, 2, \dots, n$ (13)

when

$f_{ij} = 0, f_{ij} ln f_{ij} = 0$ (14) $K = 1 / - ln m$

(4) Calculation of the entropy weight

The formula for calculating the entropy weight is as follows:

$o_{j} = 1 - E_{j} / - n - \sum_{j = 1}^{n} E_{j} j = 1, 2, \dots, n$ (15)

3.1.3 Calculation of combined weights

In this paper, to amplify the difference in the importance between the evaluation indexes, the combined weights of the evaluation indexes are determined by using the product method. The calculation formula is as follows:

$w_{j} = s_{j} \times o_{j} / - \sum_{j = 1}^{n} s_{j} \times o_{j} j = 1, 2, \dots, n$ (16)

3.2 Grey synthetic decision-making

3.2.1 Determination of the turning points or centre points of the grey classes of the evaluation indexes

The values of the hypothesis evaluation indexes j lie between [a_j, b_j]. According to the overall evaluation requirements, the evaluation indexes are divided into a total of s grey classes. Next, the turning points $λ_{j}^{1}$ and $λ_{j}^{s}$ of grey classes 1 and s and the centre points $λ_{j}^{2}$ , $λ_{j}^{3}$ . . . $λ_{j}^{s - 1}$ of grey classes k (k ∈ {2, 3, . . . , s - 1}) are determined

3.2.2 Creation of the whitenization weight functions of the corresponding grey classes

The grey classes 1 and s are constructed considering the corresponding whitenization weight functions $f_{j}^{1} [-, -, λ_{j}^{1}, λ_{j}^{2}]$ and $f_{j}^{s} [λ_{j}^{s - 1}, λ_{j}^{s}, -, -]$ of a lower measure and upper measure, respectively. The grey classes k (k ∈ {2, 3, . . . , s - 1}) are needed to connect the point (λ_k, 1) and the centre point $(λ_{j}^{k - 1}, 0)$ of the grey class k - 1 (or the turning point $(λ_{j}^{1}, 0)$ of grey class 1) as well as the centre point $(λ_{j}^{k + 1}, 0)$ of the grey class k + 1 (or the turning point $(λ_{j}^{s}, 0)$ of grey class s). Thus, the triangular whitenization weight functions of evaluation indexes j for grey classes k can be obtained. The function diagram is as shown in Fig. 2.

Fig. 2

Schematic diagram of the improved centre-point triangular whitenization weight function.

3.2.3 Calculation of the grey clustering coefficients

Using formula (17), we can calculate the grey clustering coefficients $σ_{i}^{k}$ of the alternative plans i (i = 1, 2, . . . , m) for grey classes k (k = 1, 2, . . . , s).

$σ_{i}^{k} = \sum_{j = 1}^{n} f_{j}^{k} (x_{ij}) w_{j}$ (17)

$f_{j}^{k} (x_{ij})$ represents the whitenization weight functions of evaluation indexes j for grey classes k, and w_j represents the combined weight of each evaluation index.

3.2.4 Judgement of the alternative plans corresponding to the grey classes

The order of the normalized grey clustering coefficients of alternative plans i for grey classes kis $δ_{i}^{k} = \frac{σ_{i}^{k}}{\sum_{k = 1}^{s} σ_{i}^{k}} \cdot δ_{i}^{k} (k = 1, 2, \dots, s)$ can meet the condition of $\sum_{i = 1}^{s} δ_{i}^{k} = 1$ . $δ_{i} = (δ_{i}^{1}, δ_{i}^{2}, \dots, δ_{i}^{s}) (i = 1, 2, \dots, m)$ are termed as the normalized grey clustering coefficient vectors of alternative plans i. According to the value of the $max_{1 ⩽ k ⩽ s} {δ_{i}^{k}} = δ_{i}^{k^{*}}$ , one can judge the alternative plans corresponding to the grey classes. If multiple alternative plans belong to the same grey category k^*, the alternative plans will be ranked according to the size of the normalized grey clustering coefficients.

3.2.5 Calculation of the synthetic weighted decision-making vectors

It is assumed that the total existing s grey classes, $η_{k} = (η_{k}^{1}, η_{k}^{2}, . . ., η_{k}^{s}) (k = 1, 2, . . ., s)$ are known as the synthetic weighted decision-making vectors of grey classes k. The kth component of these vectors is assigned the value s, and the kth component is taken as the midpoint. When assigning a value to the left and right components of this point, which are in descending order, the kth component is the largest contribution to the alternative plans belonging to the grey classes k; therefore, this component is assigned the greatest weight s. The calculation method is as follows:

$η_{k} = \frac{(s - k + 1, s - k + 2, . . ., s - 1, s, s - 1, . . ., k)}{\frac{s (s + 1)}{2} + [(k - 1) s - k (k - 1)]}$ (18)

3.2.6 Calculation of the grey synthetic decision-making coefficient vectors

Formula (19) can be used to calculate the initial grey synthetic decision-making coefficients of the alternative plans i for grey classes k, and $ψ_{i}^{'} = (ψ_{i}^{1}', ψ_{i}^{2}', . . ., ψ_{i}^{s}') (i = 1, 2, . . ., m)$ are known as the initial grey synthetic decision-making coefficient vectors of alternative plans i.

$ψ_{i}^{k}' = η_{k} δ_{i}^{T}$ (19)

After the normalization process, we can obtain $ψ_{i} = (ψ_{i}^{1}, ψ_{i}^{2}, . . ., ψ_{i}^{s}) (i = 1, 2, . . ., m)$ , which are known as the grey synthetic decision-making coefficient vectors of alternative plans i.

3.2.7 Calculation of grey synthetic clustering decision-making coefficients

The weight vector of the grey synthetic clustering decision-making coefficients is γ = (1, 2, . . . , s - 1, s) ^T. Using formula (20), the calculation can be performed by using the grey synthetic clustering decision-making coefficients π_i of alternative plans i.

Because $0 ⩽ ψ_{i}^{k} ⩽ 1$ , the maximum value of the grey synthetic clustering decision-making coefficient π_i = ψ_i · γ (i = 1, 2, . . . , m) of alternative plans i is s, and the minimum value is 1. We can conclude that 1 ⩽ π_i ⩽ s. At the same time, the decision-making coefficient matrix can be obtained as follows:

$\begin{matrix} π_{i} = [\begin{matrix} π_{1} \\ π_{2} \\ \dots \\ π_{m} \end{matrix}] = [\begin{matrix} ψ_{1}^{1} & ψ_{1}^{2} & \dots & ψ_{1}^{s} \\ ψ_{2}^{1} & ψ_{2}^{2} & \dots & ψ_{2}^{s} \\ \dots & \dots & \dots & \dots \\ ψ_{m}^{1} & ψ_{m}^{2} & \dots & ψ_{m}^{s} \end{matrix}] \\ \cdot (1, 2, . . ., s - 1, s)^{T} \\ π_{i} = ψ_{i} \cdot γ = \sum_{k = 1}^{s} k \cdot ψ_{i}^{k} (i = 1, 2, . . ., m) \end{matrix}$ (20)

3.2.8 Rank of the synthetic decision-making

By comparing the size of the grey synthetic clustering decision-making coefficients of alternative plans i in the same grey classes k, we can conduct a synthetic decision-making ranking process.

In this paper, the decision maker can utilize the combination weighting-grey synthetic decision-making method to solve the problems of selecting LSP of port enterprises. Firstly, by analyzing the present situation of the port enterprise’s logistics business, the combination weighting method was used to obtain the combination weights of the LSP evaluation. Besides, determing turning points or centre points of the grey classes of the evaluation indexes to build the whitenization weight functions corresponding to the grey classes. What’s more, calculating the grey clustering coefficients to judge providers corresponding to the grey classes. Finally, the comprehensive weighted decision vector and grey comprehensive clustering decision coefficient are calculated, and the comprehensive ranking is carried out to select the LSPs that are more suitable for the port enterprises.

4 Empirical Study

When choosing an LSP for a port enterprise, there are several factors to take into account. In order to reflect the objective components of a quantitative indicator, such as customer satisfaction rate, it is important to calculate the objective weight using the entropy value approach. Business diversity is a qualitative indicator; therefore, in order to calculate the subjective weight that best reflects the opinion of the indicator’s experts, one must utilize the ANP. Therefore, it is important to take into account both the subjective and objective weights of the port enterprise while analyzing each indicator of each LSP and to determine the combination weights that were generated using the combination weighting. Port enterprise A mainly produces various concrete blocks and prefabricated components. These products are widely used in port and waterway engineering and in buildings, roads and other constructions. Due to the limitation of the allocation of funds, the enterprise decides to select an LSP to help them address the inbound and outbound logistical aspects. The selection and evaluation of the alternative providers are based on the combination weighting-grey synthetic decision-making method. The evaluation data of each alternative provider are presented in Table 7.

Table 7
Evaluation index system and evaluation data of the LSP

Evaluation index Alternative LSPs

First-level indexes Second level indexes G ₁ G ₂ G ₃ G ₄ G ₅

Service quality A Customer satisfaction rate A₁ (%) 83 80 87 89 84

Order completion rate A₂ (%) 90 87 94 93 88

On-time delivery rate A₃ (%) 85 86 87 88 89

Product integrity rate A₄ (%) 90 94 91 93 94

Problem handling rate A₅ (%) 92 88 94 89 91

Business ability B Business diversity B₁ (Hundred mark) 81 77 88 85 84

Logistics network B₂ (Hundred mark) 80 78 90 86 84

Operation management ability B₃ (Hundred mark) 82 80 89 92 83

Risk coping ability B₄ (Hundred mark) 67 63 72 69 77

Logistics cost C Transportation cost C₁ (Vehicle 16M) 9300 8900 8800 8700 9600

Storage cost C₂ (Yuan/(m²day)) 2.8 3.3 3.6 3.8 3.4

Circulation processing cost C₃ (Yuan/m³) 17 20 14 12 16

Handling and carrying costs C₄ (Yuan/t1) 16 16 12 10 13

Enterprise soft power D Market share D₁ (%) 5 5 6 4 3

Enterprise qualification D₂ (Hundred mark) 87 82 92 93 90

Enterprise reputation D₃ (Hundred mark) 78 82 80 79 84

Professional talent ratio D₄ (%) 8 5 11 12 6

Cooperation E Cooperation success rate E₁ (%) 74 77 86 88 83

Informatization degree E₂ (Hundred mark) 82 72 80 68 81

Communication level E₃ (Hundred mark) 75 85 83 83 69

	Evaluation index	Alternative LSPs
First-level indexes	Second level indexes	G ₁	G ₂	G ₃	G ₄	G ₅
Service quality A	Customer satisfaction rate A₁ (%)	83	80	87	89	84
	Order completion rate A₂ (%)	90	87	94	93	88
	On-time delivery rate A₃ (%)	85	86	87	88	89
	Product integrity rate A₄ (%)	90	94	91	93	94
	Problem handling rate A₅ (%)	92	88	94	89	91
Business ability B	Business diversity B₁ (Hundred mark)	81	77	88	85	84
	Logistics network B₂ (Hundred mark)	80	78	90	86	84
	Operation management ability B₃ (Hundred mark)	82	80	89	92	83
	Risk coping ability B₄ (Hundred mark)	67	63	72	69	77
Logistics cost C	Transportation cost C₁ (Vehicle 16M)	9300	8900	8800	8700	9600
	Storage cost C₂ (Yuan/(m²*day))	2.8	3.3	3.6	3.8	3.4
	Circulation processing cost C₃ (Yuan/m³)	17	20	14	12	16
	Handling and carrying costs C₄ (Yuan/t*1)	16	16	12	10	13
Enterprise soft power D	Market share D₁ (%)	5	5	6	4	3
	Enterprise qualification D₂ (Hundred mark)	87	82	92	93	90
	Enterprise reputation D₃ (Hundred mark)	78	82	80	79	84
	Professional talent ratio D₄ (%)	8	5	11	12	6
Cooperation E	Cooperation success rate E₁ (%)	74	77	86	88	83
	Informatization degree E₂ (Hundred mark)	82	72	80	68	81
	Communication level E₃ (Hundred mark)	75	85	83	83	69

4.1 Combination weighting of the evaluation indexes for the port enterprise LSP selection

By using the combination weighting method, the combined weights of the evaluation indexes of the LSP are obtained, and the results are presented in Table 8.

Table 8
Combination weights of the evaluation index and grey class classification of the LSPs

Evaluation index Turning points or centre points of the grey

classes of the evaluation indexes

First-level indexes Second-level indexes Combination weights Lower limit Poor Medium Satisfactory Excellent Upper limit

Service quality A Customer satisfaction rate A₁ (%) 0.005 70 75 80 85 90 100

Order completion rate A₂ (%) 0.020 70 80 85 90 95 100

On-time delivery rate A₃ (%) 0.024 70 80 85 90 95 100

Product integrity rate A₄ (%) 0.015 70 80 85 90 95 100

Problem handling rate A₅ (%) 0.020 70 80 85 90 95 100

Business ability B Business diversity B₁ (Hundred mark) 0.049 60 65 75 80 90 100

Logistics network B₂ (Hundred mark) 0.087 60 70 75 85 90 100

Operation management ability B₃ (Hundred mark) 0.174 60 65 75 85 90 100

Risk coping ability B₄ (Hundred mark) 0.109 55 60 65 75 85 100

Logistics cost C Transportation cost C₁ (Vehicle 16M) 0.034 10000 9800 9400 9000 8600 8000

Storage cost C₂ (Yuan/(m²day)) 0.025 8 4 3.5 3 2.5 2

Circulation processing cost C₃ (Yuan/m³) 0.011 30 25 19 15 11 10

Handling and carrying costs C₄ (Yuan/t1) 0.018 25 22 18 15 10 8

Enterprise soft power D Market share D₁ (%) 0.036 0 1 3 5 7 10

Enterprise qualification D₂ (Hundred mark) 0.170 70 75 80 85 90 100

Enterprise reputation D₃ (Hundred mark) 0.059 60 65 75 85 90 100

Professional talent ratio D₄ (%) 0.050 1 4 7 10 13 15

Cooperation E Cooperation success rate E₁ (%) 0.018 60 70 75 85 90 100

Informatization degree E₂ (Hundred mark) 0.053 60 65 70 75 80 100

Communication level E₃ (Hundred mark) 0.023 55 60 70 80 85 100

Evaluation index	Turning points or centre points of the grey
Service quality A	Customer satisfaction rate A₁ (%)	0.005	70	75	80	85	90	100
	Order completion rate A₂ (%)	0.020	70	80	85	90	95	100
	On-time delivery rate A₃ (%)	0.024	70	80	85	90	95	100
	Product integrity rate A₄ (%)	0.015	70	80	85	90	95	100
	Problem handling rate A₅ (%)	0.020	70	80	85	90	95	100
Business ability B	Business diversity B₁ (Hundred mark)	0.049	60	65	75	80	90	100
	Logistics network B₂ (Hundred mark)	0.087	60	70	75	85	90	100
	Operation management ability B₃ (Hundred mark)	0.174	60	65	75	85	90	100
	Risk coping ability B₄ (Hundred mark)	0.109	55	60	65	75	85	100
Logistics cost C	Transportation cost C₁ (Vehicle 16M)	0.034	10000	9800	9400	9000	8600	8000
	Storage cost C₂ (Yuan/(m²*day))	0.025	8	4	3.5	3	2.5	2
	Circulation processing cost C₃ (Yuan/m³)	0.011	30	25	19	15	11	10
	Handling and carrying costs C₄ (Yuan/t*1)	0.018	25	22	18	15	10	8
Enterprise soft power D	Market share D₁ (%)	0.036	0	1	3	5	7	10
	Enterprise qualification D₂ (Hundred mark)	0.170	70	75	80	85	90	100
	Enterprise reputation D₃ (Hundred mark)	0.059	60	65	75	85	90	100
	Professional talent ratio D₄ (%)	0.050	1	4	7	10	13	15
Cooperation E	Cooperation success rate E₁ (%)	0.018	60	70	75	85	90	100
	Informatization degree E₂ (Hundred mark)	0.053	60	65	70	75	80	100
	Communication level E₃ (Hundred mark)	0.023	55	60	70	80	85	100

The results appeared in Table 8 show that in the service quality index, on-time delivery rate is more important. Besides, the operation management ability is the most important of business ability index. What’s more, the transportation cost is the most significant of logistics cost index. Otherwise, in the enterprise soft power index, enterprise qualification is more important. Last but not least, informatization degree is most crucial of cooperation index.

4.2 Grey synthetic decision-making for port enterprise LSP selection

4.2.1 Determination of the turning points or centre points of the grey classes of the evaluation indexes

According to the evaluation requirements, the evaluation indexes of the LSP are divided into 4 grey classes: poor, medium, satisfactory and excellent, as shown in Table 7.

4.2.2 Construction of the whitenization weight functions corresponding to the grey classes

Taking the customer satisfaction rate as an example, the corresponding triangular whitenization weight functions of a lower measure $f_{j}^{1} [-, -, 75, 80]$ and an upper measure $f_{j}^{4} [85, 90, -, -]$ are constructed for grey classes 1 and 4, respectively. In addition, the corresponding triangular whitenization weight functions $f_{j}^{2} [75, 80, -, 85]$ and $f_{j}^{3} [80, 85, -, 90]$ are established for the grey classes 2 and 3, respectively.

4.2.3 Calculation of the grey clustering coefficients

The grey clustering coefficients for each alternative provider are calculated, and the results are summarized as shown in Table 9.

Table 9
Grey clustering coefficients of the providers

Grey clustering coefficients Poor Medium Satisfactory Excellent

G₁ 0.004 0.346 0.506^* 0.144

G₂ 0.079 0.499^* 0.378 0.044

G₃ 0.005 0.097 0.290 0.608^*

G₄ 0.036 0.174 0.269 0.521^*

G₅ 0.036 0.197 0.480^* 0.287

Grey clustering coefficients	Poor	Medium	Satisfactory	Excellent
G₁	0.004	0.346	0.506^*	0.144
G₂	0.079	0.499^*	0.378	0.044
G₃	0.005	0.097	0.290	0.608^*
G₄	0.036	0.174	0.269	0.521^*
G₅	0.036	0.197	0.480^*	0.287

4.2.4 Judgement of the grey classes corresponding to the alternative providers

By observing the maximum value of the grey clustering coefficients for each alternative provider, the providers belonging to the grey classes can be evaluated, and the results are presented in Table 10.

Table 10
Providers corresponding to the grey classes

G₁ G₂ G₃ G₄ G₅

Satisfactory Medium Excellent Excellent Satisfactory

G₁	G₂	G₃	G₄	G₅
Satisfactory	Medium	Excellent	Excellent	Satisfactory

4.2.5 Calculation of the synthetic weighted decision-making vectors

This paper considers four types of grey classes, which can be used to calculate the synthetic weighted decision-making vectors of grey classes k. According to Formula 18, four grey classes can be calculated as follows. $\begin{matrix} η_{1} & = \frac{(4, 4 - 1, 4 - 2, 1)}{\frac{4 \times (4 + 1)}{2} + [(4 - 1) \times 4 - 4 \times (4 - 1)]} \\ = \frac{1}{10} (4, 32, 1) \\ η_{2} = & \frac{(4 - 1, 4, 4 - 1, 2)}{\frac{4 \times (4 + 1)}{2} + [(2 - 1) \times 4 - 2 \times (2 - 1)]} \\ = \frac{1}{12} (3, 4, 3, 2) \\ η_{3} & = \frac{(4 - 3 + 1, 4 - 3 + 2, 4 - 3 + 3, 3)}{\frac{4 \times (4 + 1)}{2} + [(3 - 1) \times 4 - 3 \times (3 - 1)]} \\ = \frac{1}{12} (2, 3, 4, 3) \\ η_{4} & = \frac{(4 - 4 + 1, 4 - 4 + 2, 4 - 1, 4)}{\frac{4 \times (4 + 1)}{2} + [(4 - 1) \times 4 - 4 \times (4 - 1)]} \\ = \frac{1}{10} (1, 2, 3, 4) : \end{matrix}$

4.2.6 Calculation of the grey synthetic decision-making coefficient vectors

The initial grey synthetic decision-making coefficient vectors of the alternative providers i for grey classes k are calculated. After the normalization process, the grey synthetic decision-making coefficient vectors matrix can be obtained: $ψ_{i} = [\begin{matrix} 0 . 209 & 0 . 252 & 0 . 276 & 0 . 263 \\ 0 . 246 & 0 . 271 & 0 . 259 & 0 . 224 \\ 0 . 153 & 0 . 211 & 0 . 279 & 0 . 357 \\ 0 . 174 & 0 . 223 & 0 . 272 & 0 . 331 \\ 0 . 192 & 0 . 236 & 0 . 279 & 0 . 293 \end{matrix}]$

4.2.7 Calculation of grey synthetic clustering decision-making coefficients

The grey synthetic clustering decision-making coefficient of each alternative provider is obtained, as shown in Table 11.

Table 11
Grey synthetic clustering decision-making coefficients of the providers

G₁ G₂ G₃ G₄ G₅

π _i 2.593 2.461 2.840 2.760 2.673

	G₁	G₂	G₃	G₄	G₅
π _i	2.593	2.461	2.840	2.760	2.673

In this paper, the combination weighting-grey synthetic decision-making method is applied to the empirical research of LSP selection of port enterprise. This method can effectively distinguish and rank the LSPs of the port enterprises.

4.2.8 Rank of the synthetic decision-making

According to the results presented in Tables 9 and 10, G₂ belongs to the medium grey class; G₁ and G₅ belong to the satisfactory grey class because 2.673 > 2.593, and thus, G₅ is better than G₁; G₃ and G₄ belong to the excellent grey class because 2.840 > 2.760, and thus, G₃ is better than G₄. The final ranking for the alternative providers is G₃ > G₄ > G₅ > G₁ > G₂. This result shows that provider G₃ has the largest grey synthetic clustering decision-making coefficient, and provider G₄ ranks second. From a different perspective, provider G₂ is relatively poor. Therefore, the port enterprise should choose provider G₃ as its service provider.

In order to test the reliability of the weighting-grey synthetic decision-making method proposed in this paper, the ANP method and the grey clustering method are selected to solve the same problem to investigate the consistency between the evaluation results. It can be seen from Table 12 that the method proposed in this paper is highly consistent with the evaluation results of the other two methods in LSP selection, which further verifies the reliability of the method proposed in this paper.

Table 12
Comparison of evaluation results

Method Priority line

This paper method G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂

ANP G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂

Grey clustering method G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂

Method	Priority line
This paper method	G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂
ANP	G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂
Grey clustering method	G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂

In Table 12, the ANP method alone would place an undue reliance on subjective elements like expert judgment. Sometimes the results of the grey clustering method alone do not adequately reflect the results of the clustering. Combining the ANP, entropy approach, and grey decision procedure to get at an acceptable multi-criteria decision-making solution. It is appropriate for assisting decision-makers in circumstances where they are lacking information and have a strong sense of subjectivity by supplying pertinent information for making decisions. This weighting-grey synthetic combination decision-making approach has the advantages listed below: First off, by using ANP to determine subjective weights, it is simpler to fully incorporate expert expertise into the index weight values. Furthermore, the relevance of objective aspects in the assessment index data is also reflected in the objective weights, which are determined using the entropy value approach. Additionally, the enhanced center point triangle whitening weight function is used to calculate the grey clustering coefficients, reflecting the proper handling of the problem’s grey characteristics. Moreover, the analysis’s findings are highly reliable.

4.3 Sensitivity analysis of weighting-grey synthetic decision-making method

Since this method combines the ANP method and the entropy method to determine the combination weights of evaluation indexes, it was reasonable to analyze the sensitivity of the weighted grey synthetic decision-making method. This implies that we consider how a standard weight change affects the terminal ranking of logistics supplier alternatives. Nevertheless, owing that the sum of all criteria equals to 1, if the weight of the p-th criterion changes Δp, weights of other criteria change Δj.

$Δ j = \frac{Δ_{p} \cdot w_{j}}{w_{p} - 1}$ (21)

Table 13 shows the impact of changes in the weight of service quality, business ability, logistics cost, enterprise soft power, and cooperation on the ranking of LSP alternatives. Columns 1, 3, 5, 7 and 9 respectively show the specific changes of the index weight of service quality (Δ₁), business ability (Δ₂), logistics cost (Δ₃), enterprise soft power (Δ₄) and cooperation (Δ₅). Corresponding to Δ₁ to Δ₅, column 2, 4, 6, 8 and 10 respectively represent the LSP ranked first under the new weights.

Table 13

The effect of changes in weights for the criteria indicators

Δ ₁	LSP	Δ ₂	LSP	Δ ₃	LSP	Δ ₄	LSP	Δ ₅	LSP
0.1	G₃	0.1	G₃	0.1	G₃	0.1	G₃	0.1	G₃
0.2	G₁	0.2	G₃	0.2	G₃	0.2	G₃	0.2	G₃
–0.1	G₃	–0.1	G₃	–0.1	G₁	–0.1	G₃	–0.1	G₃
–0.2	G₃	–0.2	G₃	–0.2	G₁	–0.2	G₃	–0.2	G₃

When the standard weight is increased by 0.1 and 0.2 and decreased by 0.1 and 0.2 respectively, the sum result is 0. Among them, the weight changes of the three indicators, business ability (Δ₂), enterprise soft power (Δ₄), and cooperation (Δ5), did not affect the ranking of the best suppliers. When the weight value of service quality (Δ1) is increased by 0.2, it will have a certain impact on LSP ranking. When the weight value of logistics cost (Δ3) is reduced by 0.1 and 0.2 respectively, it will have a certain impact on LSP ranking.

Therefore, through the sensitivity analysis, we can see that the business ability, enterprise soft power and cooperation meet the stable standards. The change of service quality and logistics cost will lead to the change of supplier ranking, and the stability is relatively low.

5 Conclusion

The selection of an appropriate LSP is an important strategic decision and plays a substantial role in establishing long-term relations between the LSP and the port enterprise. This paper conducts a literature review on the grey systems theory and entropy method used in LSP selection. By performing the analysis of the reliability and validity of the questionnaire, this paper determines the index system for the evaluation of the provider. Subsequently, the ANP method and the entropy method are combined to determine the combined weights, and the improved centre-point triangular whitenization weight function is used to cluster the alternative plans. Finally, the grey synthetic clustering decision-making coefficients are calculated to determine the synthetic decision-making rank of the alternative plans. The validity of this method is proven through empirical research. Compared with the ANP method and the grey clustering method, the results are consistent. It shows the reliability of combination weighting-grey synthetic decision-making method in LSP selection. From the perspective of implementation, the proposed approach can also solve the problems of pattern recognition as well as the evaluation of medical and health services.

There exist certain limitations in the interpretation of the results obtained using the proposed approach. Methodologically, the data collected are based on a self-assessment from the professionals of the port industries. In terms of the scope of this study, these questionnaires were collected only from mainland China, which may limit the generalizability of the results to other regions. In future studies, we will conduct similar studies on the selection of LSP in the presence of deterministic data and fuzzy data. The selection method of LSP will be considered to improve and classify, and it will be extended to other regions with different cultural and social backgrounds to solve more practical problems [63-65].

Footnotes

Acknowledgments

This work was supported by National Natural Science Foundation of China under Grant 71601050.

Conflict of interest

The authors declare no potential conflict of interest.

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Evaluation index			Turning points or centre points of the grey
			classes of the evaluation indexes
First-level indexes	Second-level indexes	Combination weights	Lower limit	Poor	Medium	Satisfactory	Excellent	Upper limit
Service quality A	Customer satisfaction rate A₁ (%)	0.005	70	75	80	85	90	100
	Order completion rate A₂ (%)	0.020	70	80	85	90	95	100
	On-time delivery rate A₃ (%)	0.024	70	80	85	90	95	100
	Product integrity rate A₄ (%)	0.015	70	80	85	90	95	100
	Problem handling rate A₅ (%)	0.020	70	80	85	90	95	100
Business ability B	Business diversity B₁ (Hundred mark)	0.049	60	65	75	80	90	100
	Logistics network B₂ (Hundred mark)	0.087	60	70	75	85	90	100
	Operation management ability B₃ (Hundred mark)	0.174	60	65	75	85	90	100
	Risk coping ability B₄ (Hundred mark)	0.109	55	60	65	75	85	100
Logistics cost C	Transportation cost C₁ (Vehicle 16M)	0.034	10000	9800	9400	9000	8600	8000
	Storage cost C₂ (Yuan/(m²*day))	0.025	8	4	3.5	3	2.5	2
	Circulation processing cost C₃ (Yuan/m³)	0.011	30	25	19	15	11	10
	Handling and carrying costs C₄ (Yuan/t*1)	0.018	25	22	18	15	10	8
Enterprise soft power D	Market share D₁ (%)	0.036	0	1	3	5	7	10
	Enterprise qualification D₂ (Hundred mark)	0.170	70	75	80	85	90	100
	Enterprise reputation D₃ (Hundred mark)	0.059	60	65	75	85	90	100
	Professional talent ratio D₄ (%)	0.050	1	4	7	10	13	15
Cooperation E	Cooperation success rate E₁ (%)	0.018	60	70	75	85	90	100
	Informatization degree E₂ (Hundred mark)	0.053	60	65	70	75	80	100
	Communication level E₃ (Hundred mark)	0.023	55	60	70	80	85	100

Selection of Logistics Service Provider for port enterprises: Combination of the weighting-grey synthetic decision-making method

Abstract

Keywords

1 Introduction

2.1 Preliminary creation of the evaluation index system

2.3.1 Reliability analysis

2.3.2 Validity analysis

2.4.1 Service quality

2.4.3 Logistics cost

2.4.4 Enterprise soft power

3.1 Combination weighting

3.1.1 Determination of subjective weights based on the ANP method

3.2.1 Determination of the turning points or centre points of the grey classes of the evaluation indexes

3.2.2 Creation of the whitenization weight functions of the corresponding grey classes

3.2.5 Calculation of the synthetic weighted decision-making vectors

4 Empirical Study

4.2.1 Determination of the turning points or centre points of the grey classes of the evaluation indexes

4.2.2 Construction of the whitenization weight functions corresponding to the grey classes

4.2.3 Calculation of the grey clustering coefficients

Table 9 Grey clustering coefficients of the providers Grey clustering coefficients Poor Medium Satisfactory Excellent G1 0.004 0.346 0.506* 0.144 G2 0.079 0.499* 0.378 0.044 G3 0.005 0.097 0.290 0.608* G4 0.036 0.174 0.269 0.521* G5 0.036 0.197 0.480* 0.287

Table 10 Providers corresponding to the grey classes G1 G2 G3 G4 G5 Satisfactory Medium Excellent Excellent Satisfactory

4.2.6 Calculation of the grey synthetic decision-making coefficient vectors

4.2.7 Calculation of grey synthetic clustering decision-making coefficients

Table 11 Grey synthetic clustering decision-making coefficients of the providers G1 G2 G3 G4 G5 π i 2.593 2.461 2.840 2.760 2.673

Table 12 Comparison of evaluation results Method Priority line This paper method G3 ≻ G4 ≻ G5 ≻ G1 ≻ G2 ANP G3 ≻ G4 ≻ G5 ≻ G1 ≻ G2 Grey clustering method G3 ≻ G4 ≻ G5 ≻ G1 ≻ G2

Footnotes

Acknowledgments

Conflict of interest

References

Table 9
Grey clustering coefficients of the providers

Grey clustering coefficients Poor Medium Satisfactory Excellent

G₁ 0.004 0.346 0.506^* 0.144

G₂ 0.079 0.499^* 0.378 0.044

G₃ 0.005 0.097 0.290 0.608^*

G₄ 0.036 0.174 0.269 0.521^*

G₅ 0.036 0.197 0.480^* 0.287

Table 10
Providers corresponding to the grey classes

G₁ G₂ G₃ G₄ G₅

Satisfactory Medium Excellent Excellent Satisfactory

Table 11
Grey synthetic clustering decision-making coefficients of the providers

G₁ G₂ G₃ G₄ G₅

π _i 2.593 2.461 2.840 2.760 2.673

Table 12
Comparison of evaluation results

Method Priority line

This paper method G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂

ANP G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂

Grey clustering method G₃ ≻ G₄ ≻ G₅ ≻ G₁ ≻ G₂