An approach of selecting cold chain logistics service provider based on SNAand FCE method

Abstract

In this paper, an integrated decision-making methodology is proposed to solve the subjectivity and fuzziness in the selection of cold chain logistics service providers (LSPs). Firstly, the social network analysis (SNA) method is applied to select the evaluation criteria of cold chain LSPs, which is based on the systematic literature analysis. Then, a novel combination weighting method that combines the advantages of entropy weight (EW) method and improved analytic hierarchy process (AHP) is constructed to calculate the weight of criteria. Further, the fuzzy comprehensive evaluation (FCE) method is utilized to generate a ranking order of providers and recommend the optimal provider. Finally, the illustrative example and comparison analysis are provided to prove the validity and feasibility of the approach. In addition, a sensitivity analysis is presented to discuss the stability of the proposed method. In conclusion, this paper innovatively constructs an index system of cold chain LSPs evaluation and selection, and the process of evaluation and selection is also objective.

Keywords

Cold chain logistics service provider social network analysis combination weighting method fuzzy comprehensive evaluation

1 Introduction

Due to the huge financial and material resources required to construct the cold chain logistics system, companies generally choose third-party cold chain logistics service providers (LSPs) as partners. In addition, with the increasing improvement of consumption level, consumers put forward higher demand for cold chain logistics services. Besides, cold chain consumes more cooling costs than conventional supply chain. However, because of the late development of cold chain logistics industry, the corresponding technical standards, supporting facilities and information system construction are insufficient, which result in the uneven strength of cold chain LSPs [1]. Therefore, select the optimal cold chain LSPs is crucial to the benign development and competitiveness enhancement of companies.

It is well known that the selection and evaluation of LSPs are multi-criteria decision-making (MCDM) problems, in which the determination of evaluation criteria and selection of decision-making methods are the keys to solve this question. The determination of evaluation criteria is the premise of logistics providers’ assessment, so it is vital to construct a scientific and reasonable evaluation index system. For this, Kannan et al. determined the third-party logistics (3PL) providers selection criteria by using the grey DEMATEL approach [2]. From the perspective of manufacturing logistics service, Wang et al. constructed an evaluation index system based on AHP method and the comparative analysis of literature [3]. Osorio Gómez et al. took the operational risks of 3PL providers in the supply chain as the research object and proposed corresponding risk evaluation criteria [4]. Moreover, through the qualitative analysis of previous literature, Wu et al. presented an evaluation index system for low-carbon LSPs from five dimensions [5]. Weng built an evaluation index system based on three dimensions and proposed an intuitive fuzzy preference decision-making method to select cold chain LSPs [6]. Sun et al. proposed a set of cold chain LSPs evaluation indexes that are consistent with the characteristics of typical food production enterprises [7]. Zhao used AHP to construct the evaluation index system of 3PL service providers for fresh e-commerce under the background of “Internet plus” [8]. It can be found that there are some limitations of the evaluation index system construction for LSPs selection in existing research. On the one hand, most of the evaluation criteria proposed in the above literature are rely on personal experience and subjective literature analysis, which cannot guarantee the scientificity and accuracy of the indexes. On the other hand, some evaluation index system is too complicated and not conducive to convenient practice.

At the same time, various decision-making models are proposed for the evaluation of LSPs. For example, Huang presented an evaluation approach by combining fuzzy matter-element model and AHP [9]. Gong proposed a group decision-making tool based on the three-parameter interval number [10]. Considering the expectation of customers, Cai constructed the LSPs selection model under the supply chain environment, which is based on the prospect theory [11]. Besides, Shu et al. applied DEMATEL method to select green reverse LSPs based on urban logistics and reverse logistics [12]. Huang et al. proposed an ANP-RBF method to evaluate the cruise ship supply LSPs [13]. Ejem et al. constructed a LSP selection and evaluation model by the TOPSIS method [14]. Qin et al. applied prospect theory and fuzzy measure theory in the decision-making model, and used TOPSIS to rank the alternative logistics providers [15]. Similarly, Chen et al. combined the intuitive fuzzy set theory and TOPSIS to establish a selection model of cross-border e-commerce LSPs [16]. Chen et al. used entropy weight TOPSIS to evaluate the low-carbon behavior ability of logistics service [17]. Kamran applied fuzzy DEA and fuzzy TOPSIS in the selection of sustainable logistics providers [18], while Govindan et al. combined FAHP and TOPSIS to select the sustainable forward and reverse logistic providers [19]. Moreover, Zarbakhshnia et al. integrated the fuzzy SWARA with fuzzy COPRAS for choosing the third-party reverse LSPs [20], and Govindan et al. developed a SMAA-ELECTRE I hybrid decision-making approach to solve the same problem [21]. In addition, Zou presented a two-stage decision-making model based on DEA-ANP approach to assess logistics suppliers [22]. Stefan et al. utilized the selection method based FAHP and TOPSIS to select 3PL providers [23]. Tavana et al. proposed a green reverse logistics provider evaluation framework based on COPRAS, MULTIMOORA and TOPSIS [24]. With respect for the selection problem of cold chain LSPs, Li et al. provided a method by combining dynamic intuitionistic fuzzy theory and VIKOR [25]. Singh et al. extended the AHP and TOPSIS to a fuzzy environment [26]. Furthermore, Ju developed a fuzzy multi-criteria group decision-making method by using evidence theory [27]. Later, Zhou used FAHP to choose the cold chain logistics providers of military fresh food [28]. Wang studied the selection problem of cold chain LSPs based on rough PSO-BP neural network [29]. Diriba et al. used a multicentered mixed-method approach to evaluate the pharmaceuticals management performance of cold chain LSPs [30]. It can be found that AHP is the most frequently used method for determining index weight, and TOPSIS is a common approach to deal with the problem of LSPs selection.

SNA is a mathematical analysis method derived from graph theory, which can effectively analyze extensive literatures and then select the key factors. Therefore, it is introduced into the research of this paper to construct the evaluation index system. The effectiveness of SNA in selecting evaluation criteria has also been well verified, for instance, Gao and Yang constructed a paper evaluation index system based on SNA [31]. Wang et al. presented the identifying method of patent essential technology based on SNA, and established a comprehensive evaluation index system in the field of semiconductor technology industry [32]. Wang et al. used SNA to construct measure index system to study the characteristics of international economic network [33]. And then, to select the optimal cold chain LSPs, this paper combines AHP method, EW method and FCE method to construct the evaluation model. Among them, EW method is an objective weight determination method, which has a wide application in the field of decision-making problems [34 –36]. FCE method is a comprehensive evaluation method based on fuzzy mathematics, which is suitable for solving various uncertain and fuzzy problems, such as development ability assessment [37], management performance evaluation [38], investment project selection [39] and so on.

Previous methods have made great contributions to the problem of logistics provider selection. However, few studies have focused on the assessment of cold chain LSPs, and some limitations also can be observed as follows. Firstly, the construction process of evaluation index system is subjective, and there is a lack of a universal evaluation index system of cold chain LSPs to provide reference for more enterprises. Secondly, the data source of AHP is subjective, which cannot get the objective index weight only by using this method. Thirdly, most of the decision-making methods used for LSPs selection can only get a specific result, so it is difficult to obtain more information to help companies make final decisions. According to the preceding reviews, the motivation of this paper can be elaborated as follows: (1) Because there exists only a few research about the evaluation and selection of cold chain LSPs, it is necessary to construct an objective evaluation index system for cold chain LSPs by SNA. (2) In order to reduce the influence of subjectivity on decision-making, the EW method and FCE method are effective. Therefore, this paper focuses on the MADM problem of cold chain LSPs, and proposes an integrated decision-making methodology based on SNA and FCE method.

The main contributions of the paper can be summarized as follows: (1) A new criteria system for cold chain LSPs selection is constructed, and the comprehensiveness and authority of the criteria can be ensured by the SNA. (2) A novel weight calculation model is proposed to improve the objectivity of weight, in which the AHP method is modified by constructing the judgment matrix based on the centrality of criteria, and the EW method is used to modify the criteria weight. (3) The FCE method is applied to rank the alternative providers, which can simplify the evaluation process, and give more decision-making information. (4) The sensitivity analysis and the comparative analysis are used to verify the feasibility and superiority of the proposed method.

The rest of the paper is arranged as follows: In Section 2, the detailed decision steps of the proposed method for selecting cold chain LSPs are provided. In Section 3, the illustrative example, comparative analysis and sensitivity analysis are given to demonstrate the advantages and feasibility of the presented approach. Section 4 includes the conclusion and further research.

2 Problem description

To express the decision-making model constructed in this paper more clearly, the following assumptions or notations are used to depict the considered problem.

Suppose that A = (a₁, a₂, …, a_m) is the set of alternative providers, and there is a decision-making committee of l experts are responsible for analyzing and evaluating the alternatives, denoted by E = (e₁, e₂, …, e_l). Then, let C = (c₁, c₂, . . . , c_n) represent the factor set of first-level criteria (main criteria), c_i = (c_i1, c_i2, . . . , c_ij) denote a factor set of second-level criteria (sub-criteria). Particularly, j is a variable that represents the number of indexes contained by the ith main criteria, and it will have different values corresponding to different main criteria, satisfying j = 1, 2, . . . , m and i = 1, 2, . . . , n. Then the weights of the main criteria and sub-criteria are expressed by $\bar{W} = ({\bar{w}}_{1}, {\bar{w}}_{2}, \dots, {\bar{w}}_{n})$ and W_i = (w_i1, w_i2, …, w_ij), respectively, in which ${\bar{w}}_{i} \in (0, 1)$ , $\sum_{i = 1}^{n} {\bar{w}}_{i} = 1$ , and the sum of the weights of the second-level criteria is also 1. In addition, several rating levels S = (s₁, s₂, . . . , s_k) are provided for experts to evaluate the alternative providers with respect to the criteria, where s_k represents the kth evaluation result, k is the total number of evaluation results.

3 Decision-making model

To handle the cold chain LSPs selection problem, a MCDM method combining four methods is proposed in this section. Considering that the process of criteria selection is often subjective, SNA method is used to analyze extensive relevant literatures. Moreover, the weights of criteria are usually completely unknown, a combination weighting approach based on AHP method and EW method is established to calculate the comprehensive weights. Afterwards, optimal solution can be selected by FCE method. The novelty of the proposed method can be briefly listed as follows: (1) Form theoretical perspective, the objective evaluation index system of cold chain LSPs is constructed by SNA method, and it can provide reference for enterprises. (2) From technical perspective, the comprehensive weights are determined by AHP method and EW method, so the importance of each criteria is more scientific. Besides, in order to make the decision-making process less subjective, the evaluation and selection of cold chain LSPs are based on FCE method. The decision-making procedure is shown in Fig. 1, and the specific contents of the three stages of the decision model are as follows:

Fig. 1

The evaluation process of cold chain LSPs.

In the Stage 1, through literature review and statistical analysis based on SNA, the evaluation index system is established, and the detailed steps are as follows:

Step 1: Collect the literature. According to the research object and relevant keywords, the relevant papers containing clear evaluation criteria are selected from the appropriate literature database.

Step 2: Choose the evaluation criteria by using SNA [31]. After reading the collected literature, the criteria of the same nature are merged, and the criteria that is infrequent or can be replaced by other related criteria are deleted. Then, a 0-1 relational matrix between the retained criteria and the corresponding authors is established. Further, the UCINET software is used to read the relational matrix and the centrality analysis is performed. As the centrality reflects the importance of the criteria, the criterion whose centrality is higher than the average centrality is selected, while the criterion whose centrality is slightly lower than the average centrality should be comprehensively analyzed whether to be retained.

Step 3: Determine the evaluation index system. According to the specific meaning of the criterion, the selected criteria are classified, and the system is usually divided into two levels, where each criterion belonging to the first-level will contain several second-level criteria.

In the Stage 2, to ensure the objectivity of criteria weights, the two methods are effectively combined, and the detailed steps are elucidated as follows:

Step 4: Determine the weight of evaluation criteria. AHP method is used to solve the initial weights of criteria, and the weight of the main criteria is expressed as ${\bar{w}}_{i}^{1}$ , the weight of the sub-criteria is denoted by $w_{ij}^{1}$ . In order to reflect the importance of the criteria more objectively, the judgment matrix is constructed by using the criteria centrality obtained in the step 2, and the scoring standard are shown in Tables 1 and 2 . For convenience, let c_α, c_β represent two criteria in the same factor set [26, 31].

Table 1

Scoring standard of judgment matrix for main criteria

The centrality difference	Relative	Implications
φ between c_α and c_β	score δ_αβ
24.0 < φ	9	c_α is extremely important compared to c_β
16.0 < φ < 24.0	7	c_α is very important compared to c_β
8.0 < φ < 16.0	5	c_α is important compared to c_β
0 < φ < 8.0	3	c_α is slightly important compared to c_β
φ = 0	1	c_α is as important as c_β
-8.0 < φ < 0	1/3	c_α is slightly unimportant compared to c_β
-16.0 < φ < -8.0	1/5	c_α is unimportant compared to c_β
-24.0 < φ < -16.0	1/7	c_α is very unimportant compared to c_β
φ < -24.0	1/9	c_α is extremely unimportant compared to c_β

If the value of φ is found between two standards, the median value as follows is adopted: 8,6,4,2,1/2,1/4,1/6,1/8.

Table 2

Scoring standard of judgment matrix for sub-criteria

The centrality difference	Relative	Implications
φ between c_α and c_β	score δ_αβ
9.0 < φ	9	c_α is extremely important compared to c_β
6.0 < φ < 9.0	7	c_α is very important compared to c_β
3.0 < φ < 6.0	5	c_α is important compared to c_β
0 < φ < 3.0	3	c_α is slightly important compared to c_β
φ = 0	1	c_α is as important as c_β
-3.0 < φ < 0	1/3	c_α is slightly unimportant compared to c_β
-6.0 < φ < -3.0	1/5	c_α is unimportant compared to c_β
-9.0 < φ < -6.0	1/7	c_α is very unimportant compared to c_β
φ < -9.0	1/9	c_α is extremely unimportant compared to c_β

If the value of φ is found between two standards, the median value as follows is adopted: 8,6,4,2,1/2,1/4,1/6,1/8.

Step 5: Obtain the evaluation data. In this step, the decision-making committee is asked to evaluate the alternative providers according to the rating levels and evaluation index system.

Step 6: Calculate the initial weights of main criteria ( ${\bar{w}}_{i}^{2}$ ) and sub-criteria ( $w_{ij}^{2}$ ) by the principle of EW method [41].

Step 7: Get the comprehensive weight w_ij, ${\bar{w}}_{i}$ by formula and formula by the AHP method and EW method. $w_{ij} = \frac{w_{ij}^{1} w_{ij}^{2}}{\sum_{i = 1}^{m} w_{ij}^{1} w_{ij}^{2}}$ (1) ${\bar{w}}_{i} = \sum w_{ij}$ (2)

In the Stage 3, to select the optimal cold chain LSP, the FCE method is used to analyze the evaluation information and obtain the order of alternatives, and the specific steps are listed as follows:

Step 8: Construct the factor set and comment set of FCE. Factor set U is a set composed of all evaluation indexes, and comment set S is a set of various evaluation results made by experts on the evaluated object. Based on the previous assumptions, S = (s₁, s₂, . . . , s_k), U = C = (c₁, c₂, . . . , c_n).

Step 9: Calculate the single-factor fuzzy evaluation results by formula (3). $\begin{matrix} B_{i}^{t} = (w_{i 1}, w_{i 2}, \dots, w_{ij}) \times [\begin{matrix} r_{i 11}^{t} & r_{i 12}^{t} & \dots & r_{i 1 k}^{t} \\ r_{i 21}^{t} & r_{i 22}^{t} & \dots & r_{i 2 k}^{t} \\ ⋮ & ⋮ & \dots & ⋮ \\ r_{ij 1}^{t} & r_{ij 2}^{t} & \dots & r_{ijk}^{t} \end{matrix}] \\ = (b_{i 1}^{t}, b_{i 2}^{t}, \dots, b_{ik}^{t}) \end{matrix}$ (3)

$\begin{matrix} Where r_{ijk}^{t} = \\ \frac{The number of experts who rated a_{t} as s_{k} according to c_{ij}}{Total number of experts in the evaluation}, \\ t = 1, 2, \dots, m . \end{matrix}$

Step 10: Obtain the overall comprehensive evaluation matrix $Z (a_{t})$ . $\begin{matrix} Z (a_{t}) = ({\bar{w}}_{1}, {\bar{w}}_{2}, \dots, {\bar{w}}_{m}) \times [\begin{matrix} b_{11}^{t} & b_{12}^{t} & \dots & b_{1k}^{t} \\ b_{21}^{t} & b_{22}^{t} & \dots & b_{2k}^{t} \\ ⋮ & ⋮ & \dots & ⋮ \\ b_{m1}^{t} & b_{m2}^{t} & \dots & b_{mk}^{t} \end{matrix}] \\ = (z_{1}, z_{2}, \dots, z_{k}) \end{matrix}$ (4)

Step 11: Rank alternative providers according to the total score M. The total score of each alternative can be obtained by multiplying the FCE result Z by the corresponding score set S_s. $M = {(Z (a_{1}), Z (a_{2}), \dots, Z (a_{m}))}^{T} \times S_{s}^{T}$ (5)

4 Numerical analysis

4.1 Illustrative example

To reduce operating costs and improve customer satisfaction, a fresh e-commerce enterprise needs to choose an optimal cold chain LSP as cooperation partner. After preliminary selection, there are four alternatives A = (a₁, a₂, a₃, a₄). The proposed method is applied to solve this problem and the computational procedure is summarized as follows:

Step 1: Those “Cold chain LSP/supplier selection/evaluation”, “Agricultural products logistics provider/supplier selection/evaluation”, “Cold chain provider/supplier selection/evaluation”, “Fresh cold chain logistics provider/supplier selection/evaluation” are used as the main keywords in this paper. The time range of the literature is from 2005 to 2020 and the literature type is the journal article. Through a comprehensive literature search, a total of 30 relevant literatures are selected.

Step 2: The criterion whose centrality is higher than the average centrality is selected, including cold chain equipment condition, delivery accuracy rate, staff quality, freight, service flexibility and so on. In addition, the centrality of business coverage is 17, which is lower than the average centrality of the network. However, this paper retained this evaluation criterion for the following two reasons: (1) Fresh products have a high demand for the timeliness, while the business coverage has an impact on the timeliness of distribution. (2) There is a strong correlation between the business coverage of LSPs and the business coverage of enterprises, because without the cold chain logistics for product distribution, enterprises cannot stabilize the existing market or expand the market scope. Therefore, “Business coverage” is retained. The selected criteria and their centralities can be seen from Table 3.

Table 3
The centrality of criteria

Reference Evaluation criteria Degree NrmDegree

[6 , 23-26] Cold chain equipment condition 30.0 50.000

[7 , 23-26] Cargo damage rate 28.0 46.667

[7 , 25] Delivery accuracy rate 26.0 43.333

[7 , 25] Staff quality 25.0 41.667

[6 , 25] Freight 25.0 41.667

[7 , 23] Service flexibility 25.0 41.667

[16 , 24] Information system completeness 24.0 40.000

[16 , 25] Order response time 24.0 40.000

[16 , 25] Delivery punctuality 24.0 40.000

[16 , 23] Customer satisfaction 22.0 36.667

[6, 25] Business coverage 19.0 31.667

[23] Transportation time 17.0 28.333

– Mean 18.984 31.639

Reference	Evaluation criteria	Degree	NrmDegree
[6 , 23-26]	Cold chain equipment condition	30.0	50.000
[7 , 23-26]	Cargo damage rate	28.0	46.667
[7 , 25]	Delivery accuracy rate	26.0	43.333
[7 , 25]	Staff quality	25.0	41.667
[6 , 25]	Freight	25.0	41.667
[7 , 23]	Service flexibility	25.0	41.667
[16 , 24]	Information system completeness	24.0	40.000
[16 , 25]	Order response time	24.0	40.000
[16 , 25]	Delivery punctuality	24.0	40.000
[16 , 23]	Customer satisfaction	22.0	36.667
[6, 25]	Business coverage	19.0	31.667
[23]	Transportation time	17.0	28.333
–	Mean	18.984	31.639

Step 3: According to the meaning of criteria, three main criteria C = (c₁, c₂, c₃) of service quality, enterprise strength and transportation capacity are concluded. Then the sub-criteria system for evaluating cold chain LSPs is established, where c₁ = (c₁₁, c₁₂, c₁₃, c₁₄, c₁₅), c₂ = (c₂₁, c₂₂, c₂₃, c₂₄), c₃ = (c₃₁, c₃₂, c₃₃), as shown in Fig. 2.

Fig. 2

Evaluation index system of cold chain LSPs.

Step 4: In the Tables 1 and 2, the judgment matrixes are established, where δ represents the decision matrix of main criteria. δ ₁, δ ₂ and δ ₃ represent the decision matrix of the different sub-criteria set, respectively. $\begin{matrix} δ = (\begin{matrix} 1 & 6 & 9 \\ 1 / 6 & 1 & 3 \\ 1 / 9 & 1 / 3 & 1 \end{matrix}), δ_{1} = (\begin{matrix} 1 & 2 & 4 & 4 & 6 \\ 1 / 2 & 1 & 2 & 2 & 4 \\ 1 / 4 & 1 / 2 & 1 & 1 & 2 \\ 1 / 4 & 1 / 2 & 1 & 1 & 2 \\ 1 / 6 & 1 / 4 & 1 / 2 & 1 / 2 & 1 \end{matrix}), \\ δ_{2} = (\begin{matrix} 1 & 4 & 4 & 6 \\ 1 / 4 & 1 & 1 & 2 \\ 1 / 4 & 1 & 1 & 2 \\ 1 / 6 & 1 / 2 & 1 / 2 & 1 \end{matrix}), δ_{3} = (\begin{matrix} 1 & 6 & 7 \\ 1 / 6 & 1 & 2 \\ 1 / 7 & 1 / 2 & 1 \end{matrix}) \end{matrix}$

The weight of criteria obtained through the consistency test, as shown in Tables 4 and 5.

Table 4

The weight of main criteria by using AHP method

Main criteria	Weight ( ${\bar{w}}_{i}$ )	Consistency test
c ₁	0.7703	λ_max = 3.5036;
c ₂	0.1618	CI = 0.0268;RI = 0.52;
c ₃	0.0679	CR = 0.0462

Table 5

The weight of sub-criteria by using AHP method

Sub-criteria	Weight	Final weight ( $w_{ij}^{1}$ )	Consistency test
c ₁₁	0.4389	0.3381
c ₁₂	0.2670	0.2057	λ_max = 5.01;
c ₁₃	0.1162	0.0895	CI = 0.0025;
c ₁₄	0.1162	0.0895	RI = 1.12;
c ₁₅	0.0617	0.0475	CR = 0.0022
c ₂₁	0.5947	0.0962	λ_max = 4.0104;
c ₂₂	0.1598	0.0259	CI = 0.0035;
c ₂₃	0.1597	0.0258	RI = 0.9;
c ₂₄	0.0858	0.0139	CR = 0.0039
c ₃₁	0.7582	0.0515	λ_max = 3.0324;
c ₃₂	0.1512	0.0103	CI = 0.0162;RI = 0.9;
c ₃₃	0.0906	0.0062	CR = 0.0278

Step 5: According to the evaluation criteria and the rating level S = (s₁, s₂, s₃, s₄, s₅), three relevant enterprise managers and seven industry experts are invited to give scores to evaluate the alternative providers. The voting results are shown in Tables 7–10.

Table 7

Evaluation results of provider a₁

Main criteria	Sub-criteria	s ₁	s ₂	s ₃	s ₄	s ₅
c ₁	c ₁₁	9	1	0	0	0
	c ₁₂	8	2	0	0	0
	c ₁₃	9	1	0	0	0
	c ₁₄	7	2	1	0	0
	c ₁₅	9	0	1	0	0
c ₂	c ₂₁	10	0	0	0	0
	c ₂₂	8	1	1	0	0
	c ₂₃	8	2	0	0	0
	c ₂₄	7	2	0	1	0
c ₃	c ₃₁	4	4	2	0	0
	c ₃₂	9	0	1	0	0
	c ₃₃	7	3	0	0	0

Table 8

Evaluation results of provider a₂

Main criteria	Sub-criteria	s ₁	s ₂	s ₃	s ₄	s ₅
c ₁	c ₁₁	9	1	0	0	0
	c ₁₂	9	1	0	0	0
	c ₁₃	8	2	0	0	0
	c ₁₄	5	3	1	1	0
	c ₁₅	8	2	0	0	0
c ₂	c ₂₁	7	2	1	0	0
	c ₂₂	7	1	1	1	0
	c ₂₃	8	1	1	0	0
	c ₁₁	7	2	1	0	0
c ₃	c ₁₂	7	0	0	3	0
	c ₁₃	5	1	3	1	0
	c ₁₄	8	1	1	0	0

Table 9

Evaluation results of provider a₃

Main criteria	Sub-criteria	s ₁	s ₂	s ₃	s ₄	s ₅
c ₁	c ₁₁	5	2	2	1	0
	c ₁₂	4	3	1	1	1
	c ₁₃	5	3	0	2	0
	c ₁₄	7	0	2	1	0
	c ₁₅	6	1	2	0	1
c ₂	c ₂₁	3	2	4	1	0
	c ₂₂	4	3	3	0	0
	c ₂₃	2	4	3	1	0
	c ₁₁	4	4	2	0	0
c ₃	c ₁₂	8	1	0	1	0
	c ₁₃	5	3	1	1	0
	c ₁₄	8	2	0	0	0

Table 10

Evaluation results of provider a₄

Main criteria	Sub-criteria	s ₁	s ₂	s ₃	s ₄	s ₅
c ₁	c ₁₁	3	3	2	1	1
	c ₁₂	4	2	3	1	0
	c ₁₃	3	3	3	0	1
	c ₁₄	6	3	0	1	0
	c ₁₅	4	1	3	1	1
c ₂	c ₂₁	2	4	3	0	1
	c ₂₂	2	5	1	1	1
	c ₂₃	3	2	2	2	1
	c ₁₁	3	4	2	0	1
c ₃	c ₁₂	9	1	0	0	0
	c ₁₃	4	2	2	1	1
	c ₁₄	6	2	1	1	0

Step 6: The decision matrix H is constructed by calculating the total score under the corresponding sub-criteria of each alternative. $\begin{matrix} H = \\ [\begin{matrix} \begin{matrix} 885 & 870 & 885 \end{matrix} & \begin{matrix} 840 & 870 & 900 \end{matrix} & \begin{matrix} 855 & 870 & 825 \end{matrix} & \begin{matrix} 780 & 870 & 855 \end{matrix} \\ \begin{matrix} 885 & 885 & 870 \end{matrix} & \begin{matrix} 780 & 870 & 840 \end{matrix} & \begin{matrix} 810 & 855 & 840 \end{matrix} & \begin{matrix} 765 & 750 & 855 \end{matrix} \\ \begin{matrix} 765 & 720 & 765 \end{matrix} & \begin{matrix} 795 & 765 & 705 \end{matrix} & \begin{matrix} 765 & 705 & 780 \end{matrix} & \begin{matrix} 840 & 780 & 870 \end{matrix} \\ \begin{matrix} 690 & 735 & 705 \end{matrix} & \begin{matrix} 810 & 690 & 690 \end{matrix} & \begin{matrix} 690 & 660 & 720 \end{matrix} & \begin{matrix} 885 & 705 & 795 \end{matrix} \end{matrix}] \end{matrix}$

The entropy, difference coefficient and weight are calculated respectively, as shown in Table 11.

Table 11

The weight of sub-criteria by using EW method

Criteria	c ₁₁	c ₁₂	c ₁₃	c ₁₄	c ₁₅	c ₂₁	c ₂₂	c ₂₃	c ₂₄	c ₃₁	c ₃₂	c ₃₃
Entropy	0.7380	0.6099	0.7279	0.6894	0.7454	0.5915	0.7578	0.6841	0.7647	0.6319	0.6919	0.7883
Difference coefficient	0.2620	0.3901	0.2721	0.3106	0.2546	0.4085	0.2422	0.3159	0.2353	0.3681	0.3081	0.2117
Weight	0.0732	0.1090	0.0760	0.0868	0.0711	0.1141	0.0677	0.0883	0.0657	0.1028	0.0861	0.0591

Step 7: The comprehensive weight vector of criteria can be calculated using formula (1) and (2). $\begin{matrix} \bar{W} = (0.7434, 0.1819, 0.0747); \\ W_{1} = (0.2825, 0.2559, 0.0777, 0.0887, 0.0386); \\ W_{2} = (0.1254, 0.0200, 0.0261, 0.0104); \\ W_{3} = (0.0604, 0.0101, 0.0042) . \end{matrix}$

Step 8: According to step 3, the factor set is U = C = (c₁, c₂, c₃), where c₁ = (c₁₁, c₁₂, c₁₃, c₁₄, c₁₅), c₂ = (c₂₁, c₂₂, c₂₃, c₂₄), c₃ = (c₃₁, c₃₂, c₃₃), and the comment set is S = (s₁, s₂, s₃, s₄, s₅).

Step 9: Conduct the single-factor FCE of alternatives. Take provider a₁ as an example, the fuzzy evaluation matrix of sub-criteria is constructed as follows: $R_{1}^{1} = (\begin{matrix} 0.9000 & 0.1000 & 0.0000 & 0.0000 & 0.0000 \\ 0.8000 & 0.2000 & 0.0000 & 0.0000 & 0.0000 \\ 0.9000 & 0.1000 & 0.0000 & 0.0000 & 0.0000 \\ 0.7000 & 0.2000 & 0.1000 & 0.0000 & 0.0000 \\ 0.9000 & 0.0000 & 0.1000 & 0.0000 & 0.0000 \end{matrix})$ $R_{2}^{1} = (\begin{matrix} 1.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ 0.8000 & 0.1000 & 0.1000 & 0.0000 & 0.0000 \\ 0.8000 & 0.2000 & 0.0000 & 0.0000 & 0.0000 \\ 0.7000 & 0.2000 & 0.0000 & 0.1000 & 0.0000 \end{matrix})$ $R_{3}^{1} = (\begin{matrix} 0.4000 & 0.4000 & 0.2000 & 0.0000 & 0.0000 \\ 0.9000 & 0.0000 & 0.1000 & 0.0000 & 0.0000 \\ 0.7000 & 0.3000 & 0.0000 & 0.0000 & 0.0000 \end{matrix})$

The single-factor fuzzy evaluation results of provider a₁ are as follows: $\begin{matrix} B_{1} = W_{1} \times R_{1}^{1} = (0 . 6257, 0 . 1049, 0 . 0127, \\ 0.0000, 0 . 0000) \end{matrix}$ $\begin{matrix} B_{2} = W_{2} \times R_{2}^{1} = (0 . 1696, 0 . 0093, 0 . 0020, \\ 0.0010, 0 . 0000) \end{matrix}$ $\begin{matrix} B_{3} = W_{3} \times R_{3}^{1} = (0 . 0362, 0 . 0254, 0 . 0131, \\ 0.0000, 0 . 0000) \end{matrix}$

Step 10: The membership degree of the evaluation results of a₁ can be obtained as follows: $\begin{matrix} Z (a_{1}) = \bar{W} \times B (a_{1}) = (0.4987, 0.0816, \\ 0.0108, 0.0002, 0 . 0000) \end{matrix}$

Similarly, the membership degree of other alternatives can be calculated: $Z (a_{2}) = (0.4898, 0.0830, 0.0102, 0.0084, 0 . 0000);$ $Z (a_{3}) = (0.2876, 0.1283, 0.0920, 0.0615, 0.0219);$ $Z (a_{4}) = (0.2193, 0.1543, 0.1337, 0.0509, 0.0330) .$

Step 11: The total score of each alternative is calculated according to Table 6 and formula, and the results are listed in Table 12: $\begin{matrix} M = Z \times S_{s}^{T} \\ = (\begin{matrix} 0.4987 & 0.0816 & 0.0108 & 0.0002 & 0.0000 \\ 0.4898 & 0.0830 & 0.0102 & 0.0084 & 0.0000 \\ 0.2876 & 0.1283 & 0.0920 & 0.0615 & 0.0219 \\ 0.2193 & 0.1543 & 0.1337 & 0.0509 & 0.0330 \end{matrix}) \\ \times {(90, 75, 60, 45, 30)}^{T} \\ = (51 . 6613, 51 . 2910, 44 . 4528, 42 . 6183) \end{matrix}$

Table 6

Comments and scores

Comment	s ₁	s ₂	s ₃	s ₄	s ₅
	very satisfied	satisfied	neutral	dissatisfied	very dissatisfied
Score	90	75	60	45	30

Table 12

The scores of alternative providers

Alternative providers	Very satisfied	Satisfied	Neutral	Dissatisfied	Very dissatisfied	Total scores
a ₁	0.4987	0.0816	0.0108	0.0002	0.0000	51.6613
a ₂	0.4898	0.0830	0.0102	0.0084	0.0000	51.2910
a ₃	0.2876	0.1283	0.0920	0.0615	0.0219	44.4528
a ₄	0.2193	0.1543	0.1337	0.0509	0.0330	42.6183

The proposed method is used to evaluate four alternative cold chain LSPs, and the highest score is a₁ (53.0574), indicating that a₁ has certain advantages in fresh cold chain transportation. In addition, the calculation results show that no expert is very dissatisfied with a₁ and a₂, and the degree of dissatisfaction with a₁ is much smaller than that of other providers, so the fresh e-commerce enterprise can choose a₁ as its LSP.

4.2 Sensitivity analysis

In the specific selection process, different weights of criteria would result in different ranking order of alternatives. In this section, a sensitivity analysis of criteria weights is conducted to verify the stability of the proposed method. According to perturbation method [43], the weights of the twelve evaluation sub-criteria in this paper are disturbed respectively, where parameter ς is in order at [0, 2] and the interval between values of ς is 0.05. Then, the FCE method is used to obtain the corresponding priority order when different parameters ς are taken, and a total of 492 experiments are conducted to obtain the sensitivity analysis results.

From Fig. 3, the alternative a₁ ranked first in the 487 experiments (>98.9%), and the potential change of the weights of evaluation criteria would not lead to the deviation of decision-making results, the ranking is always a₁ ≻ a₂ ≻ a₃ ≻ a₄. In conclusion, the proposed method is insensitive to the change of weight information. In other word, the proposed method is stable enough, and it can be applied in other cold chain LSP evaluation and selection problems.

Fig. 3

Sensitivity analysis results.

4.3 Comparison analysis

(1) Comparison analysis with TOPSIS method

In order to further explain the feasibility of the proposed approach, a comparison of the proposed method with TOPSIS method [42] is given.

According to the relevant steps, the positive ideal solution A^* and negative ideal solution A^- are obtained respectively. $\begin{matrix} A^{*} = \\ {\begin{matrix} 0.1185, 0.1280, 0.0345, 0.0507, 0.0160, 0.0702, \\ 0.0092, 0.0122, 0.0044, 0.0345, 0.0058, 0.0016 \end{matrix}}; \end{matrix}$ $\begin{matrix} A^{-} = \\ {\begin{matrix} 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, \\ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 \end{matrix}} . \end{matrix}$

Then, the separation measures $D^{*}$ and $D^{-}$ of each alternative from the A^* as well as A^- are calculated. $\begin{matrix} D^{*} = (0.0324, 0.0648, 0.1683, 0.1868), \\ D^{-} = (0.1919, 0.1855, 0.0543, 0.0444) . \end{matrix}$

Further, the relative closeness ζ of alternatives to the ideal solution is calculated. $ζ = (ζ_{1}, ζ_{2}, ζ_{3}, ζ_{4}) = (0.8557, 0.7412, 0.2438, 0.1919)$

Obviously, the ranking order of four alternatives is a₁ ≻ a₂ ≻ a₃ ≻ a₄, which is same as that obtained by the proposed method. However, compared with the method in this paper, TOPSIS method is complicated to calculate, and it is difficult to judge the alternatives with equal distances to the positive and negative ideal solutions. In addition, the evaluation results of FCE method are clearer and contain more decision-making information, which can provide better reference for enterprises, so the proposed method is more suitable for solving the decision-making problems with fuzziness and strong uncertainty.

(2) Comparison analysis with VIKOR method

In this part, a comparative analysis between the VIKOR method and the proposed method is presented in detail. In actual decision-making, experts may have different decision-making attitudes and then the different compromise coefficient v is adopted. With the change of v, the alternatives ranking would also be affected. Therefore, this paper values v for 10 times, and obtain 10 groups of rank order, as shown in Table 13. The results indicate that a₁ is the best choice among the four alternatives, which is the same as the result obtained by the proposed method. The compromise coefficient v in VIKOR is artificially given, which would make the final decision results have a certain subjectivity. However, the method proposed in this paper is highly systematic, and the interference of subjective factors is avoided in the calculation process. In addition, when there are fewer alternatives, the results of VIKOR may be hard to distinguish and the ranking cannot be determined, but FCE method is not limited by the number of alternatives, and alternatives can be distinguished from multiple dimensions. In this paper, alternatives can be compared from six dimensions (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied and total score), which has stronger applicability.

Table 13
The ranking results with different values v

v a ₁ a ₂ a ₃ a ₄ Ranking

0.1 0.0000 0.1566 0.8807 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.2 0.0000 0.1572 0.8771 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.3 0.0000 0.1578 0.8735 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.4 0.0000 0.1584 0.8700 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.5 0.0000 0.1590 0.8664 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.6 0.0000 0.1596 0.8629 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.7 0.0000 0.1602 0.8593 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.8 0.0000 0.1608 0.8557 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

0.9 0.0000 0.1614 0.8522 1.0000 a₁ ≻ a₂ ≻ a₃ ≻ a₄

v	a ₂	a ₃	a ₄	Ranking
0.1	0.1566	0.8807	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.2	0.1572	0.8771	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.3	0.1578	0.8735	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.4	0.1584	0.8700	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.5	0.1590	0.8664	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.6	0.1596	0.8629	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.7	0.1602	0.8593	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.8	0.1608	0.8557	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄
0.9	0.1614	0.8522	1.0000	a₁ ≻ a₂ ≻ a₃ ≻ a₄

5 Conclusion

In this paper, a comprehensive approach is proposed to select the cold chain LSPs. The main work includes the following: Firstly, an evaluation index system of cold chain LSPs is constructed by using SNA method. Secondly, the improved AHP method and EW method are combined to calculate the weight of the criteria to ensure the objectivity of weight. In addition, considering the fuzziness of cold chain LSPs selection problems, the FCE method is adopted to determine the ranking of alternatives. Finally, the numerical example, comparative analysis and sensitivity analysis are given to verify the validity and feasibility of the proposed method.

The SNA method is applied to construct the evaluation index system of cold chain LSPs, and the results show that service quality, enterprise strength and transportation capacity are the main criteria. At the same time, each main criterion has three to five sub-criteria. The details are shown in Fig. 2. Since this result is extracted from the literature by the SNA method, it can be widely used in other MADM problems of cold chain LSPs evaluation. Besides, the decision-making method in this paper does not consider the DMs’ bounded rational. Therefore, the proposed method is also available for other cold chain LSP selection.

However, there are still some limitations in this paper. In real-world, the psychological behavior of DMs is considered in the process of decision-making to make the results more realistic. Besides, due to the complexity of actual decision-making process and human’s thinking, it is often difficult for experts to give a definite evaluation value based on the evaluation criteria. Therefore, in future work, we will introduce regret theory to quantify the regret psychological of DMs. And then, this method can be improved to better depict realistic decision situations. For instance, it can be extended to other data environments, such as hesitant fuzzy numbers, Pythagoras hesitant fuzzy numbers, etc. Moreover, the new method is not only applicable to cold chain LSPs selection, but also can be applied in other fields, such as comprehensive risk warning system, investment project selection.

Conflict of interest

The authors declare that they have no conflict of interest.

Footnotes

Acknowledgments

The authors would like to thank the anonymous reviewers and editors for their insightful and constructive comments on our paper. This work was supported in part by the Humanities and Social Sciences Research General Project of Chongqing Education Commission (No. 22SKJD076, No. 19SKGH051), the open topic of the Center for International Cooperation and Innovation Development of Digital Economy (P2022-37), the youth talent plan of Science and Technology think tank (20220615ZZ07110237).

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