Performance evaluation of port supply chain based on fuzzy-matter-element analysis

Abstract

Performance evaluation of port supply chain involves various factors. These factors are characterized by fuzziness and incompatibility. It is a complicated multi-layered fuzzy evaluation issue. Based on the theoretical framework of balanced score card (BSC), this paper established a performance evaluation index system for port supply chain involving finance, customers, internal operation, learning and development. An evaluation model was constructed using fuzzy-matter-element analysis to comprehensively evaluate port supply chain performance. Results showed that the proposed evaluation method considered the fuzziness of designed indexes and combined with matter-element characteristics. The method was simple, effective and feasible.

Keywords

Fuzzy-matter-element performance evaluation port supply chain

1 Introduction

Ports are important links in the global logistics chain. The port supply chain formed around port development is the general development trend of the world port system. Port supply chain is a supply chain centered at port enterprises and its operation efficiency can influence the operating cost and service level of port systems. High-efficiency operation of supply chains integrate social resources, reduce logistics costs and improve the overall logistics service level, whereas low-efficiency operations bring enterprises extra transaction costs and information expenses, waste social resources, and weaken the competitiveness of the whole supply chain [1]. Therefore, performance evaluation is an important means for improving operation of the port supply chain.

Performance evaluation of port supply chain maily includes establishing the evaluation index system and selecting evaluation methods. Evaluation results are determined by systemization of the index system, rationale of the evaluation method and the accuracy of evaluation data. Selecting an evaluation method is the key link in supply chain performance evaluation. Different methods may bring significantly different results [2]. Selection of evaluation indexes and their weights are directly correlated with the knowledge level and personal preferences of evaluators, thus having certain subjectivity and fuzziness. Impact of subjective factors should be avoided as much as possible in performance evaluation [3]. Fuzzy mathematics is based on fuzzy transformation and the maximum membership principle and considers various factors or main factors related to the object under evaluation. It is a feasible and effective method for evaluating the fuzzy problem of port supply chain performance.

2 Literature review

The theory of matter-element analysis proposed by Cai [4] centered on promoting object transformation and solving incompatibility problems and is applicable to multi-factor evaluation. On this basis, Pan et al. [5] combined the concepts of fuzzy set and Euclid approach degree, and constructed a fuzzy-matter-element analysis method based on Euclid approach degree. Liu et al. [6] suggested using the principle of matter-element analysis and combining the concepts of fuzzy set and Euclid approach degree to introduce the entropy theory of information theory into the weight calculation. They established a fuzzy-matter-element evaluation model based on entropy. Based on Cai Wen’s matter-element analysis theory, Li [7] improved the membership function of index values to evaluation registrations and developed the compound fuzzy-mater-element matrix. They obtained weights of indexes through the mutual modification of subjective and objective weights and determined the comprehensive evaluation registration based on Hamming approach degree of weighting, thus establishing an improved fuzzy-matter-element evaluation model. In the beginning, fuzzy-matter-element analysis was used to evaluate the sustainable use of water resources and urban sustainable development. With continuous research, it is applied to more and more fields, such as performance evaluation, quality assessment, management effect evaluation, various management fields [8].

Performance evaluation of port supply chain involves various influencing factors. The relationships among different factors are uncertain and some are even incompatible with each other [9]. Supply chain performance can be evaluated by a subjective scoring method, analytic hierarchy process (AHP), fuzzy mathematics, data envelopment analysis, gray evaluation, genetic algorithm, and so on. Fuzzy processing is the most common qualitative-quantitative method, while matter-element analysis is an important method for solving the incompatibility problem. To address incompatibility and uncertain relationships among indexes, a port supply chain performance evaluation model was established through fuzzy-matter-element analysis. It was then verified by real examples.

3 Methodology

Fuzzy-matter-element analysis is an evaluation approach that combines extenics and fuzzy comprehensive evaluation. It may be described in four steps: ① establish the matter-element model; ② construct the fuzzy relation matrix; ③ calculate ordering vectors; ④ calculate comprehensive weight.

(1) Establish the matter-element model

Matter-element is the logic cell of extenics and the basic unit for object description. Given the name of an object N, its value about feature c is v and a 3-element set (R = (N, c, v)) is the basic unit to describe the evaluating object, called a matter-element. Meanwhile, the name, feature and value of objects are called the three elements of the matter-element. If one object has many features, the classical matter-element described by n evaluation index features (C₁, C₂, …, C_n) and corresponding values (V₁, V₂, …, V_n) can be expressed as:

$\begin{matrix} R (t) & = & [\begin{matrix} N & c_{1} & v_{1} \\ c_{2} & v_{2} \\ \cdot & \cdot \\ \cdot & \cdot \\ \cdot & \cdot \\ c_{n} & v_{n} \end{matrix}] \\ = & [\begin{matrix} N (t) & c_{1} (t) & < a_{1} (p), b_{1} (p) > \\ c_{2} (t) & < a_{2} (p), b_{2} (p) > \\ \cdot & \cdot \\ \cdot & \cdot \\ \cdot & \cdot \\ c_{n} (t) & < a_{n} (p), b_{n} (p) > \end{matrix}] \end{matrix}$ (1)

The matter-element is composed of N and its n features as well as the expanded standard value range (v_pi = < a_pi, b_pi >) also known as the joint domain matter-element, denoted as:

$\begin{matrix} R (t) & = & (N, C, V_{p}) \\ = & [\begin{matrix} N & c_{1} (p) & < a_{1} (p), b_{1} (p) > \\ c_{2} (p) & < a_{2} (p), b_{2} (p) > \\ c_{n} (p) & < a_{n} (p), b_{n} (p) > \end{matrix}] \end{matrix}$ (2)

Where v_i (t) ⊂ v_i (p) , i = 1, 2, …, n

Let v_ij = < a_ij (t) , b_ij (t) > (i = 1, 2, ⋯ , n ; j = 1, 2, ⋯ , m) be the extension interval number given by the jth expert. According to the formula: $v_{ij} = \frac{a_{ij} (t) + b_{ij} (t)}{2} / - \frac{\underset{max}{a_{ij} (t)} + \underset{max}{b_{ij} (t)}}{2}$ (3)

The correlation value is calculated from: $k_{i} (v_{i}) = {\begin{matrix} - ρ (v_{i}, v_{i} (t)) / | v_{i} (t) |, v_{i} \in v_{i} (t) \\ ρ (v_{i}, v_{i} (t)) / [ρ (v_{i}, v_{i} (p)) \\ - ρ (v_{i}, v_{i} (t))], v_{i} \in v_{i} (t) \end{matrix}$ (4)

where ${\begin{matrix} ρ (v_{i}, v_{i} (t)) = | v_{i} - [a_{i} (t) + b_{i} (t)] / 2 | \\ - [b_{i} (t) - a_{i} (t)] / 2 \\ ρ (v_{i}, v_{i} (p)) = | v_{i} - [a_{i} (p) + b_{i} (p)] / 2 | \\ - [b_{i} (p) - a_{i} (p)] / 2 \end{matrix}$ (5)

If v_k ∈ v_k (p), the comprehensive correlation between p and N (t) is: $k (p) = \sum_{i = 1}^{n} λ_{i} k_{i} (v_{ij})$ (6) where λ_i represents the weight coefficients of features. The judgment criterion of whether p belongs to N (t) is:

When k (p) ≥0, p ∈ N (t). When -1 ≤ k (p) ≤0, p ∈ N, but p ∈ N (t). When K (p) ≤ -1, p ∈ N and p ∈ N (t).

(2) Construct the fuzzy relation matrix

Fuzzy judgment matrix A = (a_ij)

$\begin{matrix} a_{ij} & = & S_{i} / (S_{i} + S_{j}), i = 1, 2, \dots, m; \\ j = 1, 2, \dots, n \end{matrix}$ (7)

This judgment matrix has to meet the condition of additive consistency. The discrimination formula of additive consistency of the fuzzy judgment matrix is:

$\begin{matrix} ρ & = & \frac{1}{m (m - 1) (m - 2)} \\ \sum_{i = 1}^{m = 1} \sum_{j = 1 \neq 1}^{m} \sum_{\underset{k \neq i, j}{k = 1}}^{m} | a_{i}, j - (a_{ik} + a_{kj} - 0.5) | \end{matrix}$ (8)

For the fuzzy judgment matrix which fails to attain additive consistency, the additive consistency index is ρ > 0. Higher ρ reflects the poorer consistency of the judgment matrix A. In practical application, it can fix a threshold ɛ > 0 (ɛ = 0.2). When ρ < ɛ, it can determine that A has satisfied additive consistency.

(3) Calculate the ordering vector

The ordering vector of the fuzzy judgment matrix can be calculated using the sum-product method or root method.

① Sum-product method

$\begin{matrix} w^{(0)} & = & (w_{1}, w_{2}, \dots, w_{n})^{T} \\ = & [\frac{\sum_{j = 1}^{n} a_{1 j}}{\sum_{i = 1}^{n} \sum_{j = 1}^{n} a_{ij}} \frac{\sum_{j = 1}^{n} a_{2 j}}{\sum_{i = 1}^{n} \sum_{j = 1}^{n} a_{ij}} \dots \frac{\sum_{j = 1}^{n} a_{nj}}{\sum_{i = 1}^{n} \sum_{j = 1}^{n} a_{ij}}] \end{matrix}$ (9)

② Root method

$\begin{matrix} w^{(0)} = (w_{1}, w_{2}, \dots, w_{n})^{T} \\ = [\frac{\sqrt[n]{\prod_{j = 1}^{n} a_{1 j}}}{\sum_{i = 1}^{n} \sqrt[n]{\prod_{j = 1}^{n} a_{ij}}} \frac{\sqrt[n]{\prod_{j = 1}^{n} a_{2 j}}}{\sum_{i = 1}^{n} \sqrt[n]{\prod_{j = 1}^{n} a_{ij}}} \dots \frac{\sqrt[n]{\prod_{j = 1}^{n} a_{nj}}}{\sum_{i = 1}^{n} \sqrt[n]{\prod_{j = 1}^{n} a_{ij}}}] \end{matrix}$ (10)

(4) Calculate the comprehensive weight

The higher-accuracy ordering vector (W (o)) is further calculated from the initial iteration value (V) that uses the ordering vector (W (O)) as the eigenvalue:

Step 1: V₀ = (v₀₁, v₀₂, ⋯ , v_0n) ^T is used as the initial iteration value and the eigenvector V_k+1 is calculated from V_k+1 = EV_k. The infinite norm (∥ V_k+1 ∥ _∞) of V_k+1 is calculated.

Step 2: Judge whether the iteration shall be continued. If ∥V_k+1 ∥ _∞ - ∥ V_k ∥ _∞ < ɛ (ɛ can be set 0.01), ∥V_k+1 ∥ _∞ is the maximum characteristic root λ_max. After the normalization of V_k+1, the vector W^(k) = V_i+1 gained from $v_{k + 1} = [\frac{v_{k + 1, 1}}{\sum_{i = 1}^{n} v_{k + 1, i}} \frac{v_{k + 1, 2}}{\sum_{i = 1}^{n} v_{k + 1, i}} \dots \frac{v_{k + 1, n}}{\sum_{i = 1}^{n} v_{k + 1, i}}]$ is the comprehensive weight of the evaluating object.

Step 3: Otherwise, iterate again by using $v_{k} = \frac{v_{k + 1}}{{∥ v_{k + 1} ∥}_{\infty}} = [\frac{v_{k + 1, 1}}{{∥ v_{k + 1} ∥}_{\infty}} \frac{v_{k + 1, 2}}{{∥ v_{k + 1} ∥}_{\infty}} \dots \frac{v_{k + 1, n}}{{∥ v_{k + 1} ∥}_{\infty}}]$ as the new initial value.

4 Result analysis and discussion

In this paper, port supply chain performance was evaluated by the fuzzy-matter-element model. Analysis and discussion follow.

4.1 Establishment of the evaluation index system

The performance evaluation index system for port supply chain was established according to the balanced score card (BSC), which includes four level-1 indexes: customer, finance, supply chain operation and learning & development.

Customer: customer satisfaction. In port supply chain, customer satisfaction is the evaluation of logistics service level of the port. It can be evaluated through market share, customer complaints, on-time delivery (OTD) and time flexibility.

Finance: profitability. Profitability refers to the capability of a company to earn profits within a certain period. Measuring indexes of the profitability of port supply chain include operating profit ratio, ratio of profits to cost, return on investment (ROI), profit growth rate and economic value added (EVA).

Supply chain operation. It is mainly reflected by service capability, information sharing and transfer, task delivery and rate of partner change of the port supply chain.

Learning and Development. It is the foundation of sustainable development of port supply chain and is represented by corporate culture as well as human resources. Corporate culture is beneficial to form the core competitiveness of the port supply chain, whereas human resource input is conducive to improving production efficiency and service capability.

4.2 Performance evaluation based on the fuzzy-matter-element analysis

Port supply chain A was composed of several enterprises and offered cargo-handling, transmission, storage, clearance of goods, and other services by depending on port B. Due to the policy prohibition on monopolies, each business had at least two competitive enterprises. With sufficient supply and protective policies, there was no fierce competition between enterprises in the supply chain.

Port B had 24 production berths, including 5 dead-weight tonnage (dwt) berths. Its frontage was over 5,000 m long and the annual approved throughput was 42 million tons. The water depth at the main course is 16 m, and normal entering and leaving of dwt ships was allowed. The storage yard covered an area of 1,800,000 m², and was stocked with mechanical equipment. It possessed good natural conditions, rich natural resources in the hinterland and developed transportation. Due to surrounding competitive ports, the hinterland had overlaying to a certain extent.

Values of evaluation indexes were gained through investigation analysis of the port supply chain A and expert scoring (Table 1).

In this case, full score is 10. Scores reflects performances of indexes. The relationships between scores and performances are shown in Table 2.

Weights of indexes were calculated with fuzzy analytic hierarchy process. Scores of level-1 indexes were given by decision-makers of enterprises in the supply chain and experts (Table 3).

Extension intervals of all indexes were calculated (Table 4).

Data in Table 3 were processed according to:

$a_{ij} (t) = \frac{a_{ij} (t)}{\underset{max}{a_{ij} (t)}}, b_{ij} (t) = \frac{b_{ij} (t)}{\underset{max}{b_{ij} (t)}}$ (11)

Then, the classical matter-element of Customer was calculated:

$R (c) = (N, C, V_{0}) = [\begin{matrix} N_{0} & c_{1} & < 0.867, 0.882 > \\ c_{2} & < 0.867, 1.000 > \\ c_{3} & < 0.800, 0.882 > \\ c_{4} & < 0.941, 1.000 > \\ c_{5} & < 0.933, 1.000 > \end{matrix}]$ (12)

The joint domain matter-element of Customer was:

$R (p) = (N, C, V_{p}) = [\begin{matrix} N & c_{1} & < 0, 1.000 > \\ c_{2} & < 0, 1.000 > \\ c_{3} & < 0, 1.000 > \\ c_{4} & < 0, 1.000 > \\ c_{5} & < 0, 1.000 > \end{matrix}]$ (13)

Extension intervals of Customer are shown in Table 4:

$R (c) = (N, C, V_{0}) = [\begin{matrix} N_{0} & c_{1} & 0.875 \\ c_{2} & 0.938 \\ c_{3} & 0.844 \\ c_{4} & 1.000 \\ c_{5} & 0.969 \end{matrix}]$ (14)

Then, calculate the correlation was calculated as:

$\begin{array}{l} ρ (v_{1}, v_{(0)}) \\ = | v_{1} - [a_{1} (p) + b_{1} (p)] / 2 | - [b_{1} (t) - a_{1} (t)] / 2 \\ = | 0.875 - 0.8745 | - 0.0075 = - 0.007 \\ ρ (v_{1}, v_{(p)}) \\ = | v_{1} - [a_{1} (p) + b_{1} (p)] / 2 | - [b_{1} (p) - a_{1} (p)] / 2 \\ = | 0.875 - 0.5 | - 0.5 = - 0.125 \\ v_{1} (0) = b_{1} (0) - a_{1} (0)] = 0.0115 \end{array}$

Given that v₁ ∈ v₁ (0)

$k_{1} (v_{1}) = - ρ (v_{1}, v_{1} (0)) / | v_{1} (0) | = 0.467$

Similarly, it was calculated that k₂ (v₁) =0.465, k₃ (v₁) =0.466 and k₄ (v₁) = -0.5

It can be observed in Equation (2) that k (v) =0.273. Similarly, correlations of other indexes with the overall evaluation objective were calculated (Table 5).

Then, the standard deviation is: $S_{j} = (0.432, 0.433, 0.434, 0.47)$

Establish the fuzzy matrix: $A = [\begin{matrix} 0.500 & 0.501 & 0.501 & 0.172 & 0.168 \\ 0.499 & 0.500 & 0.501 & 0.172 & 0.167 \\ 0.499 & 0.499 & 0.500 & 0.172 & 0.167 \\ 0.828 & 0.828 & 0.828 & 0.500 & 0.492 \\ 0.832 & 0.833 & 0.833 & 0.508 & 0.500 \end{matrix}]$ (15)

A satisfies additive consistency, as may be seen by calculating ρ = 0.00075 < 0.2.

The ordering vector was calculated through the sum product method or root method: W⁽⁰⁾ = (0.28, 0.28, 0.28, 0.16). Next, it was used as the initial iteration value, finding that ɛ = 0.002 < 0.01. Therefore, weights of level-1 indexes were W⁽⁰⁾ = (0.28, 0.28, 0.28, 0.16). Weights of rest levels of indexes were calculated in the same way (Table 6).

5 Conclusion

To establish a scientific and objective performance evaluation model for port supply chains, fuzzy mathematics and matter-element analysis were combined to evaluate port supply chain performance. It was concluded that:

The comprehensive evaluation value of the studied port supply chain was 8.22, indicating good performance. Supply Chain Operation and Learning and Development had higher scores than Customer and Finance, suggesting that the port supply chain needed improvement in the Customer Satisfaction and Profitability. The port supply chain required further improvement.

The port supply chain performance was evaluated by fuzzy-matter-element analysis which solved fuzzy relationships and incompatibility between indexes. The established evaluation model solved for the effect of different factors on the research problem and fuzziness in the evaluation process as well. It combined qualitative evaluation and quantitative computation organically, increasing the accuracy of supply chain performance evaluation.

Evaluation results presented high objectivity and practicability, proving that the established model was simple, effective and feasible.

Port supply chain evaluation was explored based on actual examples, reaching helpful conclusions. However, the following problems are complicated and still need further deep research: subjectivity of the model during practical usage and weighting process, comparison with other evaluation model.

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