Comparison Study on Express Companies Based on AHP-FCE and AHP-TOPSIS

Author: Weitang Yin
Mentor: Guohua Zou
The Experimental High School Attached to Beijing Normal University


This paper proceeded a quantitative analysis on customers’ satisfaction on express companies, compared four express companies’ service satisfaction based on different scoring on the survey and provided relevant developing suggestions for the companies. AHP is utilized to determine the weight, and Fuzzy Comprehensive Evaluation (FCE) and TOPSIS method are used to compare the express companies’ performance. It analyzes the results and offers a future development suggestion for the express companies based on single index score and synthesis score.

Key words: AHP, Fuzzy Comprehensive Evaluation, TOPSIS, Express Company, Service Quality Evaluation, Satisfaction

1. Introduction

With the rapid development of the Internet, online shopping has become an important form of shopping for people, and express delivery business has gradually developed into a highly influential emerging industry. According to the 52ND Statistical Report on the Development of China’s Internet[3], as of June 2023, the number of online shopping users in the country reached 884 million, and according to the operation of the postal industry in 2022[4], the volume of express delivery in the year 2022 exceeded 110.5 billion. It can be seen that the development of express delivery business has an inseparable relationship with online shopping.

Nowadays, service quality has become an important indicator related to the strength and development of enterprises. Therefore, the competition between express companies is becoming more and more fierce, and the companies are paying higher attention to their own service quality of express and the customer satisfaction of delivery services in order to further enhance the company’s durability. Because the service key points of different companies are different, the satisfaction of target customers to the service quality of different express companies also differs. Therefore it is essential for every company to notice their strengths and weaknesses in order to enhance their market position.

Previous studies have already proved the evaluation model to be successful[7]. Yet most of these studies merely proceed analysis and give suggestions to the industry as a whole[6], which neglected the difference between enterprises. Based on the customer satisfaction survey results of four listed express companies, this paper conducts a quantitative study on the customer service quality of SF Express, Yunda Express, YTO Express and STO Express. This paper used two methods to compare the enterprises instead of one, which makes the result more robust. It also quantitatively measures the customer satisfaction of each company and puts forward suggestions for improving express service of different companies.

2 Establish the Evaluation System with AHP

2.1 Hierarchy Construction

An evaluation system is constructed by combining SERVQUAL model and service standard of express delivery industry. This paper used SERVQUAL as one of the standards because SERVQUAL scale proposed that the criteria of service quality is constituted of five indexes, and the combination of SERVQUAL model and the service standards of express delivery industry has been proven to be successful[7]. The overall goal of the evaluation system – customer satisfaction on service quality –is analyzed through five indexes: Empathy, Reliability, Timeliness, Convenience, Tangibles. A total of 5 primary indexes and 19 secondary indexes were selected, as shown in table 1.

2.2 Construction of Pairwise Judgement Matrix

According to the 1-9 scale method which effectively reveal the relative importance of one index compared to another, this paper combines the importance evaluation given by experienced customer opinions and expert opinions to each index, and obtains the evaluation matrix of the primary index and the secondary index. The evaluation matrices are as follows

2.3 Index Weight and Consistency Test

After the matrix is normalized, the principal eigenroots of each matrix are calculated, the weights of each index are calculated, and the consistency of each matrix is judged according to the eigenroot method of finding vectors by pairwise judgment matrix[1].

2.3.1 Weight of Primary Indexes

Through the method of finding eigenroot of the vector, the primary indexes’ weight is calculated as follows.

WZ=(0.0456, 0.5046, 0.2830, 0.1177, 0.0491) (7)

After testing, the consistency ratio is 0.030 < 0.1, matrix Z meets the consistency requirement.

2.3.2 Weight of Secondary Indexes

Through the method of finding eigenroot of the vector, the empathy indexes’ weight is calculated as follows.

WA=(0.0595, 0.1896, 0.5727, 0.1782) (8)

After testing, the consistency ratio is 0.054 < 0.1, matrix A meets the consistency requirement. Similarly, the weight of reliability indexes, timeliness indexes, convenience indexes, and tangibles indexes is calculated as follows.

WB=(0.1399, 0.1327, 0.5994, 0.0562, 0.0718) (9)

WC=(0.0812, 0.6596, 0.1552, 0.1040) (10)

WD=(0.0680, 0.3800, 0.1420, 0.4100) (11)

WE=(0.2500, 0.7500) (12)

After testing, the consistency ratio is 0.086 < 0.1, 0.046 < 0.1, 0.029 < 0.1, 0 < 0.1, respectively. Therefore, matrix B, matrix C, matrix D, and matrix E all meet the consistency requirement.

2.4 The Evaluation Set

2.4.1 Evaluation Level

The survey sets the evaluation criteria to 5 levels. M represents the score received. M1, M2, M3, M4, M5 represents very unsatisfied(1pt), unsatisfied(2pts), general(3pts), satisfied(4pts), very satisfied(5pts), respectively.

2.4.2 Data Collected

This paper takes the form of online questionnaire to obtain data. Specifically, the questions are designed to acquire information for the corresponding indexes. For example, For index B3, the question is how frequent is the lost of item occurring. Then the questionnaire is given out both online and offline. Finally, data is collected through the questionnaire backstage. Up to now, 183 questionnaires have been collected, of which 150 are valid. As the questionnaire is a multiple choice question, the amount of valid questionnaire of each company varies.

3 Comparison based on Fuzzy Comprehensive Evaluation

3.1 Data

According to the statistical data obtained from the questionnaire survey, the relative membership degree of each secondary index is obtained, as shown in Table 2.

Similarly, the relative membership degree of the other three companies are collected. With a total number of 42 questionnaires for Yunda Express, 62 for STO Express, and 41 for YTO Express.

3.2 Fuzzy Matrix Construction

According to the collected questionnaire data, the membership degree of each index of four express delivery enterprises is shown, and the fuzzy matrix of each secondary index RA, RB, RC, RD, and RE can be obtained.

3.3 Fuzzy Comprehensive Evaluation

B = WR (13)

Through the formula above, where W is the weight of each index and R is the fuzzy matrix, the fuzzy weight vector and fuzzy matrix of each secondary index are fuzzy transformed[2]. And the fuzzy comprehensive evaluation of each secondary index is obtained as shown follows.

By the same token, the fuzzy comprehensive evaluation of each secondary index of the same three companies are obtained. From these evaluations, the fuzzy matrix RZ of the primary indexes can be obtained through combining vectors BA, BB, BC, BD, BE into a matrix as follows.

3.4 Results

As the FCE method only evaluates the degree membership of the companies, it is a qualitative analysis and is unable to determine which company is better if they both belong to the same set. Therefore, a score is added to every level of satisfaction in order to proceed a quantitative analysis. Note vector T as follows.

T =0 30 60 80 100 (15)

Using the formula

S = BT (16)

Where B is the final membership degree vector for every company as shown in table 4.
By multiplying vector B by vector T, we get a precise score of every company. After the calculation, we get Ssf=90.6670, Syd=81.5652, Sst=81.6914, and Syt=82.8017.

From the scores, it’s obvious that SF Express is significantly higher than the other three companies, YTO Express is slightly higher than STO Express, and Yunda Express got the lowest score.

4 Comparison based on TOPSIS

4.1 Introduction

As FCE is suitable for problems that concern fuzzy definitions of variables, it can successfully model the problem studied in this paper. On the other hand, the problem studied in this paper also has the feature of optimization of company strategy and relatively large sample size. Therefore, TOPSIS method is adopted in this paper as it performs well in large sample questions and it does not require an objective function to be maximized.

4.2 Data Processing

Since TOPSIS method compares the scores of different indexes, the normalized criteria is needed. Because the data collected is all maximum type index, there is no need of forward transformation of data. As the questionnaire number of each company varies, summing up all the scores is imprecise. Therefore, this paper processed the data by acquiring the mean score of every index directly: The mean of scores indicates the company’s overall satisfaction, and it is normalized itself in order to be compared between different companies. Thus, this paper used score means as the indicator of satisfaction using the formula

Where Skj is the mean score for the j th index for company k, Skij is the score received from the i th survey for the j th index for company k, Nkj is the number of survey collected for the j th index for company k.

As the weight is to be considered in this study, it is essential for the weight to be considered in TOPSIS method. For the weight of every secondary index, this paper used the product of primary and secondary weight to determine the weight of secondary indexes directly. Specifically, this paper used the formula

4.3 Solve

First, the scoring of every index among the four companies has to be determined. The formula below indicates how the scoring was determined.

where Yji is the i th index scoring from company j. Then the scoring is calculated using formula (21) and formula (22) .

Where m is the number of indexes, wj is the weight of the j th index, Z+j and Zj is the highest and lowest score of the j th index, and Zij represents the scoring of the j th index of company i. Di+ and Di indicates the distance between the optimal scoring and company i’s scoring and the distance between the pessimal scoring and company i’s scoring, respectively.[5]

4.4 Results

Formula (23) calculates the final scoring of the companies.

Through this formula, the scoring of the four companies are Ssf = .9654, Syd=0.1179, Sst=0.1173, Syt=0.2058.

Obviously, SF Express scored much higher than the other three companies, YTO scored higher than Yunda, and STO got the lowest score.

5 Results and Conclusions

5.1 Results Analysis and Further Studies

Both the FCE method and the TOPSIS method indicated that SF Express’s customer satisfaction is significantly higher than the other three companies. The scoring of the other three companies differs, but the difference is subtle: YTO Express scored higher than STO Express and Yunda Express, yet the difference is inconsequential compared to SF Express’s high score.

After the analysis by synthesis, there must exist a single index that caused the difference between the companies. Therefore, a deeper study is conducted. In FCE method, the formula F = BT can calculate every scoring of every index of every company, as shown below.

Where Bkij is the i th secondary index from the j th primary index from company k.

Where Bji is the i th primary index from company j.

These two equations allows the scoring on every single index to be revealed directly.

After analysis, we found out that index B and C are very important. Among these two indexes, B3 and C2 are the main factors.

For reliability, the four companies scored as follows: Bsf=91.33 , Byd=84.64, Bst=83.97, and Byt=85.12.

For timeliness, the four companies scored as follows: Csf=91.06, Cyd=78.30, Cst=78.18, and Cyt=80.44.

For ”Lost of Item”, the four companies scored as follows: Bsf =91.93, Byd=87.86, Bst=79.84, and Byt=88.30.

For ”Arrive on Time”, the four companies scored as follows: Csf =91.66, Cyd=79.05, Cst=78.06, and Cyt=80.24.

The ranking of these four indexes’ scores is exactly the same as the synthesis analysis. Overall, on the specific indexes, SF Express still scored the highest and the other three didn’t reveal significant difference.

Through the weight analysis, we found that reliability and timeliness hold the highest weight, they held 50% and 28% of the total weight respectively. Among the secondary indexes, ”Lost of Item” and ”Arrive on Time” hold 30% and 18% of weight of the total evaluation system. Therefore, it is essential for express companies to guarantee that the package is precise and arrives on time in order to increase customer satisfaction.

From the data provided, SF Express scored the highest, the other three companies’ score ranking is consistent with their final ranking, this further emphasized the importance of these indexes.

5.2 Suggestions

Yunda Express, STO Express and YTO Express should pay more attention to the security of their packages in the future, specifically, make sure it does not get lost. On the other hand, arriving on time should be taken attention on since these indexes constituted a high proportion of customer satisfaction. SF Express is the only company that has a absolute advantage on almost every index except for one – price. Considering SF Express’s overnight delivery service, low satisfaction caused by the high service price is inevitable. Therefore, SF Express may lower the service price a little bit based on the current situation to further increase customer satisfaction. Yet this suggestion is inconclusive since it does not consider the pricing model, further research can be conducted studying the pricing model of express companies to determine whether the prices are able to be optimized.

In fact, the significant difference between SF Express and the other three express companies may be attributed to their operating mode. After interviewing the workers at the express stations, we were informed that SF Express adopts the strategy of district management which requires workers working at SF Express to directly provide service to the assigned districts. It also regulates the company with a direct operation system to the entire corporation. The other companies adopted external contracting strategy. This kind of strategy has a main drawback that some of the contracted people lacks professional ability, this caused a higher difficulty for these companies to regulate the corporation. On the other hand, the service quality and professional level cannot be guaranteed, which caused the lower level of professional skill, leading to a lower customer satisfaction. This may be the key factor that caused the significant difference between Sf Express which adopts the direct operation system and the other three companies that adopts the external contracting strategy. Therefore, another way to improve customer satisfaction for the three companies is to change the operating mode.

6 Reflections

6.1 Advantages

When determining the weights, we took reference from different people to make the weight determination more robust and lowers the risk of wrong weight determination.

This paper used two models to conduct research on express service satisfaction. Compared to using a single model, this paper has a more robust result and avoids error caused by an inappropriate model.

Previous studies are targeted at the entire express industry’s satisfaction. Although their results are significant, they ignored the difference between companies themselves that may have caused the difference between customer satisfaction. Therefore the suggestions offered in those papers also ignore the difference between companies. This paper conducted a comparison study on different express companies, found difference between the satisfaction and the operating mode, and made different suggestions to different companies. This paper creatively adopts two different models to solve the problem. On the other hand, this paper also studies the problem and give suggestions at a more detailed perspective, which foster the improvement of express companies since the problem is more specified.

6.2 Deficiencies

This paper used AHP to determine the weights, yet this method may be influenced by subjective factors. Although this paper collected suggestions from multiple perspectives to alleviate wrong weight determination, manual weight determination is still easily influenced by subjective matters. In the future, other objective methods such as entropy weight method may be combined with AHP to determine the weight in order to mitigate subjective influence.

The two models have their own advantages and disadvantages, and these models have difference on evaluation. In future studies, model averaging methods may be used to make the results more robust.
This paper only gives suggestions for express companies based on customer satisfaction, yet in real life practices, more complicated situations such as enterprise profit, worker satisfaction have to be considered. Future work may focus on other more complicated situations to provide further suggestions and help express company’s development in the future.


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About the author


Weitang is an 11th-grader at The Experimental High School Attached to Beijing Normal University. He has participated in many mathematical competitions, including SMC, AMC, and ARML. Throughout his mathematical journey, Weitang found a deep fascination with data analysis, which illuminates real-life scenarios in a vivid manner. His passion for this field motivated his participation in the HiMCM contest, where he and his team conducted extensive research on the carbon emission problem. Inspired by this experience, Weitang has embarked on his intellectual exploration of data science and statistics, as shown in his paper. Beyond academics, Weitang is an electronic music lover who cherishes “patterns” in both the musical and mathematical realms.