Performance evaluation of websites using entropy and grey relational analysis methods : The case of airline companies

Article history: Received January 16, 2017 Received in revised format: May 22, 2017 Accepted June 23, 2017 Available online June 23, 2017 The revolutionary alterations and conversions occurring in information and communication technologies, have triggered an increase in the electronic commerce applications. Airline tickets are one of the most popular items purchased on the internet. The airline websites have become a big distribution channel for the companies to sustain their competitiveness. At this moment, the competition is increasing as airlines try to acquire and retain customers in the airline industry. To acquire and retain customers in such a highly competitive market, it is important for airlines to understand their relative levels of quality in terms of critical elements affecting their competitive advantages. In this study, an integrated two-stage multi-criteria decision-making techniques were used for the measurement of the performance of the airline websites using the Entropy Weight Method and the Grey Relational Analysis approach. The performance of 11 airline companies’ websites operating in Turkey was evaluated in terms of seven criteria. The data of quality website from airlines websites were taken more than 30 trails on various occasions on different periods of times. The data has been taken from 1 December 2016 to 31 December 2016. The weights of the attributes were calculated by Entropy Weight Method, the evaluation of the alternatives using the Grey Relational Analysis method were given ranking of websites. Growing Science Ltd. All rights reserved. 8 © 201


Introduction
Lately, we have become witness to a crucial alteration of our lives to a global community with the onset of the internet era.The web is an increasingly more vital asset in many sides of life: government, education, commerce and more.Due to the internet and e-commerce spread out, many airline companies are striving to arouse customers to shift from Word of Mouth to the Word of Web.The web site of an airline company is an imperative factor of their operations and future developments.Most of airlines supply ticketing facilities, booking a flight, planning a route and flight information via their web sites.Hence, the websites of airlines have become an indispensable part of business processing and are being leveraged to reinforce the efficiency and effectiveness of the business, and to gain competitive advantage in the rigid competition environment.Utilizing the web devices many airlines have been able to raise their being customer-focused and their attributes of products and services.The quality of website is now regarded as a crucial aspect in attracting the customers' attention.Particularly in air transportation industry, the favor of the internet and e-commerce technologies makes it necessary to enhance the quality of airlines websites to accomplish more market share and struggle with other companies in this area.It is compulsory for companies to know how good their websites are in order to be more successful in their businesses.Most of airline companies now have constituted devoted websites to complement their business activities and to tender their services, but it is likely that a importantly larger ratio has no clear knowledge of how successful their sites are or how many gaps should be filled between the status quo and an ideal e-commerce website.However, they may not be aware about the quality of their websites or the gaps which should be considered to be an ideal ecommerce website (Lee & Kozar, 2006;Phippen et al., 2004).Put it differently, how much struggle must the airlines put into developing the websites in order to carry out their coveted levels?This raises the crucial subject of how airlines can impressively ascertain the attributes of e-commerce websites.Due to the multi dimensional attributes of the website development in this context, it must be properly tended by the multi criteria decision making (MCDM) methods.Recently, there is no codified model for appraising airline websites, and the existing methods do not provide enough understanding for airlines' proprietors to ascertain whether their websites meet the recognized guidelines from the attribute of ''website quality'' (Tsai et al., 2011).
We are inspired by the absence of such an overall website assessment model which reckon the qualitative criteria from the customer's standpoint for airline websites.In our recommended model, website effectiveness was examined under the consideration of the realistic criteria which were ascertained in the previous studies with extended form.
By suggesting comprehensive measurements based on standpoint of "web site quality", the recommended model can contribute the valuable information for airlines' owners to understand the relative level of competitive of their websites in the air transportation industry.
The main aim of the study is to establish a performance assessment model for airlines' websites, and to prioritize enhancement processes in order to best allocate the convenient assets for the web site quality.To attain that, a model is aimed that integrates Grey Relational Analysis and Entropy Weight Method for evaluating airlines' websites performance companies which operate in Turkey.Airline tickets are one of the most popular items purchased via firm websites, the importance of the study reveals that decision support will be provided to decision makers.In this direction, first of all, related website evaluation literature is mentioned.Then, the website performance for evaluation is described which is used in the methodology.Finally, the weights of the attributes of the 11 airline websites were calculated by the Entropy Weight Method, the evaluation of the alternatives using Grey Relational Analysis method were given ranking of websites as an integrated two-stages multi-criteria decisionmaking techniques and suggestions were made to the decision makers.

Literature review
In the literature, many website evaluation studies can be faced including the evaluation of airline web site quality and airline service quality.In this paper, more specifically, airline website evaluation is focused on.It is realized that statistical and decision making methods such as Decision Making Trial and Evaluation Laboratory-DEMATEL (Fontela & Gabus, 1976), Analytic Hierarchy Process-AHP (Saaty, 1980), Analytic Network Process-ANP (Saaty, 1996), VlseKriterijumska Optimizacija I Kompromisno Resenje-VIKOR (Opricovic & Tzeng, 2004), Fuzzy Analytical Hierarchy Process (Chang, 1996) often have been used for the airline website evaluation.Hidalgo et al. (2007) presented a quality evaluation model of airline web sites which was based on a fuzzy linguistic approach.Jati (2009) tested the Asian flag carrier airlines via online web diagnostic tools to assess the quality of the website.Author proposed a methodology for ascertaining and quantifying the best airlines websites based on many criteria of website quality by using AHP.In addtion, the same year, Tsai et al. (2009) proposed an integrated model for evaluating the airlines' websites in terms of the perspectives of "marketing mix 4Ps" and "website quality".The DEMATEL, the ANP and the modified VIKOR methods were used for evaluating airlines' websites.Tsai et al. (2011) introduced a combined model for assessing the airlines' websites functionality.The proposed model was based on the attitudes of ''marketing mix 4Ps'' and ''website quality'', in which the criteria analyzed via DEMATEL method, and then the weight of each criterion was calculated by ANP, finally the modified VIKOR method ranked the performance of the websites.Dominic and Jati (2011) tested the Asian airlines websites to evaluate the quality of the tested websites by using the online web diagnostic tools.Researchers proposed an assessment model for ascertaining and appraising the best airlines website based on many criteria of the website quality, which combines the linear weightage model (LWM), AHP, fuzzy analytical hierarchy process (FAHP) and one new hybrid model (NHM).Khan and Dominic (2013) aimed to check the Asian airlines website quality via online web diagnostic tools.The analytical hierarchy process (AHP) was used to evaluate the website quality of each airline and the results suggested the best airline operates in Malaysia.
As indicated above, the previous works have neglected to supply an extensive and systematic attitude that quantitatively assessment a website's overall performance, and their research models must be enhanced.Distinct web site quality criterion is not always entirely independent in reality (Wu & Lee, 2007).For that reason, this study integrates Grey Relational Analysis method and Entropy Weight Method to handle the interdependence between criteria instead of adopting individual approach.The Entropy Weight Method calculated the weights of criteria, which were integrated with the Grey Relational Analysis method to calculate the extensive performance variance rate of each website Entropy Weight Method can only acquire the ranking of websites.The presented model overwhelms the obstacles of the prior works and proposes enough insights for implanters to precisely appraise the present level of their websites according to the critical criteria that regulates their competitive advantages.

Methodology
This study aims to test and to measure the both Turkish flag carrier airlines website and not flag carrier Turkish airlines website quality via online web diagnostic tools.The proposed model is applied to analyze the websites of 11 air transportation companies for determining and evaluating the best airlines websites based on many criteria of website quality in Turkey.The eleven selected airline websites are: Turkish Airlines, Pegasus Airlines, Onur Airlines, SunExpress Airlines, Sky Airlines, Corendon Airlines, Freebird Airlines, İzair Airlines, Tailwind Airlines, Borajet Airlines and Anadolujet Airlines.
In the study, first of all, performance criteria have been determined by experts.The weights of the criteria were calculated by Entropy Weight Method and then the performance rankings of the websites were taken the alternatives via Grey Relational Analysis method.The Methodological framework of the study is shown in Fig. 1.

Entropy Weight Method
Decision makers choose from the alternatives in multi-criteria decision-making problems.Decision makers must be taken into consideration criteria which affect the alternatives when making this choice.There are many criteria that influence this decision in the selection process of any alternatives and each of these criteria in different severity levels are effective over alternatives.AHP and expert opinions as subjective evaluation methods are used to determine the weight of the criteria.Criteria are categorized according to expertss opinion that is diffucult, since generalisation cannot be made clearly and the objective assessment methods should be used in case of the deficiency of pairwise comparisons.Shannon is firstly introduced Information entropy in his paper of "A Mathematical Theory of Communications", which is a measure of uncertainty, then it has been broadly used in many areas such as engineering, management and so on (Wu et al., 2011).The entropy by Shannon, can be used to ascertain the disorder degree and its utility in system information.The smaller the entropy value is, the smaller the disorder degree of the system is.The index's weight is determined by the amount of information based on Entropy Weight Method, which is one of objective fixed weight methods (Li et al., 2011).
Entropy Weight Method includes following 5 steps (Deng et al., 2000;Shemshadi et al., 2011): Step 1: Construction of a decision matrix (X).A set of alternatives . Therefore, an n×m performance matrix (the decision matrix; X) can be obtained as: (1) where ij x is a crisp value indicating the performance rating of each alternative i A with regard to each criterion j C .
Step 2: To ascertain objective weights by the entropy measure, the decision matrix in Eq. ( 1) needs to be normalized for each criterion   The Normalized decision matrix is obtained as a result of the process.(3) Step 3: Calculate the entropy measure of every index using the following equation: Step 4: The degree of divergence   j d of the average intrinsic information contained by each criterion the more j d is, the more important the criterion jth is.
Step 5: The objective weight for each criterion

Grey Relational Analysis
Ju-Iong Deng formulated the grey system theory in 1982.A White system is specified when the internal message such as architecture, operation mechanism, system characteristics and parameters are completely known.Contrarily, if one cannot acquire any information and characteristics about the system, then it is a black system.The primary description of greyness is information being incomplete or unknown, thus an element from the incomplete message is adopted as grey elements.Grey Relation Analysis method measures the relations among the factors, and its definitions in mathematics (Wang, 2008;Lu et al., 2008).Grey Relational Analysis is broadly applied in evaluating or judging the performance of a complex project with meager information (Sentilkumar et al., 2014).More specifically, traditional grey relational analysis includes the following six steps (Zhai et al., 2009;Wu, 2002): Step 1: Construction of an initial decision matrix (X).Assuming that there are n data sequences characterized by m criteria, where ) ( j x i is the entity in the ith data sequence corresponding to the jth criterion.
Step 2: Normalize the data set.Data can be used by one of the three types.Larger is better, smaller is better and nominal is best.
Larger is better Smaller is better Nominal is best where ) ( j x obj is the target value for the jth criterion, and Normalization process is completed with the aid of the above equations. Step 3: Construct the normalized matrix and generate the reference sequence based on Eqs.(8-10) Normalized Matrix is the reference value in relation to the jth criterion and is determined by the largest normalized value of each criterion.


Step 4: The distance between the normalized value with reference criteria series, measured in an absolute way and absolute value matrix is generated.


It is used to eliminate the possibility that the extreme values in the data array and is usually taken 0,5.
Step 6: Calculate the grey relational degree.If the weights   i w of criteria are determined, the degree of grey coefficient oi  is computed as:

Application
The Application part of the study consists of three phases.During the first phase, data sets of criteria for measuring performance of the airline web sites and information about the preparation of the data set are provided.In the second phase, the weights of criteria are calculated by the Entropy Weight Method and during the last phase, the performance of the website using the Grey Relational Analysis was provided decision support for decision makers.

Preparation of Data Sets
In the study, 23 criteria were identified for evaluating the performance of the website primarily.The number of criteria were reduced to 7 criteria by 4 experts.Experts experienced in software and web design who were computer engineers and web masters.The criteria were used in this study and their descriptions are as in Table 1.

Table 1
Website Performance Measurement Criteria Criteria Definition C1 (Traffic) Browser collects data and the collected data transmitted to the website of the Alexa by browser, where it is stored and analysed to form the basis for company's web traffic reporting.

C2 (Page Rank)
It is used to calculate and display the PageRank for each Website.

C3 (Design Optimization)
The scripts, HTML or CSS codes optimized for faster loading.The optimization also reduces the number of website elements such as images, scripts, html, css codes or video.C4 (Load Time) It is used to calculate the time required to load a page and its graphics.

C5 (Response Time)
A Website server should respond to a browser request within certain parameters C6 (Markup) It is utilized to assess and calculate the number of HTML errors, which exist on the website, such as orphan codes, coding errors, missing tags and etc. C7 (Broken Link) Broken links always reduces the quality of website.Websites has internal or external links.
A visitor expects the links to be valid, loads successfully to the clicked page.
Table 2 presents the list of all criteria and their website quality evaluation tools, which is examined in this study.

The determination of the weights of the criteria using the Entropy Weight method
The weights of the criteria were determined by using the Entropy Weight Method in this study.Decision Matrix consists of the mean of 30 trails on various occasions on the different periods of times represented in Table 4.The website names are hidden for confidentiality and have been renamed WS1 to WS11.Decision matrix was normalized via Eq.( 2) and the normalized decision matrix was obtained.
Finally, the objective weight for each criterion was calculated.

Conclusion
In this paper, we have proposed a hybrid model to combine Entropy Weight Method and Grey Relational Analysis for determining and evaluating the quality of airline websites with the sample of eleven airline websites.We have assessed many dimensions of quality and each dimension was measured by using online diagnostic tools.The result of this study endorsed that the performance and the quality criteria were neglected by the the airlines websites.The airline industry adopts advanced ecommerce technologies to keep their loyal customers and attract new passengers, but it is likely that not all airlines' administrator have well-defined knowledge about how many gaps should be filled between the usual and a perfect website.According to our research; airline companies make more effort to meet these criteria in the context of website design.Airline websites should follow and encourage the use of recognised guidelines when designing website, this suggestion is responsible for web developers.To get results on the quality of in the context of Turkish airline's website, we have assessed sample data from airline websites and calculated traffic, page rank, design optimization, load time, response time, mark up and broken links.The proposed model has been implemented using Entropy Weight Method and Grey Relational Analysis.This research has some limititations, which arose in the number of the sample size and time factor, this research used the limited sample size 30 data and it was taken during short period observation time.
The future aims for this work are added criteria for assessing the performance and the quality of websites, such as privacy, availability, color scheme, security and browser compatibility problem.In addition, the supreme determining factor of the quality of the website is the users, the future aims for this study also encompasses the user's perspective, which contains the objective and subjective views of the website.The Future research includes adding more criteria to measure the website performance.
As the airline industry is highly rich information based industry and has a great amount of usergenerated travel content, the future research should be done with the context of customer satisfaction.
A theoretical framework needs to be developed which identifies the factors that measure the customer satisfaction, reputation, profitability, financial performance and loyalty with airline websites.
In addition on the grounds that definitive determinant of the quality site is the clients, the future headings for this exploration likewise includes the target and subjective perspectives of the site from the client's point of view.

Table 2
Online Web-Diagnostic Tools for Data CollectionThe data in Table1was taken from more than 30 trails on various occasions on different periods of times to analyze the websites.This data has been taken from 12/1/2016 to 12/31/2016.Table3depicts the descriptive statistics of the data set.

Table 3
The Descriptive Statistics of the Data Sets Table 10 depicts the proposed Entropy Weight Method and Grey Relational Analysis model performance scores and ranks the airline websites.