Airports evaluation and ranking model using Taguchi loss function, best-worst method and VIKOR technique

Journal of Air Transport Management 68 (2018) 4e13

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Airports evaluation and ranking model using Taguchi loss function, best-worst method and VIKOR technique Payam Shojaei, Seyed Amin Seyed Haeri*, Sahar Mohammadi Department of Management, School of Economics, Management & Social Sciences, Shiraz University, Shiraz, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 February 2017 Received in revised form 21 May 2017 Accepted 22 May 2017 Available online 30 May 2017

Within the past decades both the number and quality of the airports in the world has been growing significantly. Despite this fact, research areas such as, performance evaluation and ranking of these airports based on different sets of criteria and techniques, are conspicuously untapped. This study aims to contribute to this area by proposing an evaluation and ranking model using an integration of Taguchi Loss Function, best-worst method (BWM) and VIKOR technique. The proposed model allows decision makers to set different target values and consumer's tolerance thresholds for each criterion based on which country's airports are being ranked and also reduce the amount of pairwise comparisons by using BWM. Also a real world case study is presented. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Airports ranking Taguchi loss function Best worst method VIKOR

1. Introduction Regarding expedient nature of airports, they potentially are capable of having significant influence on a country's economic development (Tovar and Martín-Cejas, 2010). Nowadays, striving to increase revenues and reduce losses are integral parts of efforts toward continuous improvement (Yang, 2010). On the other hand, global demand for air trips had an average increase of 5.2 percent annually since 1997 (Ahn and Min, 2014). Air transportation industry development is partially due to increases in international trades, and people's increasing propensity to travel. Other reasons of the air transportation industry development include creating jobs and providing an opportunity for people of different geographical locations to meet and share their cultures (Yu et al., 2008). Air traffic, cargo shipping and trip demands increase along with strict international standards and flight regulations are rendering airports as essential infrastructures of air transportation industry, operating as highly complex dynamic systems (Tovar and MartínCejas, 2010). In the current global economy conditions, airports magnitude in passengers and cargo traffic makes their performance

* Corresponding author. Department of Management, School of Economics, Management & Social Sciences, Shiraz University, Shiraz, Iran. E-mail addresses: [email protected] (P. Shojaei), amin.seyedhaeri@gmail. com (S.A. Seyed Haeri), [email protected] (S. Mohammadi). http://dx.doi.org/10.1016/j.jairtraman.2017.05.006 0969-6997/© 2017 Elsevier Ltd. All rights reserved.

assessment an indispensable task. Barros and Dieke (2008), address airports performance evaluation importance, through three main reasons as follows:
Efficient airports are imperative to the continuity of airlines services
Performance evaluation helps governments to monitor their investments efficaciousness
It provides airport managers with valuable insights about their airport rank amongst others Therefore, continuous performance evaluation through appropriate tools is paramount to effective airport management. According to the World Bank data (Air transport statistics, 1970-2015), within recent years global air transportation market enjoyed a substantial growth, and numerous international airports were either developed or constructed, hence, airports managers are obligated to meet international measures and improve airport's performance. In order to evaluate and rank airports there exist numerous criteria to be considered. Various researches addressed efficiency and productivity aspects of airport operations (see, Pels et al., 2003; Barros, 2008; Barros et al., 2010; De Nicola et al., 2013) but there are only a few researches providing decision makers (airports managers, governments, investors and etc.) with a proper tool to understand relative ranks of the airports based on a set of criteria. Lack of sufficient research in this area, along with the air

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transportation industry requirements were the main drives of this paper. In this study, an integrated method of Taguchi loss function, best-worst method (BWM) and VIKOR technique is proposed to evaluate and rank airports. First, the Taguchi loss function is applied to assess the loss of each evaluation criterion. Second, BWM is used to calculate the relative weights of criteria. Finally, by using the decision matrix developed based on BWM weights and Taguchi loss function, airports are ranked using VIKOR technique. The proposed method increase the efficiency of evaluation and ranking process by employing BWM to obtain criteria weights which reduces the number of pairwise comparisons substantially, and simultaneously provide more consistent weights. Along with efficiency this method also provides a precise ranking by enabling decision makers to set their own target values and consumer's tolerance thresholds with regard to their country's cultural context. Additionally, this model proposes a compromise solution that decreases the level of conflict among decision makers. The proposed model is capable of taking into account both data and experts opinions in an integrated manner which leads to a more effective decision making process. The rest of this paper is organized as follows. Section 2 presents a background on airports performance evaluation also researches in this area will be discussed. Through discussing various researches ranking criteria are elicited. Next section describes the methodology proposed, additionally, adopted techniques are elaborated. In sections 4 a real world case study is provided to illustrate the application of the proposed model, and in the last section, conclusions are made. 2. Review of the airports evaluation and ranking methods In the literature numerous methods proposed with the objective of airports evaluation and ranking. These methods could be categorized within two main contexts of operational efficiency and service quality evaluation. However, there only exist a few related researches in the context of service quality evaluation, a vast body of knowledge has been developing within the context of operational efficiency and productivity assessment. The proposed methods will be summarized in the following subsections. 2.1. Operational efficiency and productivity assessment The majority of researches were in the context of operational efficiency and productivity assessment using non-parametric data envelopment analysis (DEA) and Malmquist productivity index (Gillen and Lall, 1997, 2001; Parker, 1999; Fernandes and Pacheco, 2002; Sarkis and Talluri, 2004; Lin and Hong, 2006; Barros and Weber, 2009; Barros et al., 2010; De Nicola et al., 2013; Tsui et al., 2014a,b). Also other methodologies adopted to compensate for DEA method shortcomings such as econometric frontier model to investigate efficiency quantitatively (Pels et al., 2001, 2003; Barros, 2008; Martín et al., 2009). These researches incorporated various input and output variables to assess and compare efficiency and productivity of different airports. For example Sarkis and Talluri (2004) used four input measures and five output measures to evaluate and rank 44 major U.S. airports. Input measures, including airport operational costs, number of airport's employees, gates and runways, and output measures, including operational revenue, passengers flow, commercial and general aviation movement, and total cargo transportation. 2.2. Service quality evaluation In addition to the abovementioned context, there has been researches using multi criteria decision making (MCDM) techniques

5

and multi-attribute approaches, evaluating and ranking airport's service quality as another aspect of their operations (Yeh and Kuo, 2003; Kuo and Liang, 2011; Prakash and Barua, 2016). Yeh and Kuo (2003) used surveys to present a fuzzy multiattribute approach, to evaluate passenger service quality of 14 Asia-Pacific international airports. In this research they obtained an overall service performance index for each airport based on degree of optimality concept which demonstrates the relative ranking of airports in the context of passenger service attributes. This index is obtained by including the decision maker's confidence level and preference on fuzzy evaluation of the respondents. Six attributes used in this research, including comfort, processing time, convenience, courtesy of staff, information visibility and security. Kuo and Liang (2011) proposed a new fuzzy MCDM method by combining concepts of VIKOR and grey relational analysis (GRA), to deal with evaluation of service quality problems in the international airports. They used customer survey to evaluate seven Northeastern-Asian international airports service quality. A summary of researches done within both contexts are provided in Table 1. In this paper to provide a numerical example we used available data of Iran's air transportation statistical yearbooks from official website of Civil Aviation Organization-CAO (Iran’s air transport statistical yearbooks, 2006e2016) and literature, to gather six criteria and used them to assess and rank Iran's airports. The criteria used in the literature to evaluate and rank airports are summarized and presented in Table 2. These criteria are all quantitative measures and positive (benefit) in nature which means if their values increase, they are more desirable to decision makers. For example the “total passengers” criterion is a quantitative measure which means that greater values of this criterion indicate the high capacity of the airport in hosting a great number of passengers, therefore, it receives more preference in comparison to other airports. 3. The proposed integrated method Based on previous studies and available data six major criteria are used to evaluate and rank airports. In our proposed method these six criteria are incorporated into the Taguchi loss function to compute loss score for each airport. Then each criterion is weighted by BWM. In the final step, a decision matrix is developed and airports are ranked using VIKOR technique. 3.1. Taguchi loss function Taguchi's loss function is a prominent quality engineering method has been applying to a variety of situations, including healthcare (Taner and Antony, 2000), real estate (Festervand et al., 2001; Kethley et al., 2002) and supplier evaluation and selection models (Pi and Low, 2005; Liao and Kao, 2010; Ordoobadi, 2010). The prevalent quality control approach is that products determined acceptable if their characteristic's measurement falls within the specification limit. Taguchi proposes a more restricted perspective stating that a product creates quality loss if it deviates from the target value. If a characteristic's measurement is equal to the characteristic's target value, the loss is zero, therefore, making any deviation detrimental to the product quality and increasing loss. According to Taguchi, quality is “the loss imparted by any product to society after being shipped to a customer, other than any loss caused by its intrinsic function” (Ross, 1988; Antony and Kaye, 2012). Using quadratic equations proposed by Taguchi we can measure the loss before the product is shipped to the customer and take appropriate actions to systematically alleviate variations from target value (Kethley et al., 2002).

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Table 1 Researches in the context of productivity. Paper

Method

Units

Yeh and Kuo (2003) Sarkis and Talluri (2004)

Fuzzy multi-attribute Charnes Cooper Rhodes (CCR) model of DEA and Cross-efficiency

Yoshida and Fujimoto (2004) Lin and Hong (2006)

Banker Charnes Cooper (BCC) model and Charnes Cooper Rhodes (CCR) model of DEA

14 Major Asia-Pacific airports 44 U.S. airport 1990e1994 67 Japanese airport 2000 20 international airport 2003 27 Britain airports 2000e2005 16 Japanese airport 1987e2005 7 Northeaster-Asia airport 2008 30 Chinese airport 2000e2006 20 Italian airport management company 2006e2008 21 Asia-Pacific airports 2002e2011 11 major New Zealand airports 2010e2012 7 Indian airports

Barros and Weber (2009)

Charnes Cooper Rhodes (CCR) model of DEA, Banker Charnes Cooper (BCC) model of DEA, Crossefficiency DEA and Malmquist index

Barros et al. (2010)

Malmquist index

Kuo and Liang (2011)

VIKOR and grey relational analysis (GRA)

Chow and Fung (2012)

Malmquist efficiency index

De Nicola et al. (2013)

DEA and Malmquist efficiency index

Tsui et al. (2014a)

DEA

Tsui et al. (2014b)

Slacks-based Measures (SBM)-Malmquist efficiency index

Prakash and Barua (2016)

Analytical Hierarchy Process (AHP) and Fuzzy TOPSIS

Table 2 Criteria used for performance evaluation. Criteria

Paper

Operational cost and operational Sarkis and Talluri (2004), Yoshida and Fujimoto (2004), Sarkis (2000) revenue Total freight Yoshida and Fujimoto (2004), Barros and Sampaio (2004), Martín et al. (2009), Barros et al. (2010), Lin and Hong (2006) Total passengers Gillen and Lall (2001), Parker (1999), Yoshida and Fujimoto (2004), Barros and Sampaio (2004), Fernandes and Pacheco (2002), Oum and Yu (2004), Martín et al. (2009), Barros et al. (2010), Tsui et al. (2014a), Lin and Hong (2006) Aircraft movements Sarkis and Talluri (2004), Bazargan and Vasigh (2003), Tsui et al. (2014a,b), De Nicola et al. (2013), Lin and Hong (2006) Runway area Yoshida and Fujimoto (2004), Gillen and Lall (1997), Barros et al. (2010) Terminal area Gillen and Lall (2001), Yoshida and Fujimoto (2004), Pels et al. (2001)

There are three types of functions that can be used, including nominal-is-best characteristic, smaller-is-better characteristic and higher-is-better characteristic. Using the appropriate function relies on the magnitude and direction of deviations. If the target is located in the center of a specification limit, variations are allowed from both sides of the target value which is named two-sided equal or nominal-is-best loss function and it can be measured using Equation (1).

LðyÞ ¼ kðy  mÞ2

(1)

where LðyÞ is the loss associated with a particular value of equality character y; m is the nominal value of the specification; k is the average loss coefficient, and its value is a constant depending on the cost at the specification limits and the width (e.g., m ±D) of the specification limit; where is the customer's tolerance (see Fig. 2). The other two functions, including smaller-is-better characteristic and higher-is-better characteristic loss function (as shown in Figs. 3 and 4 respectively) are measured using Equations (2) and (3) where A is average quality loss and all other variables are the same as the nominal-is-best loss function.

LðyÞ ¼ k  ðyÞ2 ; . LðyÞ ¼ k ðyÞ2 ;

.

D2

(2)

k ¼ A  D2

(3)

k¼A

3.2. Best worst method This method is the latest MCDM technique proposed by Rezaei (2015), which is based on pairwise comparisons to obtain the weights of alternatives and criteria respective to various criteria. This method compensates for pairwise comparison-based methods (e.g. Analytical Hierarchy Process and Analytical Network Process) shortcomings such as inconsistency. It reduces the number of pairwise comparisons substantially by only executing reference comparisons which means that experts are only required to determine the preference of best criterion over other criteria and the preference of all criteria over the worst criterion, using a number on a 1e9 scale. By eliminating secondary comparisons this method is much more efficient and easier to obtain weights in an MCDM problem. This method had been used in a variety of contexts such as supplier selection (Rezaei et al., 2016), sustainable supply chain (Sadaghiani et al., 2015), energy efficiency of buildings (Gupta et al., 2017), urban sewage treatment technologies sustainability assessment (Ren et al., 2017), and measuring university-industry PhD projects efficiency (Salimi and Rezaei, 2016). According to Rezaei (2015) this method is executed using the following five steps: Step 1. A set of decision criteria is determined as fC1 ; C2 ; C3 …; Cn g. Step 2. The best and the worst criteria are determined by expert or panel of experts.

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Step 3. The preference of the best criterion over all other criteria is determined using a number from 1 to 9 which will results in the Best-to-Others vector as:

AB ¼ ðaB1 ; aB2 ; aB3 ; …; aBn Þ; where aBj indicates the preference of the best criterion B over criterion j and it is clear that aBB ¼ 1. Step 4. The preference of all other criteria over the worst criterion is determined are determined using a number from 1 to 9 which will results in the Others-to-Worst vector as:

AW ¼ ða1W ; a2W ; a3W ; …; anW ÞT ;

    min maxj wB  aBj wj ; wj  ajW wW  s:t: X

wj ¼ 1

wj  0; for all j

(6)

Problem (6) is rewritten as a linear optimization problem as follows:

Step 5. Find the optimal weights ðw*1 ; w*2 ; …; w*n Þ. The pairwise comparison vectors will be perfectly consistent if aik  akj ¼ aij ; i; j. As the consistency condition mentioned, the optimal weights for each criterion is the one where for each pair of wB = wj and wj = wW , we have wB = wj ¼ aBj and wj = wW ¼ ajW . In order to satisfy all these conditions for all j, we have to find a solution so that we  can minimize  the maximum absolute differences   w  wB   wj  aBj  and wWj  ajW  for all j. Having the non-negativity and   sum condition of the weights, by solving the following problem we will obtain optimal weights:

L

minx s:t:

  wB  aBj wj   xL ; for all j   wj  ajW wW   xL ; for all j X

  ( ) w  w   B   j min maxj   aBj ;   ajW   wj  wW

wj ¼ 1

j

wj  0; For all j

s:t:

(7)

As problem (7) is a linear optimization problem with a unique

wj ¼ 1

j

wj  0; for all j

(4)

This problem can also be rewritten as follows and used to obtain optimal weights:

minx s:t:   w   B   aBj   x; for all j   wj 

W

wj ¼ 1

j

wj  0; For all j

answer, values for optimal weights ðw*1 ; w*2 ; …; w*n Þ and xL* are obtained by solving it. According to Rezaei (2015) a consistency ratio should be computed for pairwise comparisons in the non-linear BWM. However, in the linear model the value of xL* can be directly used as an indicator of pairwise comparisons consistency which values close to zero, signals a high level of consistency (Rezaei, 2016). Note that as we seek to increase the efficiency of decision making process along with simplifying results interpretation, and also having a not-fully consistent comparison system with more than three criteria, we decided to use the linear model of BWM for the purpose of this paper. 3.3. VIKOR technique

    wj    a jW   x; for all j w X

obtain a unique optimal solution. He suggests that instead of minimizing the maximum value among the set of   ( )     wB   wj  wj  aBj ; wW  ajW  , we minimize the maximum among the set       of fwB  aBj wj ; wj  ajW wW g, which gives us the following problem:

j

where ajW indicates the preference of the criterion j over the worst criterion W and it is clear that aWW ¼ 1.

X

7

(5)

Rezaei (2016) argues that for not fully-consistent comparison systems with more than three criteria it is likely to have multiple optimal solutions. However this feature of BWM provides more information about the optimal solution, it is not preferred in some cases. Rezaei (2016) proposes a linear model of BWM in order to

VIKOR is one of MCDM methods, developed by Opricovic in 1998 for the first time (Chu et al., 2007). It is a method used for complex decision making situations with non-commensurable and conflicting criteria where there might be no solution satisfying all criteria simultaneously (Opricovic and Tzeng, 2007). Therefore, VIKOR proposes a compromise ranking to the decision maker based on “closeness” to the “ideal” solution (Opricovic, 1998; Chitsaz and Banihabib, 2015). This method begins with a decision matrix that is comprised of columns representing alternatives and rows depicting criteria. It is assumed that there are j alternatives and i criteria. Each alternative is evaluated according to each criterion function, and the ranking will be performed based on the closeness to ideal solution. This method uses the following Lp  metric as an aggregating function

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(Opricovic and Tzeng, 2004; Opricovic, 1998):

( Lp;j ¼

n h  . ip X Wi fi*  fij fi*  fi

)1=

p

i¼1

0  p  ∞; j ¼ 1; 2; 3; …; j

(8)

In Equation (8), Wi denotes each criterion weight, and fij is the value of alternative i according to criterion j. Also, fi* and fi denote the best and worst values of all criterion functions respectively, i ¼ 1,2,3, …, n. Therefore, if the ith function is benefit then, fi* ¼ max fij ; fi ¼ min fij . The utility function of the VIKOR method j

j

is an aggregate of L1:j and L∞:j . L1:j represents the “concordance” which provide decision makers with information about the maximum “group utility” of “majority”, and L∞:j represents “discordance”, and provide decision makers with information about minimum “individual regret” of the “opponent” (Tong et al., 2007). Ranking measures in this method are calculated using the following formulations by denoting L1:j as Sj , and L∞:j as Rj :

  n w f *  fij X i   Si ¼ fi  fij i¼1

(9)

  w fi*  fij  Ri ¼ max  i fi  fij

(10)

After computing Sj and Rj , the values Qj , j ¼ 1,2,3, …, J will be calculated by the relation

    v Si  S* ð1  vÞ Ri  R* Qi ¼  þ ; S  S* R  R*

(11)

where,

S* ¼ min Sj ;

S ¼ max Sj

R* ¼ min Rj ;

R ¼ max Rj :

j

j

j

j

The solution generated by min Sj is with a maximum group j

utility (or the “majority” rule), and the one obtained by min Rj is j

with a minimum individual regret of the “opponent”, and v is denoted as “the maximum group utility” weight which here v ¼ 0:5. After all values for Sj, Rj , and Q are computed, by sorting alternatives based on these values in decreasing order, there will be three ranking lists. The best alternative by measure Q is the one with minimum value which is assumed as a1 , and the second position alternative is denoted as a2 . The a1 alternative will be the compromise solution if the following two conditions are satisfied:
“Acceptable advantage”:

Q ða2 Þ  Q ða1 Þ  DQ where DQ ¼ 1=ðJ  1Þ ; J being the number of alternatives.
“Acceptable stability in decision making”: For alternative a1 to be the best solution, it also must be ranked

best by S or/and R. This compromise solution is stable within a decision process which v could have any value between 0 and 1 ðv  0:5 voting by majority rule, v  0:5 with veto and vz0:5 by consensus). If one of the conditions above is not satisfied, instead of a compromise solution, a set of compromise solutions is proposed, which consists of:
Alternatives a1 and a2 if only acceptable stability condition is not satisfied, or
Alternatives a1 ; a2 ; …; aM if acceptable advantage condition is not satisfied; aM is determined by relation Q ðaM Þ  Q ða1 Þ < DQ for maximum M (note that the positions of these alternatives are “in closeness”) (Sayadi et al., 2009). 4. A real world case study The following real case study is provided to demonstrate the application of the model proposed. In order to gather the appropriate data for criteria mentioned in Table 2, statistical yearbooks provided by Iran's Civil Aviation Organization (CAO) (Iran’s air transport statistical yearbooks, 2006e2016) and Iran Airports & Air Navigation Company statistical reports (Iran’s airports annual performance statistics, 2008e2014) are used. Iran's CAO was established in 1946 by the name of General Department of Civil Aviation operating under the supervisory of the Ministry of Roads and Urban Development which in 1974 renamed to CAO and now is responsible for governing Iran's air transportation industry. This organization's functions include, policy making and planning in technical, economical, international and commercial domains within air transportation industry, monitoring airport's performance, examining airport's development plans with regard to international standards and etc. (Iran’s air transport statistical yearbooks, 2006e2016). Statistical yearbooks provided by CAO are used to obtain the data for “aircraft movements” criterion represented in Table 3. Iran Airports & Air Navigation Company was established in 1991, and is one of the main companies of the Ministry of Roads and Urban Development which is responsible for optimizing the use of airports, increasing the quality of airports, increasing airports economic impacts, handling airports emission reduction projects and etc. (Iran’s airports annual performance statistics, 2008e2014). Statistical reports provided by this company encompass comprehensive data for, terminal area, runway area, total passengers, total freight and value added criteria. Based on data gathered from these two sources, Table 3 represents the data of 21 major airports in Iran during the time period of 2008e2014 for the criteria mentioned in Table 2. Note that the data in Table 3 are normalized for further computations since each criterion has different unit of measurement. The normalization procedure used is “Linear Scale Transformation (Max)”. In this method the normalized value rij for benefit (posix

ij tive) attribute is computed using rij ¼ xmax Where xij is the value of j

alternative i for attribute j, and xmax is the maximum value of all j alternatives for attribute j (Hwang and Yoon, 2012). For the purpose of this paper, relevant experts are selected as decision makers (DMs) and interviewed for different stages of the proposed model, including identifying criteria weights and setting threshold values for Taguchi loss function. All decision makers are experts from Iran's Civil Aviation Company (CAO). As it was mentioned in the beginning of this section, one of the main functions of Iran's CAO is monitoring the performance of airports. Accordingly, these experts background in airports evaluation was the principle criterion for their selection. This organization

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Table 3 Data for 21 airports. Airport Code

Value Added

Total freight

Total passengers

Aircraft movements

Runway area

Terminal area

ABD ADU OMH IFN IKA AWZ BND BUZ XBJ TBZ RAS ZAH SRY SYZ KER KSH GBT LRR MHD THR AZD

11,976,433 13,149,880 90,765,472 295207428 1,023,467,351 67,275,066 82,872,724 21,221,782 24,509,646 175186544 51,756,354 14,416,507 111174516 130466404 125451456 23,334,392 60,353,904 6,375,717 325768219 2,690,068,213 54,435,936

3071 1005 2347 20,701 98,904 16,673 7590 5021 1010 9823 3045 3732 3209 24,835 5573 3165 1520 2712 65,685 99,638 3225

354,974 203,486 350,466 2,103,633 4,986,477 1,993,991 953,366 420,772 113,019 1,235,403 317,782 408,453 314,915 2,329,428 730,477 452,858 195,607 113,836 7,321,371 13,106,391 471,164

3354 1920 2871 17,335 36,827 18,480 9860 3660 1229 9778 3526 4432 2937 24,623 4266 4314 2668 1587 51,345 108,614 4889

5370 5800 3250 8794 8447 3400 7133 8939 6162 7171 2917 4250 2650 8606 5873 3400 2993 3329 7736 8019 4100

13,920 2900 6000 26,550 78,300 7920 16,800 8077 3000 15,500 9000 8942 11,000 23,200 6700 7800 4314 2400 54,578 74,930 10,900

comprise of ten offices, including air worthiness engineering general office, flight operations office, licensing examinations and air medical office, accident investigation office, legal and international affairs office, airports, aviation companies and institutions supervisory office, aeronautical operations supervisory office, client's complaints and performance assessment office, studies and quality assurance office and flight safety office. Regarding the objective of this paper 8 experts are selected from 8 relevant offices whom they all have work experience of more than 10 years in their respective offices. By consulting with the head of each relevant office, an expert was suggested for interview. The offices had not been taken in to account are, legal and international affairs office and licensing examinations and air medical office. Background of experts from these two offices presumed to be irrelevant to the evaluation model proposed by this paper. Assume there are six criteria to evaluate and rank airports, including value added, terminal area, runway area, aircraft movements, total passengers and total freight. It is worthwhile to mention that the criterion “value added” was selected based on both available data and decision makers opinion. As it was illustrated in Fig. 1, first Taguchi loss function is used to calculate the loss score for each airport relative to each criterion. Regarding the nature of our criteria the loss function for all criteria is one-sided “higher-is-better” function. Values used to determine loss score, including consumer's tolerance (D), average loss coefficient (k) and average quality loss (A) are showed in Table 4. In order to calculate the loss value first we need to determine the loss coefficient (k) value for each criterion using Equation (3), where for each criterion consumer's tolerance and average quality loss are identified by decision makers (DMs). For example for the loss coefficient of criterion “runway area”, we have k ¼ A  D2 ¼ 100  ð:29645374Þ2 ¼ 8:7884821. By using the higher-is-better Taguchi loss function the quantity of loss associated with each criterion for each airport is computed and the results are presented in Table 5. After computing loss associated with each criterion for each airport, the weight of each criterion should be calculated using linear best-worst method as we seek to avoid generating multiple optimal weights. Based on decision makers opinion, value added and terminal size are identified as best and worst criteria respectively. The questionnaire proposed by Rezaei (2015) used to conduct reference pairwise comparisons. Eight experts were

employed as decision makers to identify weights of all criteria. Each expert was asked to conduct reference pairwise comparisons. Tables 6 and 7 are representing the results of the interviews. These results illustrate the preference of the best criterion over other criteria, and the preference of other criteria over the worst criterion respectively for each expert. Having reference pairwise comparisons we can formulate the minimizing problem mentioned in Equation (7) for each expert, and by solving these problems optimal weight of each criterion for each expert is calculated along with the values of xL* . This leads to 8 sets of weights which by making an average of them mean weights are obtained and presented in Table 8. In order to check for the consistency of pairwise comparisons as it was mentioned in Section 3.2, we can use the value of xL* as a direct measure of consistency. Since the value of xL* as presented in Table 8, is near zero for all experts (decision makers) it can be concluded that we have a very good consistency. Finally the decision matrix and criteria weights are used to rank airports based on VIKOR technique. It is of great importance to notice that before calculating loss values for each airport using Taguchi loss function, the decision matrix was normalized with its values considered to be of positive nature as it was stated in Section 2.2. However, after computing loss values the obtained decision matrix indicates losses associated with each airport regarding each criterion, therefore, all values should be considered to be of negative (cost) nature. Moreover, before using VIKOR technique, the decision matrix should be normalized. The normalization procedure employed is the same used previously (Max procedure). In this method the normalized value rij for cost (negative) attribute is x

ij . Where xij is the value of alternative i computed using rij ¼ 1  xmax j

for attribute j, and xmax is the maximum value of all alternatives for j attribute j (Hwang and Yoon, 2012). The results of computations using VIKOR technique are presented in Table 9 (note that the value of v is considered to be 0:5). As it was previously stated we will have three ranking lists, including Q , S and R values. The best airport with the minimum value of Q (IKA) is assumed as a1 , and the second airport (IFN) is assumed as a2 . In order to identify the best airport both conditions of “Acceptable advantage” and “Acceptable stability in decision making” should be satisfied. The value of Q ða2 Þ  Q ða1 Þ equals

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Selected airports

Criteria of evaluation

Identify best and worst criteria

BWM for criteria weights generation

Taguchi loss function for each criteria Determine the decision matrix for ranking

Use VIKOR technique

Ranking list of airports

Fig. 1. The integration method.

Table 4 Values and coefficients. Criteria

A

D(%)

k

Value added (C1) Total freight (C2) Total passengers (C3) Aircraft movements (C4) Runway area (C5) Terminal area(C6)

100

0.2370095

0.0005617

100

1.0086513

0.0101738

100 100 100 100

0.8623198 1.13153 29.645374 3.0651341

0.007436 0.0128036 8.7884821 0.0939505

0:000802 which is not greater that DQ ¼ 1=ð21  1Þ ¼ 0:05: Therefore, the first condition is not satisfied. Additionally, airport IKA is also ranked first by S and R values, hence, it is a stable alternative within the decision process which satisfies the second condition. As it was mentioned in Section 3.3, when acceptable stability condition is not satisfied, a set of compromise solutions as a1 ; a2 ; …; aM is proposed where aM is determined by relation Q ðaM Þ  Q ða1 Þ < DQ for maximum M. If “KER” airport is considered to be alternative M the value of Q ðaM Þ  Q ða1 Þ equals to 0:042703 which is less than DQ ¼ 0:05. Accordingly, the set of {IKA, IFN, SYZ, THR, MHD, TBZ, BND, KER} is proposed as the set of compromise solutions in order of closeness to ideal solution.

Fig. 2. Nominal-is-best loss function.

5. Conclusion Airports as the most important infrastructure to air transportation industry play a significant role in transportation

P. Shojaei et al. / Journal of Air Transport Management 68 (2018) 4e13

11

Table 7 Other criteria over worst criterion preferences.

Fig. 3. Smaller-is-better loss function.

development and subsequently country's economic development. Therefore, airport's performance evaluation and ranking became an attractive issue among both managers and scholars globally. Despite this attraction there exist a few researches focused on using multi criteria decision making approaches to address issues in this field. This paper proposes a novel integrated method using Taguchi loss function, best-worst method and VIKOR technique to address this gap in the literature. The novelty of the integrated model proposed is mainly in enabling decision makers to benefit from each method's individual

Worst criterion

Terminal area

Expert

A

B

C

D

E

F

G

H

Value added Total freight Total passengers Aircrafts movements Runway area Terminal area

9 2 4 5 2 1

9 2 5 5 3 1

8 3 3 6 3 1

9 2 4 4 2 1

8 4 5 4 4 1

9 3 4 6 2 1

9 2 3 7 4 1

8 3 6 5 2 1

advantage simultaneously. This means that by using this model, decision makers are enabled to make precise decisions using a highly efficient and simple process which results in a compromise solution that minimizes the distance from ideal solution, therefore, decreases the level of conflict between decision makers. This model is also capable of taking into account both data and experts opinions in an integrated manner which in turn leads to a more effective decision making process. At first stage of the integration process Taguchi loss function is used to compute the quality loss associated with each criteria for each airport based on decision maker's opinion. Then by using BWM reference pairwise comparisons, and by solving a minimizing linear problem we obtained weights of criteria. In the last stage, the decision matrix was determined using both quality loss values and criteria weights and by VIKOR technique three ranking lists was obtained. Also a numerical example for the application of the method was presented. Our proposed method offers decision makers a few advantages

Table 5 Decision matrix. Airport Code

Value added

Total freight

Total passengers

Aircraft movements

Runway area

Terminal area

ABD ADU OMH IFN IKA AWZ BND BUZ XBJ TBZ RAS ZAH SRY SYZ KER KSH GBT LRR MHD THR AZD

28.34021 23.50794 0.49342 0.046645 0.003881 0.898152 0.591882 9.02598 6.76681 0.132451 1.517507 19.55861 0.328888 0.238814 0.258289 7.465606 1.115957 100 0.038304 0.000562 1.371787

10.70958 100 18.33606 0.235695 0.010325 0.363333 1.753269 4.006376 99.01235 1.046752 10.89325 7.251851 9.808276 0.163758 3.252026 10.08288 43.71646 13.7326 0.02341 0.010174 9.711195

10.13701 30.84849 10.39947 0.288644 0.051371 0.32126 1.405347 7.21455 100 0.836923 12.64865 7.656296 12.88001 0.235399 2.393811 6.228434 33.38367 98.56975 0.02383 0.007436 5.753852

13.42696 40.97333 18.32472 0.502639 0.111371 0.442283 1.553638 11.27565 100 1.579806 12.14896 7.689609 17.51039 0.249128 8.299694 8.116027 21.21935 59.97219 0.057294 0.012804 6.319223

24.35247894 20.8754459 66.4852071 9.080689487 9.842077024 60.7482699 13.8021677 8.788482116 18.49474552 13.65627655 82.5313387 38.87889273 100 9.481762315 20.35971743 60.7482699 78.39318584 63.36714749 11.73434427 10.92072122 41.77572873

2.972652 68.48989 16 0.817134 0.09395 9.182736 2.040816 8.82922 64 2.397503 7.111111 7.203659 4.760331 1.070155 12.83137 9.467456 30.95011 100 0.193369 0.102591 4.848077

Table 6 Best criterion over other criteria preferences. Best criterion

Expert

Value added

Total freight

Total passengers

Aircrafts movements

Runway area

Terminal area

Value added

A B C D E F G H

1 1 1 1 1 1 1 1

5 4 5 4 6 5 6 3

3 3 5 4 4 3 2 5

2 2 3 2 2 3 4 3

7 6 6 7 6 7 5 7

9 9 8 9 8 9 9 8

12

P. Shojaei et al. / Journal of Air Transport Management 68 (2018) 4e13

A majority of researches in the context of airports evaluation and ranking are focused on the evaluation of airports productivity using DEA technique (Sarkis and Talluri, 2004; Yoshida and Fujimoto, 2004; Lin and Hong, 2006; Barros and Weber, 2009; Barros et al., 2010; Chow and Fung, 2012; Tsui et al., 2014a,b). These researches mainly employ a data-oriented approach to evaluation and ranking of airports and fail to reflect subjectiveness involved in the process of decision making. On the contrary, the proposed method in this paper enables decision makers to take in to account both data and experts opinions simultaneously. By this mean the precision of decision making process will be increased, and conflicts within the process will be decreased. Also to our knowledge there only exist a few research been conducted within the context of airports evaluation and ranking using MCDM techniques. Yeh and Kuo (2003) used a fuzzy multi attribute decision making model to evaluate and rank airports based on subjective evaluation of respondents to a survey. Their research also neglects the important role of data in the process of decision making. In other researches (Kuo and Liang, 2011; Prakash and Barua, 2016) the method used to identify the criteria weights is Analytical Hierarchy Process (AHP) which imposes a huge computational complexity when there is a large number of alternatives to be taken in to account (Nine et al., 2009). Nonetheless, the proposed model by this paper shows superiority to those models by significantly decreasing computational complexity using best-worst method which consequently increases the efficiency of the decision making process. The proposed model can be used to evaluate and rank airports and be compared with other available models. Also multi criteria

Fig. 4. Higher-is-better loss function.

as follows. Taguchi uses a common value to evaluate the performance of airports which is quality loss. This provides a common and understandable language in decision making, hence, by using it airports comparison will be much easier and meaningful. Taguchi allows decision makers to set target values and consumer's tolerance level that is very important in the context of airports evaluation and ranking since each country with different cultures might have different criteria with different acceptable specification limits (note that this only holds true for domestic and non-international airports due to the fact that international airports should meet globally accepted standards). This feature enables decision makers to perform the most precise airports evaluation and ranking with respect to condition of their country's culture. The process of selecting evaluation criteria for this paper to provide a numerical example was unfortunately restricted due to available data. As a result we did not have any culturally sensitive criterion. But this method allows decision makers to also incorporate these criteria in the process of decision making by setting their own acceptable thresholds. Additionally, since the loss function is quadratic it places higher values on measurements that shows smaller deviation from the target value. Accordingly, it makes those airports with more deviation from the target value, to have higher quality losses than those closer to target value. This makes the comparisons and the ranking process more meaningful and precise. Another method used in this paper, BWM, enables decision makers to reduce pairwise comparisons, hence, conducting comparisons much easier with higher consistency rate. By incorporating the aforementioned method's results into VIKOR technique, we are able to obtain ranking lists complying with “maximum group utility” and “minimum individual regret” of the “opponent”, providing the closest solution to the ideal.

Table 9 S, R, and Q measures of the airports. Airport code

S

Airport code

R

Airport code

Q

LRR XBJ ADU GBT ABD SRY ZAH OMH RAS KSH BUZ AZD AWZ KER BND TBZ SYZ MHD IFN THR IKA

0.790818 0.514878 0.375081 0.2167 0.188719 0.147222 0.146936 0.13066 0.128194 0.11735 0.079176 0.068186 0.054751 0.039881 0.014702 0.011213 0.002988 0.002909 0.002372 0.001871 0.001196

LRR XBJ ABD ADU ZAH SRY RAS GBT OMH AWZ KSH BUZ AZD KER BND TBZ MHD THR SYZ IFN IKA

0.4267 0.1982 0.120926 0.1108 0.083455 0.0799 0.064598 0.060973 0.050542 0.045516 0.045516 0.038512 0.028896 0.016427 0.004392 0.004264 0.002581 0.001868 0.001017 0.000971 0.000923

LRR XBJ ADU ABD GBT ZAH SRY RAS OMH KSH BUZ AWZ AZD KER BND TBZ MHD THR SYZ IFN IKA

1 0.556938 0.36578 0.259665 0.206978 0.189204 0.185211 0.155192 0.140247 0.125917 0.09352 0.086279 0.075269 0.042703 0.012626 0.010267 0.003031 0.001537 0.001245 0.000802 0

Table 8 Criteria weights. Criteria

Value added Total freight Total passenger Aircrafts movements Runway area Terminal area

xL*

Mean weights

0.4267 0.1108 0.1435 0.1982 0.0799 0.0408

Criteria weights regarding each expert A

B

C

D

E

F

G

H

0.4248 0.0903 0.1505 0.2257 0.0645 0.0443 0.0266

0.4008 0.1120 0.1493 0.2240 0.0747 0.0393 0.0472

0.4587 0.1101 0.1101 0.1835 0.0917 0.0459 0.0917

0.4304 0.1200 0.1200 0.2187 0.0685 0.0423 0.0494

0.4167 0.0833 0.1250 0.2500 0.0833 0.0417 0.0833

0.4405 0.1028 0.1713 0.1713 0.0734 0.0408 0.0734

0.4226 0.0888 0.2142 0.1332 0.1065 0.0347 0.1100

0.4195 0.1793 0.1076 0.1793 0.0768 0.0376 0.1183

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