Research Article Operational Efficiency Evaluation of Iron Ore Logistics at the Ports of Bohai Bay in China: Based on the PCA-DEA Model

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1 Mathematical Poblems in Engineeing Volume 2016, Aticle ID , 13 pages Reseach Aticle Opeational Efficiency Evaluation of Ion Oe Logistics at the Pots of Bohai Bay in China: Based on the PCA-DEA Model Jihong Chen, 1,2 Zheng Wan, 1,3 Fangwei Zhang, 1 Nam-kyu Pak, 4 Xinhua He, 1 and Weiyong Yin 1 1 College of Tanspot and Communications, Shanghai Maitime Univesity, Shanghai , China 2 Shanghai Intenational Shipping Institute, Shanghai , China 3 InstituteofTanspotationStudies,UnivesityofCalifoniaDavis,Davis,CA95616,USA 4 School of Pot Logistics, Tong Myong Univesity, Busan , Republic of Koea Coespondence should be addessed to Zheng Wan; mwan@ucdavis.edu Received 19 July 2015; Revised 26 Novembe 2015; Accepted 3 Decembe 2015 Academic Edito: Segio Peidikman Copyight 2016 Jihong Chen et al. This is an open access aticle distibuted unde the Ceative Commons Attibution License, which pemits unesticted use, distibution, and epoduction in any medium, povided the oiginal wok is popely cited. Opeational efficiency is significant fo the compehensive competitiveness of a pot. In this study, we use a pincipal component analysis-data envelopment analysis (PCA-DEA) integated model to evaluate the opeational efficiency of ion oe logistics at the pots of Bohai Bay, China. The key indicatos and systematic famewok ae established fo logistics efficiency eseach. We conside the PCA-DEA integated model as a pactical tool fo evaluating and analyzing the elative efficiency of the ion oe logistics of each pot in that aea. The poposed method consists of a two-stage eseach and analysis that begins with PCA. In the fist stage, we use PCA to obtain 6 synthetic indicatos, including 4 input indicatos and 2 output indicatos, fom 15 oiginal indicatos. In the second stage, the standad DEA appoach is used with the specific synthetic indicatos. The evaluation esults of the selected pots fom the integated PCA-DEA model ae compaed and discussed. The compaison of the evaluation esults indicates that the PCA-DEA model povides a pactical and poweful tool fo the investigation of the pot logistics poblem. With this integated model, a compaison analysis and futhe eseach into the ion oe logistics efficiency of diffeent pots in the aea ae pesented. Finally, discussions and suggestions ae povided. 1. Intoduction China s apid ubanization pocess has empoweed its infastuctue constuction and tiggeed the need fo stategic mateials, such as ion oe and steel. In ecent yeas, the expoted quantity and pot thoughput of ion oes in China have constantly inceased. Ion oe logistics in coastal pots has become an impotant pat of pot development. The pots ofbohaibayseveasthepivotalbasefothetanspotand handling of ion oe in China. The annual thoughput of ion oe accounts fo ove 60% of the total thoughput of China. As the contadiction of demand and supply of ion oe and the cost awaeness of entepises on logistics intensify, ion oe has become an inceasingly impotant commodity at the pots of Bohai Bay, China. The competition in ion oe tanspot and logistics sevices among the pots of Bohai Bay is escalating. The evaluation of ion oe logistics in each pot and the incease in logistics efficiency ae the majo pathways to impove the ion oe logistics sevice and to enhance the competitiveness of the pots. Pot efficiency evaluation aims to pomote the development of pots and enhance thei pefomance competitiveness. As fo the ion oe pot logistics management, efficiency evaluation is not only a poweful tool fo pot authoities to impove pot management pefomance but also a useful appoach fo the govenment to gain vey impotant infomation on ion oe pot planning and development. The pupose of this pape is to intoduce an extension to opeational efficiency evaluation poblem in pot industy, namely, opeational efficiency evaluation of ion oe logistics of pots, to popose an integated mathematical model of pincipal component analysis (PCA) and data envelopment

2 2 Mathematical Poblems in Engineeing analysis (DEA) fo this kind of evaluation eseach wok and to evaluate the model by the means of an empiical study of the main pots of Bohai Bay in China. The est of this pape is stuctued as follows. Section 2 contains a desciption of elevant, existing liteatue. In Section 3, evaluation indicatos and evaluation model ae descibed. Specific empiical study on the evaluation of the opeational efficiency of the ion oe logistics in Bohai Bay in China is caied out in Section 4. Section 5 concludes. 2. Liteatue Review The study on pot efficiency can be dated back to the 1980s with the use of one o seveal indicatos. With egad to the development pefomance of pots and elevant egions, many studies have been conducted using diffeent methods and pespectives. The methods fo evaluating the development pefomance of pots and elevant egions ae divided into nonpaametic o paametic. The epesentative nonpaametic method is the data envelopment analysis (DEA). Depending on thei needs, scholas can select vaious input and output indicatos fom diffeent aspects. The model fo the evaluation of pot opeational efficiency is constucted, and diffeent pots ae used fo the evaluation. RollandHayuthusedDEAappoachasatooltoevaluate pot pefomance and the model was demonstated by a hypothetical numeical example whee the pefomances of 20 pots ae compaed [1]. Diffeent pots and thei efficiencies have been compaed and Tongzon selected some typical Austalian and othe intenational pots fo efficiency measuement using data envelopment analysis [2]. In ode to incopoate diffeent pot efficiency measues, some scholas used pincipal component analysis (PCA) [3]. Tongzon and Heng applied a stochastic fontie model to investigate the quantitative elationship between pot owneship stuctue and pot efficiency [4]. Wu and Lin conducted evealed compaative advantage (RCA) analysis to investigate India s logistics competitiveness and used data envelopment analysis (DEA) to analyze the efficiency of India s containe pot opeations [5]. To impove the application of DEA model in efficiency evaluation, some scholas made special emphasis on the input and output factos selected in the DEA models employed in diffeent fields o pot aeas [6, 7]. Cullinane et al. intoduced the time facto into the pot efficiency evaluation model. Using panel data, the main containe pots in the wold wee selected as samples to analyze elative efficiency [8]. Chen et al. investigated the spatial distibution chaacteistics and fomation mechanism of the pot sevice industy in Guangzhou. The location facto of logistics efficiency in the pot sevice industy was discussed [9]. Wang and Ducuet synthesized the theoetical models of Hayuth and Notteboom to study the evolutionay mechanism of a containe pot system and the diffeent phases of pot logistics development [10]. Liang et al. used thedataofpotlogisticsentepisesinshanghai.methods such as geogaphic infomation system spatial analysis and mathematical statistics wee utilized to obseve the spatial patten and evolution of pot logistics entepises and to identify the key influence factos [11]. Lan et al. used the DEA-Malmquist total facto poductivity index to evaluate the dynamic efficiency of the main coastal pots in Chinese mainland, Taiwan, Hong Kong, and Macao. The competitive status and potentials of diffeent habos wee compaed [12]. Using the DEA method, Sun and Xiao compaed the elative economic opeational efficiency of pots in the 11 coastal povinces of China fo one specific yea and poposed suggestions fo the sustainable development of the pot economy [13]. Tan et al. used the pot logistics efficiency indicato system fo the analysis of pot logistics efficiency in Liaoning Povince duing By establishing the indicato system fo the coodinated development between pot logistics and hinteland economy, they calculated the coodination degee between pot logistics and hinteland economy in , with 2001 as the base yea [14]. Li et al. intoduced the DEA-based binay elative evaluation model into the measuement of pot logistics efficiency. Taking the poduction efficiency and X-efficiency as basis, they poposed the model fo estimating compehensive pot logistics efficiency [15]. Lee et al. used slacks-based data envelopment analysis model to assess the envionmental efficiency of pot cities [16]. Yuen et al. investigated how the involvement of foeign and local owneships, inta- and intepot competition, and hinteland affects the containe teminal efficiency in China and its neighboing counties [17]. Pjevčević et al. applied DEA method in measuing and analyzing the efficiencies of pots on the ive Danube. DEA window analysis was used to detemine the efficiency of pots and to obseve the possibility of changes in the pot efficiency ove time [18]. The paametic method fo pot efficiency evaluation is mainly stochastic fontie analysis (SFA), which calculates the deviation degee of sample pots fom the pot of efficiency fontie to estimate pot efficiency. In fact, the pot of efficiency fontie does not actually exist but is called so because it is the optimal efficiency used to compae othe pots. The pot of efficiency fontie vaies with diffeent sets of pot samples. Aigne et al. poposed an SFA fo pefomance measuement, which lays the theoetical foundation fo futhe development. The stochastic fontie method can be conveniently applied in many fields [19]. Relevant scholas have used this method fo pot efficiency evaluation [20 25]. As a typical paametic method, the SFA consides the eos caused by statistics and obsevations. Howeve, the pesumed fontie function has cetain subjectivity [26]. The evaluation indicatos ae uncetain in eithe the paametic o the nonpaametic method fo pot pefomance evaluation. An inconsistency among statistical evaluation indicatos of diffeent pots may also be obseved [24]. In ecent yeas, seveal multiattibute decision-making methods have been adopted fo pot efficiency o pefomance evaluation; these methods include fuzzy analytical hieachy pocess, quality function deployment, and fuzzy analytic netwok pocess [27 31]. Although these methods ae flexible and easy to use, the appopiate evaluation indicatos ae difficult to design, and the intefeence between indicatos may be consideable. As a nonpaametic method, the DEA has been extensively applied in pot efficiency evaluation despite its defects.

3 Mathematical Poblems in Engineeing 3 Thus, the evaluation method fo eal applications should be selected depending on the conditions and sample data [32]. The DEA method cannot compae the units of technology efficiency. Consideing the effect of stochastic factos on the system, the technology efficiency of the DEA method can be significantly affected when an anomaly exists in the samples. The defects of the DEA method have been addessed though anumbeofimpovementsthatfitthespecificapplications o though the combination of othe methods. Simões and Maques evaluated the pefomance of a set of Euopean seapots by means of obust nonpaametic appoaches using ode-m and bootstap pocedues [30]. Cavalho et al. pesented the majo featues of Ibeian seapots, analyze thei govenance model, and evaluate thei inefficiency based on the nonpaametic fontie technique of data envelopment analysis(dea)andonabootstapesamplingmethod[33]. In some cases, a completely diffeent method is used to eplace the DEA method. Al-Eaqi et al. used the DEA decomposition of the Malmquist index as an impovement ofthedeamodeltoevaluatepotefficiency[34].leeetal. establishedanimpovedrdeamethodtoankaangeof containe pots by efficiency. This anking was used as basis in the identification of countemeasues fo enhancing pot efficiency [35]. Wan et al. implemented a two-stage appoach of DEA and Tobit egession. Fist, the containe pot efficiency was measued by data envelopment analysis (DEA). Then, Tobit egession analysis was undetaken to exploe the elationship between DEA scoes and gound tanspotation conditions [36]. Jiang et al. intoduced the stongly efficient fontie (SEF) and stongly inefficient fontie (SIF) and then poposed seveal models to calculate vaious distances between DMUs and both fonties [37]. DEAwasaveyusefulmethodtoevaluatepotand logistics efficiency. Howeve, due to the mutual intefeence of the evaluation index, the application of DEA method is limited. Theefoe, scholas have actively impoved the DEA method,eliminatingthemutualintefeenceoftheevaluation index. With a focus on the defects of the DEA method, scholas usually use the pincipal component analysis (PCA) in combination with the DEA method fo efficiency evaluation. In this manne, the intefeence between indicatos is expected to be emoved [38, 39]. In the pesent study, we adopt the integated PCA-DEA model to evaluate the opeational efficiency of ion oe logistics at the pots of Bohai Bay. The integated model fully utilizes the advantage of PCA in extacting chaacteistic indicatos. By ovecoming mutual intefeences between the indicatos and tansfoming multiple indicatos into a few synthetic indicatos, the integated model fulfills the function of the DEA model in the evaluation of the elative efficiency of the decision-making unit (DMU). 3. Evaluation Indicatos and Evaluation Model 3.1. Evaluation Indicato System. A pot logistics system has a complex intinsic stuctue. The evaluation indicatos constitute a system with intinsic connections. Many factos influence the opeational efficiency of the ion oe logistics of pots. Typical factos include the natual conditions of the pot, infastuctues elated to ion oe logistics, scale and capacity of the ion oe logistics sevice, and ion oe collection and distibution system. The natual conditions of a pot ae the peconditions fo the ion oe logistics opeation of the pot. Seving as the basic opeation conditions fo the ion oe logistics system, the natual conditions ensue that ships can ente and depat conveniently. The majo indicatos in this aspect ae the wate depth of the navigation channel, width of the main navigation channel, and wate depth at the beth. The infastuctues elated to ion oe logistics sevice eflect the hadwae and sevice capacities of a pot in ion oe logistics opeation. Infastuctues elated to ion oe logistics sevice ae diectly elated to the actual poduction capacity and development potential of the ion oe logistics of the pot.theindicatosinthisaspectincludethetotallength of the beth, numbe of beths, aea of the ion oe stoage yad, and numbe of ion oe loading machines. The scale and capacity of ion oe logistics sevice ae the coe of ion oe logistics activities and pefomance. This facto canbeusedtoevaluatetheeffectoftheionoelogistics business of a pot. The capacity and efficiency of the ion oe logistics of a pot ae lagely detemined by this aspect. The elevant indicatos include ion oe caying capacity, ion oe thoughput, and gowth of ion oe thoughput. The ion oe collection and distibution capacity of a pot eflects the ability of the pot to coodinate loading and unloading opeations, centalization, and commodity distibution. The capacity in this field diectly influences the ion oe logistics efficiency of the pot. The elevant indicatos include the length of the ailway line in the pot, ship-loading efficiency of a single ion oe line, and ion oe unloading efficiency. The afoementioned influence factos and elevant indicatos ae summaized. The factos that have an impact on the ion oe pots of China and ion oe logistics efficiency ae consideed. The input and output attibutes of the indicatos ae taken into account to detemine the evaluation system fo the indicatos of the opeational efficiency of the ion oe logisticsatthepotsofbohaibay,china(seetable1).the oiginal data of the influence factos and elevant indicatos can be got fom China Pot Yeabook and China Statistical Yeabook Evaluation Method. PCA is aimed at educing dimensionality and tansfoming multiple indicatos into few synthetic indicatos. This method can eliminate the coelations among the indicato samples. The epesentative indicatos ae extacted unde the pemise of peseving the key infomation of the samples. In the analytic pocess, the weights of the majo indicatos ae calculated, and the pincipal components ae taken as the values of the synthetic indicatos of the DMU [38]. If only the DEA method is adopted in the ion oe logistics efficiency evaluation of the pots, then the design of the evaluation indicatos will significantly affect the evaluation esults. The ion oe logistics efficiency evaluation involves seveal indicatos, and weighing between the numbe and independence of the indicatos is difficult.

4 4 Mathematical Poblems in Engineeing Table 1: Evaluation system fo the indicatos of the opeational efficiency of the ion oe logistics at the pots of Bohai Bay, China. Pimay indicato Seconday indicato Popeties and symbols of the indicatos Natual conditions of the pots Wate depth of the navigation channel Input indicato X 1 Width of the main navigation channel Input indicato X 2 Aveage wate depth of the beth Input indicato X 3 Total length of the beth Input indicato X 4 Infastuctues elated to ion oe logistics sevice Numbe of beths Input indicato X 5 Numbe of beths of ove 150,000 tons Input indicato X 6 Aea of the ion oe stoage yad Input indicato X 8 Volume of the ion oe stock Input indicato X 9 Scale and capacity of the ion oe logistics sevices of the pot Ion oe collection and distibution capacity Numbe of loading and unloading machines Input indicato X 11 Designed ion oe caying capacity Input indicato X 7 Ion oe thoughput Output indicato Y 1 Gowth of ion oe thoughput Output indicato Y 2 Length of the ailway line in the pot Input indicato X 10 Ship-loading efficiency of a single ion oe line Output indicato Y 3 Ion oe unloading efficiency Output indicato Y 4 Establishment of evaluation system fo the indicatos of the opeational efficiency of ion oe logistics at the pots Input indicatos Output indicatos Nomalization of indicato data and PCA Pincipal components of the input indicatos Pincipal components of the output indicatos Nonnegative values of the pincipal components of the input indicatos Nonnegative values of the pincipal components of the output indicatos Calculation based on the DEA model Evaluation esults of the opeational efficiency of the ion oe logistics at the pots of Bohai Bay, China, and compaative analysis Figue 1: Pocedues of the PCA-DEA evaluation of the opeational efficiency of the ion oe logistics at the pots of Bohai Bay, China. PCA can educe the dimensionality of the coelated oiginal evaluation indicatos though linea tansfomation while minimizing the infomation loss. The oiginal multidimensional vaiables ae eplaced by seveal synthetic vaiables that ae mutually independent. In this manne, the subjectivity of and the intefeence fom the oiginal indicatos can be educed. Theefoe, the input and output indicatos fo the DEA method ae mutually independent synthetic indicatos. This popety ensues the objectivity and accuacy of the evaluation esults. In this study, the integated PCA-DEA model is adopted to evaluate the opeational efficiency of the ion oe logistics at the pots of Bohai Bay, China [39]. The evaluation famewok is shown in Figue Steps of the Evaluation Using the PCA-DEA Model. The PCA and DEA methods ae combined to fom the integated modelusedtoevaluatetheopeationalefficiencyoftheion oe logistics at the pots of Bohai Bay. Fist, featue extaction is conducted fo the oiginal indicatos using the PCA submodel. The indicatos with lage weight-to-pot logistics efficiency ae sceened. The indicatos obtained by featue extaction ae the input and output indicatos of the DEA model, which is mainly used to impove the uneasonable input and output indicatos [39]. The pocedues fo the efficiency evaluation using the PCA-DEA integated model ae as follows. (1) Nomalization of the oiginal indicatos.

5 Mathematical Poblems in Engineeing 5 Suppose the existence of n samples, each of which contains p vaiables. An (n p)th-ode data matix is then fomed and expessed as follows: X 11 X 12 X 1p X 21 X 22 X 2p X= [...,. ] [ X n1 X n2 X np ] that is, X = (X ij ), i=1,2,...,n; j=1,2,...,p. The nomalization of the indicato data can emove the influence of dimensionality on the diffeent indicatos. The nomalization fomula is witten as (1) X ij = X ij X j δ j, (2) whee X j = (1/n) n i=1 X ij isthesamplemeanandδ j = (1/(n 1)) n i=1 (X ij X j ) 2 is the sample vaiance. (2) The matix R of the coelation coefficients of the samples is established based on the indicato data. The chaacteistic value and chaacteistic vecto of R ae calculated. Conside p p R= [..., (3). ] [ p1 p2 pp ] whee ij (i,j = 1,2,...,p) is the coelation coefficient between the oiginal vaiables x i and x j. R is the eal symmetic matix; that is, ij = ji.onlytheuppeolowe tiangulaelementscanbecalculatedusingthefollowing fomula: ij = n k=1 (X ki X i )(X kj X j ) n k=1 (X ki X i ) 2 n k=1 (X kj X j ) 2. The chaacteistic equation λi R = 0is solved. The chaacteistic values obtained ae anked by magnitude: λ 1 λ 2 λ p 0.Then,thechaacteisticvectol i (i = 1,2,...,p) coesponding to the chaacteistic value λ i is calculated. The calculation equies that l i = 1;thatis, p j=1 l2 ij =1,wheel ij is the jth component of vecto l i. (3) The contibution ate of each pincipal component and accumulative contibution ate ae calculated. The fomula of the contibution ate is λ i (4) p k=1 λ (i=1,2,...,p). (5) k The fomula of the accumulative contibution ate is i k=1 λ k p k=1 λ k (i=1,2,...,p). (6) aesolved.basedonthesolutionsof thedeamodel,theelative,scale,andtechnologyefficiencies of the ion oe logistics opeation of the pots ae calculated. The units that fail to each the DEA efficiency should be egulated. The fist, second, and mth (m p) pincipal components coesponding to the chaacteistic values λ 1,λ 2,...,λ m with an accumulative contibution ate of appoximately 85% ae selected. (4) Fo the analysis of the pincipal components, the elatively impotant indicatos fo the evaluation of the ion oe logistics of the pots ae selected. These indicatos ae theinputandoutputindicatostobeusedinthedea model.giventhattheinputandoutputvaluesofthedea model should not be negative, e ( ) is used as the base numbe, and powe tansfom is conducted on the PCA esults. As such, all the input and output indicatos ae positive. (5)Thedataonthepincipalcomponentsoftheindicatos ae intoduced into the C 2 R-DEA model. The optimal solutions θ 0, λ 0 j, S0 i,ands Analysis Based on the DEA Method. Afte the PCA of the indicatos of the opeational efficiency of ion oe logistics, the pincipal indicatos ae fomed into synthetic indicatos, which ae then subjected to the DEA method. DEA is a tool fo evaluating the elative efficiency of the pefomance of simila schemes based on linea pogamming. Gounded in the concept of elative efficiency, the DEAmethodisespeciallysuitablefotheelativeefficiency evaluation of DMUs involving multiple input and output indicatos [40]. Suppose that n DMUs exist. The synthetic indicato is composed of s input indicatos and t output indicatos. That is, each DMU has s types of input indicatos and t types of output indicatos denoted by X j and Y j,espectively: X j =(X 1j,X 2j,...,X sj ) T, Y j =(Y 1j,Y 2j,...,Y tj ) T, whee X ij 0is the jth type of the input quantity of the jth DMU DMU j ; Y j 0is the jth type of the output quantity of the jth DMU DMU j ; i = 1,2,...,s, = 1,2,...,t, j= 1,2,...,n.FoDMU j0, X 0 =X j0, Y 0 =Y j0,andj 0 [1,n]. The C 2 R-DEA model (D ε C 2 R ), which was poposed by Coope et al. and has a non-achimedean infinitesimal quantity ε,is used [40, 41]. One has n j=1 Min [θ ε ( s i=1 t S i + S + )] =1 x ij λ j +S i θx ij0 =0, i=1,2,...,s, n j=1 y j λ j S + =y j 0, =1,2,...,t, (7)

6 6 Mathematical Poblems in Engineeing λ j 0, j=1,2,...,n, S i 0, i=1,2,...,s, theactualinputandoutputofthedmu.theefoe,the subjective factos ae excluded. In the DEA model, the input and output ae mutually coelated and esticted. Each input is coelated to one o seveal outputs. S + 0, =1,2,...,t, (8) whee λ j is the weight and S i and S + ae the slack vaiables oftheinputandoutput,espectively.thepositivenumbe ε esults in the optimal solution θ 0. λ 0 j (j = 1,2,...,n) of the D C 2 R model satisfies θ 0 = 1, S 0 i = 0,andS 0+ = 0. Then,DMU j0 eaches the DEA efficiency. ε = 10 6 is consideed duing calculation. The optimal solution to the linea pogamming model is solved as θ 0, λ 0 j, S0 i,ands 0+. DEA efficiency and its economic significance ae analyzed based on the values of the solution. We detemine whethe the logistics opeation of the pot has technology and scale efficiencies. The following conclusions ae obtained [40]. (1) If θ 0 =1, S 0 i =0,andS 0+ =0, then the DMU DMU j0 has DEA efficiency. Moeove, the logistics activity of DMU DMU j0 has technology and scale efficiencies. The esouces aefullyutilized,andtheinputelementshavetheoptimal combination. Thus, the maximum output effect is achieved. (2) If θ 0 = 1 and the slack vaiable of eithe input o output is lage than 0, that is, S 0 i >0o S 0+ >0, then the DMU DMU j0 has weak DEA efficiency. At this point, DMU DMU j0 does not have technology and scale efficiencies simultaneously. If S 0 i >0, then the ith type of the input indicato S 0 i is not fully utilized. If S 0+ >0,thenS 0+ diffeence exists between the th type of the output indicato and the optimal output value. (3) If θ 0 < 1, then the DMU DMU j0 does not achieve DEA efficiency. Economic significance is manifested as logistics activities of DMU DMU j0 that have neithe optimal technology efficiency no optimal scale efficiency. In addition, the optimal solutions θ 0 and λ 0 j (j = 1, 2,...,n) of θ and λ j of the D ε C 2 R model ae usually used to detemine the scale efficiency of the DMU. The following conclusions ae obtained [40]: (1) If (1/θ 0 ) n j=1 λ0 j = 1, then the scale benefit of the DMU stays constant. (2) If (1/θ 0 ) n j=1 λ0 j < 1, then the scale benefit of the DMU inceases pogessively. (3) If (1/θ 0 ) n j=1 λ0 j > 1, then the scale benefit of the DMU deceases pogessively. DEA is based on the concept of elative efficiency. As such, DEA is suitable fo elative efficiency evaluation involving multiple input and output indicatos. The DEA model uses the optimization tool and takes the weight coefficients of multiple input and output indicatos as the decision vaiables. The evaluation is conducted in the optimal sense. Thus, the detemination of the weight coefficient of the indicato in the statistical sense is avoided. In this case, the DEA method has intinsic objectivity. Without making any assumption on weight, the optimal weight is calculated based on 4. Empiical Study on the Evaluation of the Opeational Efficiency of the Ion Oe Logistics in Bohai Bay Bohai Bay is the majo steel poduction base in China and occupies a pivotal status in the steel industy in the county. Many national key steel entepises, including Shoudu Ion and Steel Company, Anshan Steel, Tangshan Steel, Handan Steel, Baotou Steel, Tonghua Steel, Benxi Steel, and Jixi Steel, ae located in this egion. These entepises have a high demand fo ion oe and ely on the pot logistics sevices in BohaiBayfothetadeandtanspotofionoe.Accoding to the Plan of Coastal Pot Layout eleased by the Ministy of Communication of the People s Republic of China in 2006, Chinahasfivemajopotclustes,namely,BohaiBay,Yangtze Rive Delta, southeast coastal egion of China, Peal Rive Delta, and southwest coastal egion of China. Such division is based on the economic development featues, cuent status of the pot, tanspot between pots, and economic ationality of the tanspot of main commodities. The geneal layout consists of eight majo logistics systems, namely, coal, oil, ion oe, containe, food, automobiles, oll-on and olloff tanspot, and passenge tanspot. The ion oe tanspot system is located nea the steel entepises, with the aangement of pofessional beth being tons. The ion oe logistics sevice system is equipped with the infastuctues fo seconday unloading and tansfe. The pot cluste in Bohai Bay is composed of pot clustes in Liaoning, Tianjin, Hebei, and the coastal egions of Shandong. This cluste mainly seves the social and economic development of the coastalegionofnothandinlandchina.thelayoutinbohai Bay is dominated by thee hub pots (Dalian, Tianjin, and Qingdao) and supplementay unloading pots in Yingkou, Tangshan, Rizhao, and Yantan. Seven ion oe logistics pots in Dalian, Yingkou, Tianjin, Rizhao, Tangshan, Qingdao, and Yantai in Bohai Bay ae selected as the samples. The opeational efficiency of ion oe logistics is compaatively studied PCA of the Evaluation Indicatos of the Opeational Efficiency of the Ion Oe Logistics of Pots. As indicated in the analysis pesented peviously, the numbe of input and output indicatos should be easonable when the DEA model is used fo evaluation. Given that the oiginal data contain ovelapping infomation, the accuacy of the analysis esult will be affected. Fist, PCA is conducted to tansfom the oiginal data into seveal mutually independent indicatos that peseve most of the infomation in the oiginal data. China Pot Yeabook and China Statistical Yeabook ae the souces of the oiginal data fo the evaluation of the opeational efficiency of the ion oe logistics in Bohai Bay. The PCA model is used (Steps (1) to (4)). Using the Statistical Package fo the Social Sciences

7 Mathematical Poblems in Engineeing 7 Table 2: Results of the nomalization of the oiginal input and output indicato data. Indicato Dalian Yingkou Tianjin Rizhao Tangshan Qingdao Yantai X X X X X Input indicato X X X X X X Y Output indicato Y Y Y Table 3: Matix of the coelation coefficients of the input indicatos (coelation matix). X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X 11 X X X X X X X X X X X (SPSS) 19.0, calculation and PCA ae conducted fo the indicato data of the seven majo pots. The oiginal data ae nomalized using SPSS Next, 11 input indicatos and 4 output indicatos ae subjected to nomalization to emove the influence of dimensionality. The specific esults ae listed in Table 2. The coelation coefficients of indicato and the data ae analyzed using SPSS. The matices of the coelation coefficientsoftheinputandoutputindicatosaeealsymmetic matices (Tables 3 and 4). A lage coelation coefficient indicates a stong coelation among the vaiables. Thus, moe ovelapping infomation will be obtained. Tables 3 and 4 show a numbe of ovelapped indicato data. Accoding to the coelation coefficient in Tables 3 and 4, some vaiables have stong coelation. Fo example, X 1 has stong negative coelation with X 3 and X 10, with the coelation coefficient of and 0.598, espectively; X 3 and X 10 have stong positive coelation, with the coelation coefficient as high as 0.742; X 4 has vey stong positive coelation with X 6, X 7, and X 10, with the coelation coefficient eaching 0.707, 0.914, and 0.716, espectively; the positive coelation coefficient of X 8 and X 9 also eaches up to 0.873; futhemoe, the output Table 4: Matix of the coelation coefficients of the output indicatos (coelation matix). Y 1 Y 2 Y 3 Y 4 Y Y Y Y vaiable Y 3 also has obvious positive coelation with output vaiables Y 1 and Y 2, with the coelation coefficient of and 0.485, espectively. Othe vaiables also have simila coelation. In ode to educe the infomation intefeence between these vaiables, it is necessay to extact the pincipal components of all elevant indexes. SPSS 19.0 is used fo the extaction of the pincipal components of all input and output indicatos. Of the 11 input indicatos, 4 pincipal components ae obtained. The accumulative contibution ate of these fou pincipal components eaches appoximately 91%. Of the fou output

8 8 Mathematical Poblems in Engineeing Table 5: Component matix of the input and output indicatos. Indicato Load of the pincipal components of the input indicatos Load of the pincipal components of the output indicatos Indicato X Y X Y X Y X Y X X X X X X X Table 6: Chaacteistic vectos of the input and output indicatos (column vecto). Indicato Chaacteistic vecto of the input indicatos Chaacteistic vecto of the output indicato Indicato X Y X Y X Y X Y X X X X X X X indicatos, two pincipal components ae obtained. Thei accumulative contibution ate eaches appoximately 85%. The loads of the pincipal components of the input and output indicatos ae shown in Table 5. The chaacteistic vectos of the matices ae detemined based on the loads of the pincipal components and the chaacteistic values of the matices of the coelation coefficients in Table 5 (see Table 6). The chaacteistic vectos in Table 6 coespond to the coefficient of each pincipal indicato. Using the data in Table 6, the fomula of the synthetic indicatos of the opeational efficiency of the ion oe logistics at the pots of Bohai Bay can be expessed as follows. Fo the input indicatos (fou pincipal components denoted as I 1, I 2, I 3,andI 4 ), I 1 = 0.355X X X X X X X X X X X 11, I 2 = 0.204X X X X X X X X X X X 11, I 3 = 0.165X X X X X X X X X X X 11, I 4 = 0.022X X X X X X X X X X X 11. (9) Fo the output indicatos (two pincipal components denoted as o 1 and o 2 ), o 1 = 0.593Y Y Y Y 4, (10) o 2 = 0.063Y Y Y Y 4.

9 Mathematical Poblems in Engineeing 9 Table 7: Values of the pincipal components of the input and output indicatos. Pot samples Pincipal components of the input indicatos Pincipal components of the output indicatos I 1 I 2 I 3 I 4 o 1 o 2 Dalian Yingkou Tianjin Rizhao Tangshan Qingdao Yantai Table 8: Negative-to-positive tansfom of the pincipal components of the input and output indicatos. Pot sample Pincipal components of the input indicatos Pincipal components of the output indicatos I 1 I 2 I 3 I 4 o 1 o 2 Dalian Yingkou Tianjin Rizhao Tangshan Qingdao Yantai The nomalized data of the input and output indicatos in Table 2 ae substituted into Fomulas (9) and (10). Thus, the values of the pincipal components of the indicatos ae obtained (Table 7). Given that the input and output values of the DEA model should not be negative, e ( )isusedasthebasenumbe, and powe tansfom is conducted on the PCA esults. The esults of the negative-to-positive tansfom of the pincipal components of the input and output indicatos ae shown in Table 8. The nonnegative data of the pincipal components in Table8aeanalyzedusingtheDEAmodel DEA Evaluation of the Opeational Efficiency of the Ion Oe Logistics. I 1, I 2, I 3,andI 4 ae the input vaiables, and o 1 and o 2 ae the output vaiables. The DEA model shown in Fomula (8) is used to evaluate the opeational efficiency of the ion oe logistics at the pots of Bohai Bay. In the DEA model, the numbe of DMU is 7, s=4,andt=2.allthe values of the input and output indicatos ae tansfomed into positive values to fom the synthetic indicatos. We take the DMU DMU of Dalian Pot as an example. The fomula is expessed as follows based on the input and output data: Min [θ 10 6 (s 1 +s 2 +s 3 +s 4 +s+ 1 +s+ 2 )] 0.381λ λ 2 +2λ λ λ λ λ 7 +s θ = 0, 0.380λ λ λ λ λ λ λ 7 +s θ = 0, 0.933λ λ λ λ λ λ λ 7 +s θ = 0, 0.900λ λ λ λ λ λ λ 7 +s θ = 0, 0.607λ λ λ λ λ λ λ 7 s + 1 = 0.607, 0.445λ λ λ λ λ λ λ 7 s + 2 = 0.445, λ 1,λ 2,λ 3,λ 4,λ 5,λ 6,λ 7 0, s 1,s 2,s 3,s 4,s+ 1,s (11) Similaly, the DEA models fo the othe six pots, namely, Yingkou, Tianjin, Rizhao, Tangshan, Qingdao, and Yantai, ae established using the synthetic input and output indicatos. The LINGO12.0 softwae is used to solve the peviously pesented linea pogamming models. The esults of the DEA evaluation ae shown in Table 9. The DEA evaluation data shown in Table 9 ae analyzed. With egad to DEA efficiency, fo five DMUs (Yingkou, Tianjin, Rizhao, Qingdao, and Yantai pots), θ 0 =1, S i =0 (whee i = 1, 2, 3, 4), and S + =0(whee =1,2). Theefoe, the five pots ae DMUs with DEA efficiency. The input and output states of the five pots have technology and scale efficiencies. That is, the input and output states and efficiency

10 10 Mathematical Poblems in Engineeing Table 9: DEA-based evaluation of the opeational efficiency of the ion oe logistics in Bohai Bay. Pot DMU θ 0 λ 0 1 θ 0 λ0 S 0 1 S 0 2 S 0 3 S 0 4 S 0+ 1 S 0+ 2 Dalian < Yingkou Tianjin Rizhao Tangshan > Qingdao Yantai Table 10: Efficiency of the DEA evaluation of the opeational efficiency of the ion oe logistics in Bohai Bay. Pot DMU Relative efficiency Scale efficiency Technology efficiency Dalian No DEA efficiency Retun to scale inceases pogessively Inefficient Yingkou DEA efficiency Unchanged scale benefit Efficient Tianjin DEA efficiency Unchanged etun to scale Efficient Rizhao DEA efficiency Unchanged etun to scale Efficient Tangshan No DEA efficiency Retun to scale deceases pogessively Inefficient Qingdao DEA efficiency Unchanged etun to scale Efficient Yantai DEA efficiency Unchanged etun to scale Efficient ae optimal. Fo two DMUs (Dalian and Tangshan pots), θ 0 <1. As such, these pots achieve neithe DEA efficiency no technology efficiency. With egad to the etun to scale, θ 0 =1fo five DMUs (Yingkou, Tianjin, Rizhao, Qingdao, and Yantai pots). When λ 0 =1and (1/θ 0 ) λ 0 =1,theetuntoscaleemains unchanged. Fo the DMU of Dalian pot, (1/θ 0 ) λ 0 = / = < 1, whichmeansthattheetun to scale inceases pogessively. Thus, by inceasing the input quantityfodalianpot,theoutputquantitywillincease.fo the DMU of Tangshan pot, (1/θ 0 ) λ 0 = / = > 1, which means that the etun to scale deceases pogessively. This finding indicates that the excess input of the ion oe logistics opeation in Tangshan pot cannot fully enhance the output unde the existing conditions. Table 10 shows the efficiency of the DEA evaluation of the opeational efficiency of the ion oe logistics in Bohai Bay. As shown in Tables 9 and 10, not all the DMUs of the pots achieve DEA efficiency. Some of these DMUs ae analyzed to identify the easons fo thei failue to achieve DEA efficiency and to povide efeences fo impovement. Theefoe, discussing the pojection of the DMUs on the elative efficiency plane is necessay. The DMUs that fail to achieve DEA efficiency ae tansfomed into those that do have DEA efficiency. Fo n DMUs of pots, the synthetic indicato is composed,and of s input indicatos and t output indicatos. θ 0, λ 0 j, S0 i aetheoptimalsolutionsofthelineapogammingofthe S 0+ jth DMU DMU j of a given pot. We let X 0 =θ 0 X 0 S 0 and Y 0 =Y 0 +S 0+,whee(X 0,Y 0 ) is the pojection of (X 0,Y 0 ) coesponding to DMU DMU j0 on the elative efficiency plane. This pojection constitutes a new DMU of the given pot. Then, the new DMU (X 0,Y 0 ) has DEA efficiency in elation to the oiginal n DMU [40], whee the input and output data coesponding to DMU j0 ae X 0 =X j0, Y 0 =Y j0, and j 0 [1,n];vectoS 0 = (S 0 i ), i = 1,2,...,s;vecto S 0+ =(S 0+ ), =1,2,...,t. In this manne, pojection analysis is conducted fo the DMUs of the Dalian and Tangshan pots without DEA efficiency. Then,thepojectionoftheDMUofDalianpotonthe elative efficiency plane is expessed as X 0 =θ 0 X 0 S 0 = (0.381, 0.380, 0.933, 0.900) (0.1641, 0, 0, ) = (0.1672, , , ), Y 0 =Y 0 +S 0+ = (0.607, 0.445) + (0, ) = (0.6070, ). (12) Similaly,thepojectionoftheDMUofTangshanpoton the elative efficiency plane is expessed as X 0 =θ 0 X 0 S 0 = (53.441, 2.234, 1.801, 0.492) ( , , 0, 0) = (0.3170, , , ), Y 0 =Y 0 +S 0+ = (1.2350, ) + (0, ) = (1.2350, ). (13)

11 Mathematical Poblems in Engineeing 11 Accoding to Tables 9 and 10, the decision-making units of five pots, Yingkou Pot, Tianjin Pot, Rizhao Pot, Qingdao Pot, and Yantai Pot, have achieved the best scale and efficiency and the poduction input of the five pots matches thei efficiency output. In contast, Dalian Pot and Tangshan Pot have lage potential to impove thei inputoutput efficiency. The pojection analysis shows that Dalian Pot and Tangshan Pot failed to sufficiently utilize input esouces and had a low output. If Dalian Pot fully utilizes its esouces, the output value can be inceased fom the fome (1.2350, ) to (1.2350, ) while the input is only 0.87 times of the cuent input. Compaed with pots with efficient DMU, Tangshan Pot has a moe seious poblem in the utilization of input esouces. Afte the impovement of utilization efficiency, the output value of Tangshan Pot can be inceased fom the fome (1.2350, ) to (1.2350, ) while the input is loweed by 32%. 5. Discussion and Conclusion The integated PCA-DEA model is used in this study to analyze the evaluation method fo the opeational efficiency of the ion oe logistics in Bohai Bay, China. The compaison shows that the opeational efficiency of the ion oe logistics of the diffeent pots in this egion pesents vaying featues. The pot authoity and opeating manages can implement coesponding pot development stategies accoding to these esults of efficiency evaluation. The Qingdao, Tianjin, and Dalian pots ae the thee majo hub pots in this egion. Howeve, only the Qingdao and Tianjin pots have ion oe logistics with high opeational efficiency. These two pots have technology and scale efficiencies. Thus, these two pots ae efficient DMUs. Theefoe, consideing the sound pefomance of Qingdao Pot and Tianjin Pot, the manages of the two pots should maintain thepesentopeatingscaleandpoductionmodesoasto maintain elatively high poduction efficiency. The oveall efficiency value of the ion oe logistics of Dalian pot is less than 1. Hence, the DMU is inefficient in tems of eithe technology efficiency o scale efficiency. This finding indicates the need fo impovement in the opeational efficiency of the ion oe logistics of Dalian pot, which is one of the hub pots in the coastal egion of Noth China. The pojection analysis also eveals that the infastuctues of Dalian pot fail to fulfill its functions to the maximum extent and thus cause esouce wastage. The evaluation esults show that the scale etun of Dalian pot inceases pogessively. Fo Dalian pot, integating the existing poduction esouces and fully utilizing the infastuctues ae necessay to addess its lack of DEA efficiency. Futhemoe, Dalian pot has immense development potential. The scale of the pot can be expanded by inceasing the numbe of beths and impoving the ion oe collection and distibution system. These measues ae impotant to achieve optimal scale etun. Among the othe pots, the Yingkou, Rizhao, and Yantai pots have ion oe logistics with high opeational efficiency given thei cuent scale. The oveall ion oe logistics efficiency value is 1, which indicates the DEA efficiency of these DMUs. The evaluation esults indicate that these pots fully utilize thei infastuctues and maximize thei ion oe caying capacities. Futhemoe, the scale etun of these pots emains unchanged. The cuent scale of the pots has aleady yielded the optimal benefits. Consequently, the management authoity of Yingkou Pot, Rizhao Pot, and Yantai Pot should maintain thei cuent development pattenandkeeptheefficientfunctioningofionoelogistics system, so as to bette seve local social and economic development. Tangshan Pot has ion oe logistics with low opeational efficiency. The oveall opeational efficiency of its ion oe logistics is less than 1. Hence, this DMU is inefficient in tems of eithe technology efficiency o scale efficiency. Pojection analysis indicates that, unlike othe effective DMUs, Tangshan Pot cannot fully utilize its esouces. The eason fo the low efficiency of Tangshan Pot is its failue to maximize the benefits of its infastuctues. The scale benefit of the opeational efficiency of ion oe logistics of Tangshan Pot deceases pogessively. Even when Tangshan Pot inceases the input in its infastuctues, the benefits of pot logistics baely incease. Theefoe, the management staff of Tangshan Pot should pay attention to and concentate on impoving the compehensive sevice of ion oe logistics system of the pot and the oveall opeational efficiency of theintegatedlogisticssystem.thatmeansthatthekeytasks fo Tangshan pot is to enhance the coodination between the vaious links of its ion oe logistics and to fully utilize its pot infastuctues. This study mainly evaluates the ion oe pots of Bohai Bay, China, using the ion oe logistics data of these pots as data souces. PCA is utilized to extact the pincipal components of the oiginal indicatos, which ae then taken as the input and output data of the DEA model. Ion oe logistics is evaluated using the DEA model. The elative efficiency of the DEA evaluation of the ion oe logistics of the pots is also detemined. The PCA-DEA integated model is deemed suitable fo the evaluation of pot logistics efficiency with high accuacy and pacticability. Moeove, the findings of the pesent wok povide theoetical and decision-making bases fo the impovement of pot logistics efficiency. Conflict of Inteests The authos declae that thee is no conflict of inteests egading the publication of this pape. Acknowledgments This study is suppoted by the National Natual Science Foundation of China (Gant nos , , and ), the Young Schola Pogam of Humanities and Social Science of the Ministy of Education of China (14YJC630008), Shanghai Municipal Education Commission Poject (14YZ109), TUP-GLS (Tong Myong Education Pogam fo Next Geneation Global Logistics Specialists), Shanghai Science & Technology Committee Reseach Poject ( ), and the fund of Shanghai Maitime Univesity ( ).

12 12 Mathematical Poblems in Engineeing Refeences [1] Y. Roll and Y. Hayuth, Pot pefomance compaison applying data envelopment analysis (DEA), Maitime Policy & Management,vol.20,no.2,pp ,1993. [2] J. Tongzon, Efficiency measuement of selected Austalian and othe intenational pots using data envelopment analysis, Tanspotation Reseach Pat A: Policy and Pactice,vol.35,no. 2, pp , [3] R.J.Sánchez, J. Hoffmann, A. Micco, G. V. Pizzolitto, M. Sgut, and G. Wilmsmeie, Pot efficiency and intenational tade: pot efficiency as a deteminant of maitime tanspot costs, Maitime Economics & Logistics,vol.5,no.2,pp ,2003. [4] J. Tongzon and W. Heng, Pot pivatization, efficiency and competitiveness: some empiical evidence fom containe pots (teminals), Tanspotation Reseach Pat A: Policy and Pactice,vol.39,no.5,pp ,2005. [5] Y.-C. J. Wu and C.-W. Lin, National pot competitiveness: implications fo India, Management Decision, vol.46,no.10, pp ,2008. [6] R. Makovits-Somogyi, Measuing efficiency in tanspot: the state of the at of applying data envelopment analysis, Tanspot,vol.26,no.1,pp.11 19,2011. [7] A. Jaašūnienė, L. Geičiūnė, and A. Šakalys, Reseach of competitive envionment of Klaipėda Seapot compaing to othe seapots in the easten Baltic Sea egion, Tanspot,vol. 27, no. 1, pp. 5 13, [8]K.Cullinane,D.-W.Song,P.Ji,andT.-F.Wang, Anapplication of DEA windows analysis to containe pot poduction efficiency, Review of Netwok Economics,vol.3,no.2,pp.1 23, [9] Z.Q.Chen,X.P.Yan,andX.S.Cao, Thespatialchaactesand associated mechanism of pot sevice industies in Guangzhou, Scientia Geogaphica Sinica,vol.30,no.1,pp.31 37,2010. [10] C. J. Wang and C. Ducuet, Theoetical model of containe pot system and its empiical eseach in Yangtze Rive Delta, Geogaphical Reseach,vol.30,no.3,pp ,2011. [11] S. Liang, Y. Cao, and W. Wu, Spatial patten evolution of pot logistics entepises in Shanghai metopolitan aea, Geogaphical Reseach,vol.32,no.8,pp ,2013. [12] L. I. Lan, L. Jun, and L. Chun, Analysis of dynamic efficiency of main pots in mainland China, Hongkong and Taiwan based on DEA-malmquist poductivity index, Soft Science,vol.25,no. 5, pp , [13] C. Z. Sun and S. Xiao, Relative efficiency evaluation of the pot economy in the coastal povinces and cities based on DEA method, Aeal Reseach and Development, vol. 28, no. 1, pp , [14] L. Tan, W. Li, and W. Yu, Reseach on synegetic development between efficiency of pot logistics and its hinteland economy in Liaoning Povince, Economic Geogaphy, vol. 32, no. 9, pp , [15] D.-S. Li, S.-Z. Zhang, and L.-F. Yuan, Reseach on measuement of compehensive efficiency fo pot logistics, Jounal of Tanspotation Systems Engineeing and Infomation Technology,vol.13,no.5,pp ,2013. [16] T. Lee, G.-T. Yeo, and V. V. Thai, Envionmental efficiency analysis of pot cities: slacks-based measue data envelopment analysis appoach, Tanspot Policy, vol. 33, pp , [17] A. C.-L. Yuen, A. Zhang, and W. Cheung, Foeign paticipation and competition: a way to impove the containe pot efficiency in China? Tanspotation Reseach Pat A: Policy and Pactice,vol.49,pp ,2013. [18] D. Pjevčević, A. Radonjić, Z. Hle, and V. Čolić, DEA window analysis fo measuing pot efficiencies in Sebia, PROMET Taffic&Tanspotation,vol.24,no.1,pp.63 72,2012. [19] D. Aigne, C. A. Lovell, and P. Schmidt, Fomulation and estimation of stochastic fontie poduction function models, Jounal of Econometics,vol.6,no.1,pp.21 37,1977. [20] K. Cullinane, D.-W. Song, and R. Gay, A stochastic fontie model of the efficiency of majo containe teminals in Asia: assessing the influence of administative and owneship stuctues, Tanspotation Reseach Pat A: Policy and Pactice, vol. 36,no.8,pp ,2002. [21] K. Cullinane, T.-F. Wang, D.-W. Song, and P. Ji, The technical efficiency of containe pots: compaing data envelopment analysis and stochastic fontie analysis, Tanspotation Reseach Pat A: Policy and Pactice,vol.40,no.4,pp ,2006. [22] M. M. González and L. Tujillo, Refoms and infastuctue efficiency in Spain s containe pots, Tanspotation Reseach Pat A: Policy and Pactice,vol.42,no.1,pp ,2008. [23] Y.-C. J. Wu and M. Goh, Containe pot efficiency in emeging and moe advanced makets, Tanspotation Reseach Pat E: Logistics and Tanspotation Review, vol.46,no.6,pp , [24] H. Yang, K. Lin, O. R. Kennedy, and B. Ruth, Sea-pot opeational efficiency: an evaluation of five Asian pots using stochastic fontie poduction function model, Jounal of Sevice Science and Management,vol.4,no.3,pp ,2011. [25] M. Maloni and J. A. Paul, Evaluating capacity utilization options fo US west coast containe pots, Tanspotation Jounal,vol.52,no.1,pp.52 79,2013. [26] T. L. Yip, X. Y. Sun, and J. J. Liu, Goup and individual heteogeneity in a stochastic fontie model: containe teminal opeatos, Euopean Jounal of Opeational Reseach, vol. 213, no.3,pp ,2011. [27] M. M. González and L. Tujillo, Efficiency measuement in the pot industy: a suvey of the empiical evidence, Jounal of Tanspot Economics and Policy,vol.43,no.2,pp ,2009. [28] J.-F. Ding, Applying fuzzy quality function deployment (QFD) to identify solutions of sevice delivey system fo pot of Kaohsiung, Quality & Quantity, vol. 43, no. 4, pp , [29] M. R. Books, T. Schellinck, and A. A. Pallis, A systematic appoach fo evaluating pot effectiveness, Maitime Policy & Management,vol.38,no.3,pp ,2011. [30] P. Simões and R. C. Maques, Seapot pefomance analysis using obust non-paametic efficiency estimatos, Tanspotation Planning and Technology,vol.33,no.5,pp ,2010. [31] S. Onut, U. R. Tuzkaya, and E. Toun, Selecting containe pot via a fuzzy ANP-based appoach: a case study in the Mamaa Region, Tukey, Tanspot Policy,vol.18,no.1,pp ,2011. [32] J. Odeck and S. Båthen, A meta-analysis of DEA and SFA studies of the technical efficiency of seapots: a compaison of fixed and andom-effects egession models, Tanspotation Reseach Pat A: Policy and Pactice, vol. 46, no. 10, pp , [33] P.Cavalho,R.C.Maques,Á. Fonseca, and P. Simões, Govenance and compaative pefomance of Ibeian Peninsula seapots. An application of non-paametic techniques, Intenational Jounal of Tanspot Economics,vol.37,no.1,pp.31 51, 2010.

13 Mathematical Poblems in Engineeing 13 [34] A.S.Al-Eaqi,A.T.Khade,andA.Mustafa, DEAMalmquist index measuement in Middle East and East Afican containes teminals, Intenational Jounal of Shipping and Tanspot Logistics,vol.1,no.3,pp ,2009. [35] H. S. Lee, M. T. Chou, and S. G. Kuo, Evaluating pot efficiency in Asia Pacific egion with ecusive data envelopment analysis, Jounal of the Easten Asia Society fo Tanspotation Studies, vol. 6, pp , [36] Y. Wan, A. C.-L. Yuen, and A. Zhang, Effects of hinteland accessibility on US containe pot efficiency, Intenational Jounal of Shipping and Tanspot Logistics,vol.6,no.4,pp , [37] J.L.Jiang,E.P.Chew,L.H.Lee,andZ.Sun, DEAbasedon stongly efficient and inefficient fonties and its application on pot efficiency measuement, OR Spectum, vol. 34, no. 4, pp , [38] N. Adle and B. Golany, Including pincipal component weights to impove discimination in data envelopment analysis, Jounal of the Opeational Reseach Society, vol. 53, no. 9, pp ,2002. [39] N. Adle and E. Yazhemsky, Impoving discimination in data envelopment analysis: PCA DEA o vaiable eduction, Euopean Jounal of Opeational Reseach, vol.202,no.1,pp , [40] W.W.Coope,L.M.Seifod,K.Tone,andJ.Zhu, Somemodels and measues fo evaluating pefomances with DEA: past accomplishments and futue pospects, Jounal of Poductivity Analysis,vol.28,no.3,pp ,2007. [41] A. Chanes and W. W. Coope, The non-achimedean CCR atio fo efficiency analysis: a ejoinde to Boyd and Fäe, Euopean Jounal of Opeational Reseach,vol.15,no.3,pp , 1984.

14 Advances in Opeations Reseach Advances in Decision Sciences Jounal of Applied Mathematics Algeba Jounal of Pobability and Statistics The Scientific Wold Jounal Intenational Jounal of Diffeential Equations Submit you manuscipts at Intenational Jounal of Advances in Combinatoics Mathematical Physics Jounal of Complex Analysis Intenational Jounal of Mathematics and Mathematical Sciences Mathematical Poblems in Engineeing Jounal of Mathematics Discete Mathematics Jounal of Discete Dynamics in Natue and Society Jounal of Function Spaces Abstact and Applied Analysis Intenational Jounal of Jounal of Stochastic Analysis Optimization