Port Efficiency in apec 1

Transcription

1 Pot Efficiency in apec 1 Zoe Infante 2 Aiel Gutiéez 3 Abstact The ain goal of this eseach is to identify and analyze factos that ay significantly affect the levels of pot efficiency in apec counties (paticulaly the infastuctual capacity). The assessent of such efficiency is a task that ust play an ipotant ole in the anageent of pots in ode to ipove the possibility of developent and success in coecial activities in thei hoe counties. The copetition aong aitie pots is inceasing continuously; the ain pupose of such pots is to becoe the best option fo copanies to cay out thei tading activities, paticulaly ipoting and expoting. Dawing on Data Envelopent Analysis, this pape develops a anne of assessing the copaative efficiency of pots. It applies this assessent ethod to a set of 33 pots in the apec tade alliance ove a span of tie fo The possibility of benchaking the distinction of pot efficiency in apec though this type of efficiency analyses will enhance and deteine new ethodological paths to achieve continuous ipoveent in the activities of aitie pots. Keywods: efficiency, pot s infastuctue, Asia-Pacific Econoic Coopeation (apec), Data Envelopent Analysis (dea) and benchaking. 1. Atículo ecibido el 23 de octube de 2012 y dictainado el 1º de diciebe de Pofesso and Reseache of the Institute of Econoic and Entepeneuial Reseach at Univesidad Michoacana de San Nicolas de Hidalgo and Technical Secetay of the Mexican Consotiu of apecs Centes. 3. PhD Student of Science of Intenational Business of the Institute of Econoic and Entepeneuial Reseach at Univesidad Michoacana de San Nicolás de Hidalgo. Eneo abil de Análisis 41

2 Zoe Infante y Aiel Gutiéez Resuen Este tabajo de investigación tiene el objetivo de identifica y analiza los pincipales factoes (desde el punto de vista infaestuctual) que deteinan los niveles de eficiencia potuaia en los países iebos de apec. La evaluación de la eficiencia es una actividad que desepeña un papel uy ipotante en la adinistación de los puetos aítios con la intención de ejoa el desaollo y el éxito en las actividades coeciales que se ealizan en los países de oigen. La copetencia ente los puetos aítios se ha inceentando constanteente, en donde el objetivo pincipal de los puetos es convetise en la ejo opción paa que las epesas ealicen sus actividades coeciales de ipotación y expotación. En este atículo se utiliza el Análisis Envolvente de Datos (Data Envelopent Analysis, dea), paa edi y evalua la eficiencia de 33 puetos que petenecen a APEC, en el peiodo de 2003 a A tavés del análisis de eficiencia se puede ealiza un benchaking con especto a los puetos eficientes de apec, lo que peite deteina nuevas etodologías paa loga una ejoa continua en las actividades de los puetos aítios. Palabas clave: eficiencia, infaestuctua potuaia, Coopeación Econóica Asia-Pacífico (apec), Análisis Envolvente de Datos (dea) y benchaking. Intoduction The econoic elevance of pots deives fo the fact that ost of the intenational tading activities ae pefoed at sea, aounting to oe than 80% of all echandise taded intenationally. Globalization -which iplies a decentalization of the poduction pocess-, econoic libealization, and the ceation of tade aeas have esulted in an on-going expansion of coecial intechange though aine taffic and pot activity. Thus, aitie pots and the pot facilities, achiney and equipent used in intenational tade play a fundaental econoic ole. Pots, being a subsyste of the total tanspotation netwok and a eeting point fo seveal diffeent tanspotation eans, constitute econoic infastuctue that is necessay to handle doestic and intenational cago (Pak and De, 2004: 53). Pots contibute to a county s developent not only as a esult of thei ajo significance fo outbound taffic but also thei function as gowth pootes in thei own ipact aeas, poducing cetain taffic lines, geneating national incoe (though pot duty fees), and ceating jobs aong othe effects (Rúa, 2006: 2). 42 México y la Cuenca del Pacífico. Eneo abil de 2013

3 Thee is, howeve, wide vaiation in the extent to which pots can be consideed efficient: any fail to avoid dead ties with thei ganty canes and ake inadequate use of the othe pot facilities. Efficiency levels in pots geatly affect the copetitiveness of counties as pots epesent an essential link in the tanspotation chain. Efficient conduct esults lowe expot pices, favoing the copetitiveness of intenational aket poducts. Inefficient pot functioning affects the cost of ipoting and expoting goods, having a negative effect on a nation s copetitiveness. In an inefficient pot and its inefficient logistic chain, a thoough edefinition of pocesses and opeations ust be developed poptly (Doe and Sánchez, 2006: 7-14). In ode to aintain a copetitive position in such akets, nations need to know the factos that affect pot efficiency and to establish fequent copaisons of efficiency aong all pots that ake up thei national secto and contast the with pots Pot Efficiency in apec Pots, being a subsyste of the total tanspotation netwok and a eeting point fo seveal diffeent tanspotation eans, constitute econoic infastuctue that is necessay to handle doestic and intenational cago (Pak and De, 2004: 53). Pots contibute to a county s developent not only as a esult of thei ajo significance fo outbound taffic but also thei function as gowth pootes in thei own ipact aeas, poducing cetain taffic lines, geneating national incoe (though pot duty fees), and ceating jobs aong othe effects fo diffeent egions. (González, 2004: 9-11). Moeove, an efficient pot inceases the poductivity of the piay factos of poduction (labo and capital) as well as the feasibility of poduction units, which allow geate levels of poduction, incoe and eployent. Efficiency optiization in a pot syste ipoves a nation s access to intenational akets, leading to an incease in tade and, theefoe, potentially to a highe incoe. Monitoing a pot s pefoance in an eve-changing envionent is cucial fo easuing its efficiency levels as well as its copetitiveness (Pak and De, 2004: 53-54). Eneo abil de Análisis 43

4 Zoe Infante y Aiel Gutiéez Unde this copetitive envionent, pot efficiency assessent is not only a poweful adinistative tool, but it also constitutes the ost ipotant input needed to coplete egional and national opeation epots and pot planning (Wang, Cullinane & Song, 2003: 699). Despite the clea econoic ipotance of pot efficiency, thee ae deficiencies in the anne in which this efficiency is assessed. Dawing on liteatue on the efficiency of fis, we develop two annes of assessing and copaing the efficiency of pots. The ain attaction of dea is that it can deal with ultiple inputs and outputs. The units in any dea assessent ae geneally hoogeneous and independent units pefoing the sae function, and it is of ost use whee thee ae a lage nube of units poviding an identical sevice in elative isolation (Szczepua, Daviles & Fletche, 1992: 3). In addition, Roll and Hayuth (1993: 160) agued that dea is an easily adaptable appoach fo obtaining such atings. It also opens the possibility fo a seies of seconday analyses, all poviding a deepe insight into pot pefoance and pointing out potentials fo ipoveent. Intenational tade oganizations -such as that established by the Asia-Pacific Econoic Coopeation (apec) teaty- hold potential to incease the efficiency of pots within thei ebe counties by inceasing tade volue. We thus constain ou analysis to pots in the ebe states of apec. In what follows, we discuss efficiency theoy and deive ou two easues fo pot efficiency. Then we assess the efficiency of 33 pots in ebe counties of apec ove an eight-yea peiod fo We discuss the iplications of the two easueents and the boade iplications fo the adinistation of aine pots. Efficiency Theoy In the long un, efficiency iplies benefit axiization and cost iniization. Faell (1957: 254) fist intoduced the basic theoetical faewok to study and assess efficiency. He poposed onitoing efficiency fo a eal, athe than ideal, pespective, and suggested that each fi o poductive unit be evaluated in elation to those taken fo a epesentative and hoogenous goup. This way, the efficiency easue will be elative, not absolute, and the added value of efficiency in a paticula fi will coespond to a deviation fo those consideed efficient. Faell (1957: ) also divided the concept of efficiency into two coponents, technical efficiency and allocative efficiency, which in cobination povide a easue of oveall econoic effi- 44 México y la Cuenca del Pacífico. Eneo abil de 2013

5 Pot Efficiency in apec ciency. This easue indicates the need fo a society to axiize its benefits within its liited esouces (Azubi and Bebel, 2002: 106). Thus, econoic efficiency is consideed to be the achieveent of axiu poduction at the lowest pice possible (Pinzón, 2003: 17). Moeove, Faell hiself defined econoic efficiency as the capacity of a fi to poduce a pedeteined quantity of output at iniu cost fo a given level of technology. A coect povision of both technical and allocative efficiency is necessay in ode fo cost efficiency, incoe efficiency, and benefit efficiency to exist. The following sections outline the key points of technical and allocative efficiency. Technical o Poductive Efficiency The fist coponent of econoic efficiency is technical, o poductive, efficiency, which has been defined in seveal diffeent annes in the liteatue. To Koopans (1951: 33) a poduce is technically efficient if an incease in any output o a decease in any input equies a decease in at least one othe output, o an incease in at least one input. Thus, fo each technology fo which isoquant and efficient subset divege, thee is a potential conflict between both technical efficiency concepts. Debeu (1951: 16) and Faell (1957: 259) developed a easue of technical efficiency, initially teed as the coefficient of esouce utilization, and defined as one inus the axiu equipopotionate eduction in all inputs that still allows the poduction pocess to continue. Yaad (1990: 183) concus that technical efficiency consists of obtaining axiu physical poduction possible, based on existing technology, fo cetain nube of inputs. On the othe hand, González-Páao (1995: 40) affis that technical o poductive efficiency in a copany is given by its capacity to tansfo inputs (labo, capital, and othe factos) into outputs (goods o sevices) in the context of a technology, which can be suaized with a poduction function setting axiu value o the bodeline of attainable output within seveal input cobinations. Tillo (2002: 5) agues that the study of technical o poductive efficiency ainly focuses on the use of huan esouces o capital in the poduction of one o any goods and sevices. In othe wods, he focuses on using physical units, which iplies that the cost o pice of factos and the valuation of the incoe eceived though poduction eain beyond analysis. Eneo abil de Análisis 45

6 Zoe Infante y Aiel Gutiéez The concept of efficient poduction function eans that technical efficiency in any fi is assessed in elation to the goup of fis fo which such function has been estiated. If any oe fis ae intoduced in the analysis, they could cause a eduction, but not an incease in the technical efficiency of a cetain fi. The heteogeneity of factos will not be elevant as long as it is equally distibuted in elation to all copanies. Technical efficiency in a fi will deonstate input quality and anageial efficiency when soe diffeences in the aveage quality of fis (specifically in quality distibution) aise. If such quality diffeences ae physically easuable, it would be possible to educe this effect by defining a wide nube of elatively hoogenous poduction factos. Howeve, it would neve be possible to eliinate the copletely in pactice. Fo this eason, technical efficiency in a fi should, to a cetain extent, display input quality; it is ipossible to easue anageial efficiency apat fo its factos. Thus, technical efficiency is defined in elation to a cetain goup of fis and to a cetain goup of paticulaly easued factos. Any change ade to such specifications will affect easueent (Faell, 1957: ). Pue technical efficiency shows the extent to which the analyzed poductive unit fulfills axiu exploitation of the physical esouces available. Moeove, efficiency of scale is elevant when poduction technology pesents vaiable yields of scale. This type of efficiency shows if the analyzed poductive unit has eached optial scale point. Yields of scale esult fo equally inceasing the quantity of all factos involved in the poduction function. Thee ae thee kinds of yields of scale (Vaian, 1998: ): 1. Constant Retun Scale. If the quantity of each facto inceases, poduction inceases in the sae popotion. 2. Gowing Retun Scale. If the quantity of each facto inceases, poduction inceases in a geate popotion. 3. Deceasing Retun Scale. When the quantity of each facto inceases, poduction inceases in a ino popotion. In this anne, global technical efficiency epesents the cobination of both pue technical and scale efficiencies. Technology is consideed a key eleent to undestand the concept of technical efficiency. Copanies confont technological estictions since thee ae only a few feasible facto cobinations needed to obtain a cetain aount of poduction. Copanies, then, should liit theselves to adopting poduction plans that appea feasible fo a 46 México y la Cuenca del Pacífico. Eneo abil de 2013

7 Pot Efficiency in apec technological point of view. Thus, the goup of all facto cobinations and technologically feasible poducts ae called poduction goup. This goup shows all possible technological choices in the copany. In the event that factos epesent a cost to the copany, it becoes necessay to analyze the axiu poduction possible coesponding to a cetain nube of factos. This is what is known as the bodeline of the poduction goup, which easues the axiu poduction value that can be obtained though a cetain nube of factos. This leads to the concept of the isoquant, which is the total su of all possible cobinations of factos needed to obtain a cetain aount of poduction (Vaian, 1998: ). Allocative Efficiency Allocative efficiency is based on the icoeconoic theoy, paticulaly on Paeto s theoy (Ali, 1994: 4). Nonetheless, othe authos have povided definitions accoding to its function as an eleent of econoic efficiency, as pesented hee: In icoeconoics, allocative efficiency is achieved when esouces ae not wasted and Paeto s pinciple is obseved. Thee ae thee basic conditions to be eet efficiency in allocation: Econoic Efficiency, which involves technological efficiency (o technical), as well as the use of poduction factos in such popotions in which costs ae iniized. Consue Efficiency, which occus when consues fail to ipove afte eassigning thei budgets. Maginal cost equality (cost of poducing an additional poduct unit, including extenal costs) and aginal social benefit (benefit of an additional consuption unit, including extenal benefits). Henández Laos (1985: 44) clais that allocative efficiency efes to the allocation of esouces, which eans assigning a fixed nube of esouces in fluctuating situations with the pupose of axiizing the poduct s quantity o satisfaction, whethe the analysis focuses on the poduction o the consuption aea. Yaad (1990: 183) agues that allocative o cost efficiency efes to the fact that the total onetay investent in inputs used to poduce a cetain nube of goods is the iniu possible accoding to the pice of such inputs. González-Páao (1995: 41) affis that allocative o pice efficiency happens when a copany axiizes benefits o iniizes costs: when the Eneo abil de Análisis 47

8 Zoe Infante y Aiel Gutiéez adinistato of a poduction unit has anaged to not only eaches the bodeline goup of poduction but also selects the cobination of factos that allows hi to iniize costs at a cetain poduction level (Bosch, Navao & Giovagnoli, 1999: 7). Unde this condition, pice signals should eain efficient in tes of econoy; that is, they should appoach an optial allocation as pe (Ali, 1994: 4-5). Geneal Featues of Data Envelopeent Analysis (dea) Models The use of the dea technique has been focused on the field of poduction fo the assessent of efficiency; that is, fo poviding the necessay estiates of poductivity. We push the use of dea odels into the assessent of the efficiency of aine pots. Although this is not the custoay use of this kind of analysis, we believe is an appopiate eans the efficiency of these units, and taking into consideation factos such as labo costs, which have peviously been ignoed. The definition of efficiency used in the odel is povided by (Mecado, Díaz & Floes, 1997: 17): Efficiency = Total outputs / Total inputs Oveall, efficiency can be defined as: E= Ouputs Inputs (1) O foally: E N i= 0 = N i= 0 viyi uixi (2) Whee E epesents efficiency, x i and y i ae inputs and outputs espectively, wheeas u i and v i epesent paaetes that show the elative ipotance of each one of the paaetes. If the elative ipotance of each one of the inputs and outputs wee known a pioi, the ain poble of efficiency evaluation would be ove; howeve, this infoation is geneally unknown. Efficiency assessent 48 México y la Cuenca del Pacífico. Eneo abil de 2013

9 Pot Efficiency in apec usually involves ultiple inputs and outputs; thus, they ust be selected accoding to the definition of the poble unde study. Methodologically, the eseach stuctue of dea odels, in which these aspects and eleents ae obseved, leads not only to poductivity analysis based on the dea technique but also to an altenative poposal to ipove efficiency. The cental concen is pefoance evaluation, in paticula the evaluation of activities in oganizations such as business fis, govenent agencies, hospitals, educational institutions, etc. Such evaluations adopt a vaiety of annes in a habitual analysis. Soe exaples include cost pe unit, benefit pe unit, satisfaction pe unit, and so on. These ae established easueents in the fo of a elation as follows: Ouput Input (3) This efficiency easueent is coonly used. The usual easueent of poductivity also adopts a elation used to evaluate the pefoance of a woke o eployee. Output pe woke-hou and output pe eployee woke ae exaples with sales, benefits o any othe easueents of output appeaing in the counte. Such easueents ae soeties efeed to as patial poductivity easues. This teinology is oiented to telling the apat fo the so-called easues of total poductivity of factos since it ais to obtain an input-output value elation that consides all inputs and outputs. Moving away fo the patial easueents of poductivity and towad the total poductivity easues of factos, cobining all inputs and outputs in ode to obtain a unique elation, helps avoid the isattibution of the eanings of cetain input o output to a diffeent one. Fo instance, an output eaning esulting fo a capital incease o ipoved adinistation could istakenly be attibuted to labo (when a unique output-input elation is being used). Howeve, intending to ove fo patial to total easueents will bing about difficulties such as choosing the inputs and outputs to be consideed and the weights to be used in ode to obtain a elation of only one output to only one input. This will coe down to only one way. Othe pobles and liitations can also occu in taditional effots to evaluate poductivity o efficiency when ultiple outputs and ultiple inputs Eneo abil de Análisis 49

10 Zoe Infante y Aiel Gutiéez need to be taken into account. The elatively new appoach incopoated in dea does not equie that the use pescibe weights to be attached on each input and output, as in the case of the taditional appoaches of nube indexes. No does it equie pesciption of functional fos necessay in statistical egession appoaches. Rathe dea uses techniques such as atheatical pogaing that can handle geat nubes of vaiables and elations (estictions).this wates down the equieents usually found when thee is the liitation of choosing only a few inputs and outputs because of the liitations of the technique in use. Relaxing conditions about the nube of candidates to be used in calculating the desied evaluation easueents akes it easie to deal with coplex pobles and to deal with othe consideations that would pobably be confonted in seveal contexts of social policy and anageent. In addition, the wide aay of theoy and ethodology available fo atheatical pogaing can be caied out in ode to affect calculations. This is due to the fact that a geat potion of what is needed has aleady been developed and adapted fo use in any pio dea applications (Coope, Seifod & Tone, 2000: 1-2). The Basic Model cc (Chanes, Coope & Rhodes) In ode to allow applications fo a wide vaiety of activities, the te decisionaking unit (du) will be used to efe to any entity (pot) that is evaluated in tes of its capability of conveting inputs into outputs. Such evaluations ay involve govenent agencies and non-pofit oganizations along with business fis (Coope, Seifod & Zhu, 2004: 8). Optial weights can (and geneally do) vay fo one du to anothe. Fo this eason, the so-called weights in the dea ae deived fo data instead of eaining fixed befoehand. Each DMU is assigned the best weight goup with anging values fo one du to anothe (Coope et al., 2000: 22). Assuing thee ae n dus; du 1, du 2,, du n. Soe coon ites of inputs and outputs fo each one of the j =1,, n DMUs ae selected as follows: Nueical data ae available fo each input and output, with data assued to be positive fo all dus. The ites (inputs, outputs and the election of dus) should bing foth an inteest in analysis and anageent of coponents that will take place in the evaluation of du s elative efficiency. By pinciple, salle aounts of input and geate aounts of output ae pefeable; thus, the efficiency outcoes ust illustate such pinciples. 50 México y la Cuenca del Pacífico. Eneo abil de 2013

11 inteest in analysis and anageent of coponents that will take place in the eva DMU s elative efficiency. By pinciple, salle aounts of input and geate a output ae pefeable; thus, the efficiency outcoes ust illustate such pinciples Pot Efficiency in apec The easueent units of the diffeent inputs and outputs ae not necessaily The Soe easueent of the ay units involve of the a diffeent nube inputs of people, and outputs oo availability, ae not necessaily conguent. Soe of the ay involve a nube of people, oo expenditues, e availability, expenditues, etc. Supposing Supposing inputs inputs and and s outputs s outputs ae selected ae selected with with the above the above entioned entioned popetie popeties Being 1 the and input 2. Being and the output input data and fo output DMU data j (xfo lj, xdu 2j,..., j (xx j lj, x) and 2j,..., x(y j ) lj, y 2j,..., y sj ), e and (y Input lj, y 2j,..., X data y sj ), espectively. atix and input Input X Y data atix and ay input be laid Y data out atix as follows, whee X ay n) be atix laid out and as follows, Y is an whee (s x n) X atix is an ( (Coope x n) atix et al., and 2000: Y is 22-23): an (s x n) atix (Coope et al., 2000: 22-23): (4) (5) Each du consues quantities of diffeent inputs to poduce diffeent s outputs. Specifically, the du j consues i x ij input aounts and poduces y j output Each aounts. DMU consues This assues quantities x ij > 0 and of ydiffeent j > 0, and that inputs each DMU to poduce has diffeent s at least Specifically, one positive the input DMU value and one positive output value (Coope, et j consues i x ij input aounts and poduces y j output al., 2004: 8). This assues x Now, we etun dea s ij > 0 and y atio-fo. j > 0, and that each DMU has at least one positive in In this fo, as intoduced by Chanes, Coope and and one Rhodes, positive the output output-to-input value (Coope, elation et is al., used 2004: fo assessing 8). elative efficiency of du j = du o, which is evaluated in elation to atios of all j = 1, 2,..., Now, n duwe j. The etun constuction DEA s can atio-fo. be intepeted In this as a eduction fo, as of intoduced the output-bultiple Rhodes, / input-ultiple the output-to-input situation elation (fo each is du) used towad fo assessing a unique vitual elative efficiency of Chanes, Co output and a unique vitual input. Fo a paticula du, the elation between DMU o, which is evaluated in elation to atios of all j = 1, 2,..., n DMU j. The co a unique vitual output and a unique vitual input povides an efficiency easue can be that intepeted epesents as a function a eduction of the of ultiplies. the output-ultiple In the atheatical / input-ultiple situation language, DMU) this towad elation, a unique which is vitual axiized, output akes and a up unique the objective vitual function input. Fo a paticula D fo a elation paticula between du to a be unique evaluated, vitual sybolically: output and a unique vitual input povides an easue that epesents a function of the ultiplies. In the atheatical lang elation, which is axiized, akes up the Eneo objective abil de function Análisis fo 51 a paticula D evaluated, sybolically:

12 = uyo Zoe Infante y Aiel Gutiéez ax h 0 ( u, v) / vixio (6) i Whee it is noted that the vaiables ae u s and v i s ; wheeas y o s and x io s epesent, espectively, the obseved output and input values of the du o and the du to be evaluated (Coope et al., 2004: 8-9). A goup of noalized estictions (one of each du) illustates the fact that elation between vitual output and vitual input in each du, including du j = du o, ust be ino o equal to the unit. The poble of atheatical pogaing could be established as 4 ax h 0( u, v) uyo / vixio = i Subject to: uyj / vixij 1 i Fo j = l,..., n, u, v i 0 fo all i and. (7) The elation lay-out entioned above poduces an infinite nube of solutions; if (u*, v*) is optial, then (αu*, αv*) is also optial fo α > 0. Howeve, the tansfoation developed by Chanes, Coope & Rhodes (1962: 182) fo the lineal factional pogaing selects a epesentative solution and poduces the equivalent poble of lineal pogaing in which a change of vaiables fo (u, v) to (µ, v) is the esult of a tansfoation. Chanes- Coope, cited by Coope, et al. (2004: 9), ax z = = µ 1 s yo 4. Obsevation: a oe coplete and igoous developent would eplace u, v i 0 fo i= 1 u, u ε > 0 vixio vixio i= 1 Whee ε epesents a non-achiedean eleent salle than any eal nube. This condition guaantees that the solutions ae positive in such values. This leads to the second stage in the optiization of slacks. (Coope et al., 2004: 9). 52 México y la Cuenca del Pacífico. Eneo abil de 2013

13 ax tansfoation. z yo Chanes-Coope, cited by Coope, et al. (2004: 9), 1 Subject ax z to: 1 s Subject Subject to: to: yj vix 1 i1 s v x y 1 i io j i1 1 i1, v i 0 vixio 1 i1 Pot Efficiency in apec Fo which, the dual poble of LP (lineal pogaing) is Fo * in which, the dual poble of LP (lineal pogaing) is θ* = inθ Subject Subject * to: to: s vixij yo 0 Fo, which, vi 0 the dual poble of LP (lineal pogaing) is in n Subject to: xijj x j1 n n j 1 j1 io xijj x yjj yo io = 1, 2,, s; ij 0 i = 1, 2,, ; i = 1, 2,, ; (8) (8) (8) j 0 j = 1, 2,, n. (9) (9) This last This odel last odel is occasionally is occasionally efeed to efeed as the Faell to as the odel Faell because odel it is because it is th the only he used. one he In used. the econoic In the econoic section section of the of liteatue the liteatue on on DEA s, dea s, it it is is said to be adju said to be adjusted to the assuption of stong disposition since it ignoes assuption of stong disposition since it ignoes the pesence of non-zeo s the pesence of non-zeo slacks, also efeed to as weak efficiency. In efeed obsevation to as of weak the dual efficiency. theoe of lineal pogaing, z* = θ*. We can solve (9) to obtain an efficiency esult. A solution will always exist due to the fact that In obsevation we can locate of θ = the 1 and dual λ*k theoe = 1 (labda) of lineal with λ*k pogaing, = λ*o, and the z* est = θ*. We can s with obtain λ*j = 0. an Futheoe, efficiency this esult. solution A solution iplies will θ* always 1. The optial exist due solution, to the fact that we ca θ*, poduces = 1 and an λ*k efficiency = 1 (labda) outcoe fo with a paticula λ*k = λ*o, du. and The the pocess est epeats with λ*j = 0. Futhe fo each du j. dus fo which θ* < 1 ae inefficient, wheeas dus fo which solution iplies θ* 1. The optial solution, θ*, poduces an efficiency outc θ* = 1 epesent bodeing points (Coope et al., 2004: 9-10). paticula DMU. The pocess epeats fo each DMU j. DMUs fo which θ* inefficient, wheeas DMUs fo which θ* = 1 epesent bodeing points (Coo Eneo abil de Análisis : 9-10). Soe bodeing points ay be weakly efficient since we have non-zeo slacks

14 2004: 9-10). Soe bodeing points ay be weakly efficient since we have non-zeo slack see distubing because Zoe Infante an y Aiel optial Gutiéez altenative could have slacks diffeent fo Soe soe bodeing solutions points but ay not in be othes. weakly Howeve, efficient since we can we have avoid non-zeo distubance, even in slacks. by This binging ay see up the distubing following because lineal an poga optial altenative in which slacks could have adopt thei axiu slacks diffeent fo zeo in soe solutions but not in othes. Howeve, we can avoid distubance, even in such cases, by binging up the following lineal poga in which s ax s i slacks s adopt thei axiu values. j1 s 1 + ax s i + s j= 1 = 1 Subject to: Subject to: n x ijj s i * j1 i = 1, 2,, ; n j1 y jj s = 1, 2,, s; y o x io j, s, s 0 (10) - + Hee is noted that the s i and s options do not affect the optial θ* deteined in odel. These advances now lead us to the definitions about elative efficiency. An efficient dea: DMU o s pefoance is totally efficient (100%) - + if and only if θ* = 1 and all slacks s i = s = 0. By contast, a weakly efficient DEA is one in which DMU o s pefoance is weakly efficient if and only if θ* - + = 1 and s i 0 and/o s 0 fo any i and in any optial altenative (Coope et al., 2004: 10-11). It is ipotant to ention that the developent of the quantities entioned above is useful to solve the following poble in two steps: inθ ε ( i j= 1 i, j, s + = 1 s i s + ) (10) 54 México y la Cuenca del Pacífico. Eneo abil de 2013

15 in ( Subject to: j 1 1 s j1 1 s i s ) Pot Efficiency in apec Subject n to: Subject to: xijj s i xio j1 n i = 1, 2,, ; xijj s i xio jn 1 i = 1, 2,, ; yjj s yo j1 n = 1, 2,, s; j, sy jj s yo i, s 0 i, j, (11) j1 = 1, 2,, s; j Whee, si, s - 0 i and s + ae i, slack j, vaiables used fo conveting inequalities (11) in (9) (11) into equ equations. Hee ε > 0 is also a non-achiedean eleent ino to any positive eal n - + Whee This s i and ae slack vaiables used fo conveting inequalities (9) into Whee is equivalent s - i and s + ae to solving slack vaiables (9) in two used stages, fo fist conveting iniizing inequalities θ, and then in (9) aanging into equ equivalent equations. Hee ε > 0 is also a non-achiedean eleent ino to as equations. in (7), whee Hee slacks ε > 0 is ae also axiized a non-achiedean without alteation eleent of ino the pe-deteined to any positive eal value n any positive eal nube. This is equivalent to solving (9) in two stages, fist θ*. iniizing This Foally, is θ, equivalent this and then aanging to is equivalent solving θ = (9) to θ* in giving as two in (7), stages, pefeential whee fist slacks iniizing pioity ae axiized θ, to and the then deteinatio aanging without in as (8). in alteation (7), whee of the slacks pe-deteined ae axiized value without of θ = alteation θ*. Foally, of the this pe-deteined is value equivalent θ*. Foally, to giving pefeential this is equivalent pioity to giving to the pefeential deteination pioity of θ* in (8). to the deteinatio Altenatively, in (8). one one could have coenced with the output side and consideed the consideed output the elation vitual instead output elation of the instead vitual of input the vitual elation. input This elation. would eoient the g This would axiizing Altenatively, eoient towad the one goal could iniizing, of have axiizing coenced as in (10), towad with iniizing, obtain: the output as side in (10), and consideed the to obtain: output elation instead of the vitual input elation. This would eoient the g axiizing Min vixio / towad uyoiniizing, as in (10), to obtain: i Subject to: i io i o Subject Min to: v x / u y vixij / uyj 1 i Fo j = 1,, n, Subject to: u, v i ε > 0 fo all i and. (12) (12 Again, the tansfoation Chanes, et al. (1962: 182) fo factional lineal pogaing Again, poduces the tansfoation a ultiplying Chanes, odel, with et the al. dual (1962: poble 182) associated fo factional lineal p to the envelopent odel, as descibed: poduces a ultiplying odel, with the dual poble associated to the envelop as descibed: in q i1 Subject to: vixio Eneo abil de Análisis 55 s

16 Subject vixij to: Subject to: Zoe Infante y Aiel Gutiéez, vi,, i s (13) (13) yo 1 1, vi,, i (13) + ax + ( s ax φ ε ( s s s i i + s s ) ) j1 1 j= 1 = 1 Subject ax to: ( s Subject to: s i s ) n j1 1 xijj s i xio j1 Subject to: i = 1, 2,, ; n xij yj j si x io yo j 1 (14) i = 1, 2,, ; n = 1, 2,, s; yjj s j 0 yo 1 j = 1, 2,, n. (14) = 1, 2,, s; Hee, we ae using j Hee, we ae the 0using odel the with odel a goal with oiented a goal to output, oiented in contast to output, with in contast wit an input oientation. j = oientation. 1, 2,, Howeve, n. Howeve, as as entioned befoe, odel odel is calculated is calculated in a in a two-stag (14) two-stage pocess. Fist, we calculate ignoing slacks, and then we optiize slacks aanging the following lineal pogaing poble, Hee, we ae using the odel with a goal oiented to output, in contast wit s + ax oientation. s i + Howeve, s as entioned befoe, odel is calculated in a two-stag j= 1 Subject in q to: s i1 i1 1 s yo 1 vixij 1 i1 1 s vixio y y = 1 j j México y la Cuenca del Pacífico. Eneo abil de 2013

17 ax s s i s j1 1 Subject to: Subject to: n j1 xij j s i x io Pot Efficiency in apec i = 1, 2,, ; (15) y jj s * yo = 1, 2,, s; j 0 j = 1, 2,, n. (15) n j1 Then, the Then, pevious the input-oiented pevious input-oiented definition of dea definition efficiency of is DEA odified efficiency into is odifi the following output-oiented vesion vesion (Coope (Coope et al., 2004: et al., 11-13). 2004: du 11-13). o is DMU o is effi -* +* efficient only if and if = only 1 y if s -* i = 1 = y ss +* i = s 0 = fo 0 fo all all i and i and values. DMU du o o is is weakly efficient if = -* +* efficient y/o if s = +* 1 y s i 0 y/o s 0 fo any i and value in any optial altenative. Thus, the cc output-oiented envelopent odel is the one used 0 fo any i and value in any optial altenative. Thus, the CCR out envelopent odel is the one used fo caying out the easueent of effici fo caying out the easueent of efficiency in pot containe teinals. containe teinals. The bcc Model (Banke, Chanes & Coope) The BCC Model (Banke, Chanes & Coope) As peviously discussed, the cc odel is built on the assuption of constant etun scales in activities descibed by the fontie of poduction in the case As peviously discussed, the CCR odel is built on the assuption of con of an only input and an only output shown. Geneally, it is assued that the poduction scales possibility in activities set has descibed the following by the popety: fontie If (x, of y) poduction is a feasible point, in the case of an on then (tx, an ty) only fo any output positive shown. t is also Geneally, feasible. This it is assuption assued that can be the odified poduction possibility in ode following to allow poduction popety: If possibility (x, y) is sets a feasible with diffeent point, then postulates. (tx, ty) In fo fact, any positive t is a since the This beginning assuption of dea can studies, be odified any extensions in ode to to allow the cc poduction odel have possibility sets w been poposed, postulates. aong In fact, which since the the bbc beginning odel (Banke, of DEA Chanes studies, & Coope) any extensions is to the epesentative. The bcc odel has its poduction fonties spanned by the have been poposed, aong which the BBC odel (Banke, Chanes & convex hull of the existing du s. The fonties have piecewise linea and concave chaacteistics epesentative. which The leads BCC to odel vaiable has etuns its poduction to scale chaacteizations fonties spanned by the con with (a) the inceasing existing etuns DMU s. to The scale fonties followed by have (b) deceasing piecewise etuns linea and to scale concave chaacte and (c) leads constant to vaiable etuns to etuns scale occuing to scale at chaacteizations the point whee the with tansition (a) inceasing etu fo the followed fist and by to (b) the deceasing second segents etuns is to ade. scale and (c) constant etuns to scale occ point whee the tansition fo the fist and to the second segents is ade. Eneo abil de Análisis 57

18 The BBC and CCR odels diffe only in that the foe, but not the latte, in Zoe ninfante y Aiel Gutiéez j 1 j convexity condition 1 The bbc and cc odels diffe only in that the foe, but not the latte, n includes the convexity condition j = λ = 1, λj 0, in its constaints. Reason j 1 being, they shae coon popeties, as expected, and pesent diffeences. (Coope et al., 2000: 87-91). Next is pesented the bcc odel. Assuing a elation n dus whee each du j, j = 1, 2,, n, poduces the sae outputs in diffeent quantities, y j ( = 1, 2, 3,, s), using the sae inputs, x ij (i = 1, 2,, ), also in diffeent quantities. The efficiency of a specific du o ay be evaluated with the bcc odel of the dea, in an enveloping fo and output-oiented as follows (Banke, Coope & Rhodes, 1984: 1080):, λj 0, in its constaints. Reason being, they sha popeties, as expected, and pesent diffeences. (Coope et al., 2000: 87-91). Next is pesented the BCC odel. Assuing a elation n DMUs whee each DM 2,, n, poduces the sae outputs in diffeent quantities, y j ( = 1, 2, 3,, s) sae inputs, x ij (i = 1, 2,, ), also in diffeent quantities. The efficiency of DMU o ay be evaluated with the BCC odel of the DEA, in an enveloping output-oiented as follows (Banke, Coope & Rhodes, 1984: 1080): axφ + ε ( Subject to: to: jj= 1 s + s ii + s ) s = 1 n j1 xij j s i x io i = 1, 2,, ; n j1 y jj s = 1, 2,, s; y o (16) n j1 j 1 j, s, s 0 i i,, j (16) Whee ε > 0 is a non- Achiedean defined eleent ino to any positive eal nube. Whee ε > 0 is a non- Achiedean defined eleent ino to any positive eal nu Benchaking Faell s oiginal idea has been successfully couted to its epiical applicatio basically two ethodologies: the estiation of stochastic bodelines easueents. The fist one iplies the use of econoetics and the second on lineal- pogaing algoiths and on benchaking. 58 México y la Cuenca del Pacífico. Eneo abil de 2013

19 Pot Efficiency in apec Benchaking Faell s oiginal idea has been successfully couted to its epiical application though basically two ethodologies: the estiation of stochastic bodelines and dea easueents. The fist one iplies the use of econoetics and the second one elies on lineal- pogaing algoiths and on benchaking. Benchaking can be defined as the easue of an activity in copaison to that of the best copanies of its class. It deteines how the best one has achieved such levels of activity, and it uses infoation as a basis to the objectives, stategies and application of the copany itself (Beowski, 1991: 21). The pocess of benchaking equies: Deteining the appopiate chaacteistics of the eception pocess and utilizing the to copae one pocess to anothe. Developing data on the best-pacticed activity inside o outside an oganization that equies the application of benchaking. Copaing and evaluating the pocess o pocesses accoding to data elated to easued chaacteistics. Developing easues of continual ipoveent based on new data. Applying planned changes to pocess. Contolling the effectiveness of such changes. Benchaking equies, theefoe, a planned action towad evaluation and application, the goal of which is to odify pocesses based on newly acquied knowledge about a oe effective pocess. Benchaking can be divided in thee aeas: 1. Intenal. It is an evaluation of pactices within an oganization. 2. Copetitive. It is vey liited in eal pactice since it equies copetitos that coopeate to the ipoveent of one o both copanies. 3. Inte-industial. These ae evaluations aong opeations in diffeent industies. Benchaking eans adapt best pactices instead of copying the. It iplies using the knowledge of a pocess to identify what is usable in the dono pocess. This way, the entality o cultue suounding the benchaking ust be one of ipoving and exceeding the action diension of the dono pocess. Eneo abil de Análisis 59

20 Zoe Infante y Aiel Gutiéez Futheoe, benchaking is a pocess diected at acquiing useful infoation that helps an oganization ipove its pocesses; it ust, theefoe, be pefoed continuously. The DEA technique, then, will allow an identification of those aspects equiing changes and ipoveents to becoe efficient. The above entioned technique has its basis on the use of lineal pogaing as a tool to cay out the necessay calculations fo the application of benchaking. This way, it is ipotant to ceate a space to eview the fundaentals of lineal pogaing. dea odels applied in the pot industy Cuently, thee is little eseach on the application of dea odels to easue efficiency in the pot industy, specifically with egad to the containe teinals. Howeve, these studies ae useful as a basis to select the vaiables that wee used in this eseach. Ove the past two decades, dea has becoe a popula ethod fo evaluating the elative efficiencies of decision-aking units within a elatively hoogenous set. The application on pots o teinals, howeve, is only incidental. Roll and Hayuth (1993: ) is pobably the fist pape to discuss the applicability of dea on pot secto. It uses a hypothetical exaple of 20 pots to geneate siulated esults. Matinez-Budia et al. (1999: ) used a dea-bcc odel to analyze 26 Spanish pots by defining the as high coplexity, ediu coplexity and low coplexity pots. It coes to the conclusion that pots with high coplexity appeaed to be oe efficient. In ecent yeas, the eseach on pots tends to focus oe on containe pots fo thei hoogeneous chaacteistics. Tongzon (2001: ) agued that to estict the scope of analysis to a liited nube of pots and a specific type of cago is necessay fo the ultiplicity of pots and cago handled. It uses both dea-cc and dea-additive odels to analyze the efficiency of 4 Austalian and 12 othe intenational containe pots fo the yea This analysis is a eaningful exploation, but the esult is not pleasing fo the elatively less saples. Afte that, a few papes have focused on the containe pots. Valentine and Gay (2001: 1-16) studied 31 containe pots aong wold s top 100 containe pots in Cullinane, Song & Wang (2005: 73-92) analyzed 25 containe pots out of wold s top 30 ones fo Fo the liteatue, we find that ost ecently eseaches tend to switch the dus to containe teinals since 60 México y la Cuenca del Pacífico. Eneo abil de 2013