WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza A Data Evelopmet Aalysis Evaluatio ad Fiacial Resources Reallocatio for Brazilia Olympic Sports RENATO PESCARINI VALÉRIO LIDIA ANGULO-MEZA Departameto de Egeharia de Produção Uiversidade Federal Flumiese Av. dos Trabalhadores 420, 27255-125, Volta Redoda, RJ BRASIL reato_pv@yahoo.com.br lidia_a_meza@pq.cpq.br Abstract: - This paper proposes the use of a Data Evelopmet Aalysis model to evaluate the Brazilia Olympic sports efficiecy ad also to reallocate the fiacial resources received by them. The sports selected were those that received fiacial resources from the Agelo/Piva Law i 2011. As proposed i previous works, we use as iputs the fuds received ad medals offered, as a proxy for difficulty measure i wiig a medal; ad the results obtaied (gold, silver ad broze medal) as outputs. We proposed to use the results from the Pa-America Games, specifically from the 2011 Pa-America Games, sice we believe that the Olympic Games results were scarce to assess the sports efficiecy as there are may ull results for lots of sports. Therefore, the medals related to the 2011 Pa America Games are used i this paper. A DEA o-radial model with weights restrictios is formulated to perform the Olympic sports efficiecy evaluatio. With these results a fiacial resources reallocatio is proposed usig a ZSG-DEA o-radial approach. Results show that usig data with miimal ull medals leads to a good fiacial resources reallocatio, based o the sports efficiecy, without the eed of icludig aymore variables or imposig additioal weight restrictios. Key-Words: - Data Evelopmet Aalysis, Olympic sports, sports efficiecy, fiacial resources reallocatio 1 Itroductio Brazil will be soo the host coutry of two major world sportig evets: the 2014 FIFA World Cup ad the 2016 Olympic Games. It represets a uique opportuity for the coutry to take advatage of the large ivestmet that will be made ad to leave a great impressio all over the world, whether the evets are well orgaized ad achieved. Moreover, i this positio of great iteratioal visibility, the coutry performace i both evets is a growig cocer. I order for the coutry to achieve a good performace durig the sportig evets, it is ecessary a high ivestmet i sports. The mai source of fiacial fuds for Brazilia Olympic Sports is the Agelo/Piva Law. This Law was sactioed i 2001 ad determies that 2% of the gross reveues from the Brazilia federal lotteries must be destied to the Brazilia Olympic Committee. Sice the creatio of this Law, we have t bee oticig great improvemets o the Brazilia sportig performace ad, cosequetly, the Brazilia Olympic Committee have bee sufferig harsh criticism regardig the applicatio of the fuds ad how it has bee distributed [1, 2]. With the aim of cotributig o the improvemet of its sportig performace, this paper proposes the use of Data Evelopmet Aalysis (DEA) to firstly evaluate some Brazilia Olympic sports efficiecy, based o the coutry results i the 2011 Guadalajara Pa-America Games. Posteriorly a fiacial resources reallocatio is made cosiderig the fuds trasferred to each sport committee as defied by the Agelo/Piva Law i 2011. Therefore, those who have good performace (high efficiecy) will receive more fuds; ad those who have t, will receive smaller fuds as they are ot usig them properly, i.e., trasformig them ito results. This paper is divided ito five sectios. I sectio 1 a itroductio ad the motivatio of the work are preseted. Posteriorly, i sectio 2, the E-ISSN: 2224-2678 627 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza theoretical explaatio of the methodology used ad its mai features are exposed. Still i this sectio, some studies usig DEA cocerig fiacial resources destied to sports are preseted. I sectio 3, it is show how Data Evelopmet Aalysis was used to reach the results preseted i sectio 4, where it is foud a discussio about these results. Fially, i sectio 5, fial commets are made. 2 Data Evelopmet Aalysis Data Evelopmet Aalysis (DEA) [3] is a mathematical techique used to evaluate the efficiecy of a group of uits, called Decisio Makig Uits (DMUs). The DEA method ivolves the use of Liear Programmig (LP) to determie the relative efficiecy of each DMU. A group of DMUs represets productive uits i a broader sese, ot oly those ivolved i productio processes, but uits with the same targets ad with the use of the same kid of resources (iputs), geeratig the same kid of products (outputs). Traditioally, DEA models ca have two orietatios: iput orietatio, whe the objective is to decrease the iputs while maitaiig outputs level costat, ad output orietatio, whe the objective is to icrease the outputs keepig the iputs level costat. The DEA efficiecy is obtaied by the ratio of the outputs weighted sum to the iputs weighted sum. There is o impositio of fixed values for the weights used o the iputs ad outputs weighig, which allows each DMU to fid the most favourable weights set for itself. This flexibility represets a advatage of DEA, sice the DMUs cosidered iefficiet caot claim that such iefficiecy is due to a ufair weights distributio. There are two DEA classical models. The first oe is the most basic DEA model ad it is called CCR, that stads for Chares, Cooper e Rhodes, the model s creators [3]. This model works with costat returs to scale, beig used for situatios where iputs variatios cause proportioal variatios o the outputs. The secod DEA classical model is the BCC, that stads for Baker, Chares e Cooper [4]. The BCC model works with variable returs to scale, beig suitable for a set of DMUs i differet scales, avoidig possible problems caused by imperfect competitio situatios. The iput orieted versio of the BCC model is preseted i (1). Mi h0 Subject to hx λ x, i 0 i0 k ik y λ y, j j0 k jk λ = 1 k λk 0, k (1) I this programme, h0 is the efficiecy of the DMU o, if h 0 is equal to 1, the DMU o is efficiet, if h 0 <1 the DMU o is iefficiet. Also, x ik ad y jk represet, respectively, the value of iputs i ad outputs j of a DMU k ; λ k represets the cotributio of each DMU k i the compositio of the target of the DMU o. This model is called the evelopmet model; its dual is called the multipliers model. Both models provide the efficiecy of the DMU uder evaluatio, h o, but they deliver differet iformatio: bechmarks ad targets (evelopmet model) ad the variables weights (multipliers model) [5]. Sice the very first DEA model, may others have bee proposed accoutig for several differet characteristics of the variables, case studies, etc. I this paper, we use a o-radial model, which basically meas that ot all iputs (outputs) reduce (icrease) proportioally. I our case, we will use a o-radial model proposed by [6], which takes ito accout the existece of o-cotrollable variables, variables that caot be modified by the decisio maker (for more iformatio about o-cotrollable variables see, for istace, [7]). The iput orieted model that takes ito accout variable returs to scale ad o-cotrollable iputs is preseted i (2). E-ISSN: 2224-2678 628 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza Mi h0 Subject to C C 0 i0 λk ik hx x, i C NC NC i0 λk ik x x, i NC y λ y, j j0 k jk λ = 1 k λk 0, k (2) As metioed previously, programmes (1) ad (2) are very similar beig the oly differece that i programme (2) the iputs are divided ito two groups, the cotrollable iputs deoted by C, ad the o- cotrollable iputs deoted by NC. We ca observe that the first set of restrictios cocers oly the cotrollable iputs, which are multiplied by the term h 0 i the left part of the equatio. However, the secod set of restrictios, very similar to the first oe, cocers oly the o-cotrollable iputs, that are ot multiplied by the term h 0 i the left part of the equatio. Moreover, i this paper we have additioal iformatio to iclude i the model. Whe a priori iformatio or value judgemets about the variables must be take ito accout we use weight restrictios [8]. There are differet types of weights restrictios, depedig o the kid of iformatio available. I our case, we will use the Assurace Regio Method, as termed by Thompso et al. [9]. This type of weight restrictios makes a direct compariso betwee the variables. Whe we compare either iputs, or outputs, we are usig Assurace Regio I, or ARI, as used by [10] ad Korbluth [11]. The Assurace Regio II, also proposed by [10], is used for comparisos betwee iputs ad outputs. Sice we just eed to compare two variables, these are the most used weight restrictios, ad at the same time they preserve the DEA spirit of providig some freedom to determie T variables weights. I (3), A γ represets the coefficiets matrix of the outputs weights restrictios, Au 0, as preseted i [12] ad also used i [13]. The compositio ad form of this matrix will be explaied i the ext Sectio. Mi h0 Subject to C C 0 i0 λk ik, NC NC i0 λk ik, T j0 λk jk γi hx x i x x i y y A, j λ = 1 k λk 0, k (3) So far, model (3) is used for the performace evaluatio. Oce the evaluatio is performed, we also propose a fiacial resources reallocatio usig the iput targets from the o-radial model. This reallocatio is made based o a ZSG o-radial approach, as i Satos et al [14]. The DEA Zero Sum Gais model (DEA-ZSG) was proposed to solve problems where the total sum of some iputs or outputs values must be costat [12, 15]. As the total sum of the fiacial resources received by all sports i this study must be costat, ad the targets determied by model (3) will ot esure that, the reallocatio is made based o this approach. Equatio (4) shows how the reallocatio of a iput is calculated usig the ZSG o-radial approach. The term x reallocated io is the ew value of the iput i t arget for the DMU o ; xio is the target of the iput i for the DMU o obtaied with the o-radial model (3); origial t arget xik is the origial iput i for a DMU k ; xik is the target of the iput i for a DMU k obtaied with the o-radial model; is the total umber of DMUs. reallocated t arget origial t arget io = io ik ik k= 1 k= 1 x x ( x x ) (4) At the ed of the reallocatio, all DMUs must be efficiet ad the model is ru agai to verify that all have reach maximum efficiecy. Also, those who were efficiet previously would receive more iput ad the iefficiet oes will lose some iput. Sometimes, whe usig a o-radial model with weight restrictios, it is ecessary to perform may E-ISSN: 2224-2678 629 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza iteratios, i.e., reallocate iput ad verify efficiecy of DMUs, for all DMUs to be efficiet [13]. 2.1 DEA i sports Data Evelopmet Aalysis has bee used i sports, especially i determiig rakigs i Olympic sports or other iteratioal evets. A brief survey of DEA i sport ca be foud i [16]. Amog, all this papers, we highlight the works of [12] that preset ad use the ZSG-DEA model to show a redistributio of medals amog coutries for all to be efficiet ad also to rak wiig medal coutries. A applicatio of DEA i determiig a fial rakig for the Olympic Games ca be foud i [17]. Also [18] determie a rakig ad proposed a way to bechmark iefficiet coutries ad [19] proposed a model to rak coutries takig ito accout iteger values. Moreover, regardig target settig ad redistributio we have [20] ad [14]. 3 Brazilia Olympic sports Evaluatio ad Fiacial Resources Reallocatio Sports are i the spotlight i Brazil due to the two upcomig worldwide evets to be host i the coutry: the 2014 FIFA World Cup ad the 2016 Olympic Games. Therefore there is bee more iterest i the results obtaied by Brazilia represetatives i iteratioal evets. Moreover, the below average performace of some popular sports has raised issues about the fiacial fuds received by Olympic sports i geeral. The mai source of fiacial fuds for Brazilia Olympic Sports is the Agelo/Piva Law, sactioed i 2001. This law determies that 2% of the gross reveues from the Brazilia federal lotteries must be destied to the Brazilia Olympic Committee (COB Comitê Olímpico Brasileiro i Portuguese), which receives 85% of the amout, ad to the Brazilia Paralympic Committee, which receives the 15% remaiig. Both these Committees must ivest 75% i the Brazilia Olympic Cofederatios. COB uses the fuds i expeses related to sports, hirig iteratioal coaches, the maiteace of maagerial ad techical staff, equipmet ad material acquisitio, maiteace of the traiig cetres, traiig abroad, Brazilia techical staff qualificatio, the participatio of delegatio o atioal ad iteratioal evets, etc [21]. However, as metioed earlier, results obtaied i these sports were below expectatio, which carried harsh criticism ad questioig about the distributio of fuds amog the sports beig made based o political ageda ad popularity istead of techical basis. I this paper, we proposed a DEA model to assess the sports efficiecy regardig their results, takig ito accout the fuds received ad the opportuities give to wi a medal, that is, the efficiet sports will be the oes which succeeded better at obtaiig medals compared to the others, by meritocracy. Moreover, the reallocatio of fiacial resources will be based o their efficiecy, how well did they performed i compariso to the others. This reallocatio will be made based o techical reasos, i a objective way, ad this is possible usig DEA. We observed that work of Satos et al [14] was t reallocatig the fuds properly for the efficiet coutries, they eve suggested icludig additioal variables. However, we ca also observe that Brazilia results i the Olympics were very scarce, with may ull values i the data set, as o medals were wo. Therefore, we propose to use the results, medals wo, i the 2011 Guadalajara Pa America Games, as Brazil has always a better performace at the Pa America Games [22]. As we wat to evaluate how well the fiacial resources were used by the Olympic Committees to obtai results, the Olympic sports are the DMUs. These were the oes who participated i the 2011 Guadalajara Pa America Games ad that also received fuds from the Agelo/Piva Law i 2011. It is importat to poit out that some sports, as Soccer, Bowlig, Karate ad Squash, despite havig take part of these Games, are ot cosidered as DMUs i this paper sice they did t receive ay fuds comig from this Law. O the other had, Hockey o Grass is cosidered as a DMU sice it received fuds from aforemetioed Law, eve ot havig participated i the games. It is also importat to highlight that it was ecessary to group some sports accordig to the Cofederatios to which they belog. This is the case of Water Sports, Gymastics ad Volleyball. It was ecessary because Agelo/Piva Law fuds are distributed E-ISSN: 2224-2678 630 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza amog the Cofederatios ad ot for each sport idividually. I total there are 26 Sports Cofederatios cosidered as DMUs i this study. The model was formulated usig two iputs ad three outputs, which values of each DMU cosidered o this paper are preseted i Table 1. Olympic Cofederatios Iputs Fiacial Resources (R$) Gold Medals Offer Gold Medals Outputs Silver Medals Boze Medals Athletics 3.000.000,00 47 10 6 7 Badmito 1.300.000,00 5 0 0 1 Basketball 2.100.000,00 2 0 0 1 Boxig 1.700.000,00 13 0 2 5 Caoeig 2.300.000,00 12 0 2 2 Cyclig 2.300.000,00 18 0 0 0 Water Sports 3.000.000,00 46 10 9 11 Fecig 1.100.000,00 12 0 0 3 Gymastics 2.800.000,00 24 6 3 5 Hadball 3.000.000,00 2 1 1 0 Horse Ridig 2.900.000,00 6 0 1 2 Hockey o Grass 1.300.000,00 2 0 0 0 Judo 3.000.000,00 14 6 3 4 Weightliftig 1.100.000,00 15 1 0 0 Wrestlig 1.500.000,00 18 0 1 1 Moder Petathlo 1.300.000,00 2 0 1 0 Oar 1.900.000,00 14 0 2 0 Rugby 500.000,00 1 0 0 0 Taekwodo 1.200.000,00 8 0 0 1 Teis 1.800.000,00 5 0 1 1 Table Teis 2.300.000,00 4 1 0 0 Archery 1.300.000,00 4 0 0 0 Sports Shootig 2.000.000,00 15 1 0 5 Triathlo 2.000.000,00 2 1 0 1 Sailig 3.000.000,00 9 5 1 1 Volleyball 3.000.000,00 4 4 0 0 TOTAL 52.700.000,00 Table 1 Iputs ad Outputs Values The first iput is represeted by the fuds comig from the Agelo/Piva Law that were trasferred to each Olympic Cofederatio by the Brazilia Olympic Committee i 2011. This iput measures the amout of fuds that each oe receives for ivestmets i maiteace ad developmet of the athletes. It is importat to say that i this paper the fiacial resources cosidered are oly the oes comig from the Agelo/Piva Law, which meas that fuds comig from other sources, as private sposorship, are ot beig take ito accout. The secod iput is the umber of gold medals offered for each sport at the 2011 Guadalajara Pa America Games. The use of this variable i the model allows us to cosider the disparity i chaces of wiig a medal for each sport, idicatig a proxy for the difficulty that each oe has to wi a medal. It is ecessary to cosider this iput sice each sport has a differet umber of competitios ad, the more competitios they have, the easier it is to wi a medal. Sports like swimmig or athletics, for example, have a much larger umber of competitios tha basketball or hadball, which have oly two possible medals each oe, oe of their me's team ad the other oe of their wome's team. That is the way for the model to take ito accout the difficulty i wiig a medal, as a gold medal i basketball may be cosidered more valuable tha a gold medal i swimmig i term of the effort ivolved. This secod output represets the o-cotrollable variable of the problem, sice this iput values for each Sport is defied by the Committee resposible for the Pa America Games orgaizatio ad it caot be chaged. As various sports are aggregated ito cofederatios, the gold medals offered were added. The outputs are the umber of gold, silver ad broze medals wo by each cofederatio durig the 2011 Guadalajara Pa America Games. These three outputs represet the results obtaied by each sport ad it is liked to the ivestmets made usig the fiacial resources of the Agelo/Piva Law, sice everythig that is ivolved i the athletes traiig eeds fuds to happe. For the Cofederatio of Hockey o Grass, which received fuds from the Agelo/Piva Law i 2011 but did ot have Brazilia represetatives at the 2011 Pa America Games, ull values were assiged to its three outputs. As we kow, the differet medals, gold, silver ad broze, do t have the same importace. The fial classificatio of the Pa America Games, as well as other iteratioal evets, is based o the umber of gold medals wo by each coutry. The umber of silver medals ad, posteriorly, the umber of broze medals are oly used if there is a draw betwee two or more coutries. This is a multicriteria method called the Lexicographic Method, which mai disadvatage is the overvaluatio of the gold medal [12]. I order to take ito accout these differeces, i other words, to take ito accout that each medal must have a E-ISSN: 2224-2678 631 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza differet weight without imposig a actual weight value, this additioal iformatio was icluded i the form of weight restrictios, of the Assurace Regio I, metioed i the previous sectio. So, i our o-radial model we will use the same restrictios used by Lis et al [12]. The three weight restrictios icluded ca be see i (5), (6) ad (7). (For other methods to iclude value judgemets or other iformatio i a DEA model see [23]) u u gold silver u (5) u (6) silver broze u u u u (7) gold silver silver broze The first weight restrictio (5) idicates that the gold medal associated weight must be equal to or greater tha the silver oe, which meas that the gold medal is more importat, or at least equal to the silver medal. The secod oe (6) idicates that the silver medal associated weight must be equal to or greater tha the broze oe, which meas that the silver medal is more importat or at least equal to the broze. Fially, the third weight restrictio (7) idicates that the differece betwee the gold medal ad the silver medal associated weights must be equal to or greater tha the differece betwee the silver medal ad the broze medal associated weights. Those statemets were also used i [24] ad [25]. The weight restrictios i geeral are itroduced i the multiplier versio of the DEA models. I (2) we preseted the evelopmet model versio, so it is ecessary to formulate the dual form of these restrictios (5-7). Sice oe is dual of the other, additioal restrictios i the multipliers model (primal) geerate ew variables i the evelopmet form (dual). Takig the variables o the restrictios left had side, we may express the coefficiet of these restrictios as a matrix A show i (8). 1 1 0 A = 0 1 1 1 2 1 (8) The, the traspose of the matrix A was multiplied by the vector of the dual variablesγ, which has three compoets, γ 1, γ 2 ad γ 3, each oe for a Assurace Regio added to the model. T Fially, each lie of the matrix A γ could be icluded i the associated output restrictio of the Evelopmet Model, which results i (3). We use the data show i Table 1 ad the iput orieted o radial model, show i (3) to evaluate the performace of the 26 Cofederatios. This evaluatio aims to idetify the oes that better use the fuds received, obtaiig good results, ad also the oes that could t obtai good results, which will be cosidered iefficiet. The model is iput orieted sice the objective is to reallocate the fiacial resources, which represet a iput of the modelig. Oce the efficiecy evaluatio if performed, the reallocatio of the fiacial resources is doe usig a ZSG o-radial approach, based o the results obtaied by the performace evaluatio. This reallocatio aims to allow all DMUs to be efficiet. Therefore those who have bee efficiet will receive more fuds ad those who were ot will receive fewer fuds. 4 Results ad discussios This sectio is divided ito two parts: first of all we aalyse the results cocerig the efficiecy of each sport regardig the fiacial resources received ad the results obtaied by each sport at the 2011 Pa America Games. Also, based o the efficiecy idex we perform the fiacial resources reallocatio. These results are depicted i Table 2. By aalysig the secod colum of this table we ca ote that there are eight DMUs with maximum efficiecy: Athletics, Water Sports, Hadball, Judo, Rugby, Triathlo, Sailig ad Volleyball. Amog these eight DMUs, all of them wo at least oe gold medal, except the Rugby Cofederatio. This Cofederatio was amog the DMUs with maximum efficiecy, i spite of ot havig wo ay medal, sice for the models with variable returs to E-ISSN: 2224-2678 632 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza scale, the DMU with the smallest values of iputs has maximum efficiecy, eve if it has ull outputs. Besides, the Cofederatio of Athletics was ot cosidered Pareto Efficiet, eve havig reached the maximum efficiecy ad, cosequetly, beig i the efficiecy frotier. While the sports metioed above are cosidered the most efficiet oes, there is a group of sports eedig urget performace improvemet: Badmito, Basketball, Caoeig, Cyclig, Horse Ridig, Hockey o Grass, Wrestlig, Oar, Taekwodo, Teis, Table Teis ad Archery. Together, these 12 Cofederatios received approximately 42% of the total amout of fuds distributed by the Agelo/Piva Law i 2011 ad they had together 98 gold medals beig offered durig the 2011 Guadalajara Pa America Games, that is 98 possibilities of wiig a medal. However, they wo oly oe gold medal, which shows their iefficiecy. Regardig the Fecig ad Weightliftig efficiecies idex, it is possible to otice the actio of the weight restrictios preseted i (5), (6) ad (7). If the weight of the gold, silver ad broze medals were the same, probably Fecig would achieve a efficiecy idex higher tha the Weightliftig oe, sice both received the same amout of moey, R$ 1,100,000.00, Fecig was offered fewer gold medals tha Weightliftig, ad the total umber of medals wo by Fecig is greater tha that achieved by Weightliftig, as we ca see i Table 1. However, takig ito accout the weight restrictios that added to the model a greater importace to the gold medals, ad kowig that the three medals wo by Fecig are broze medals ad the oly medal wo by Weightliftig is a gold oe, both DMUs reached the same efficiecy idex i the modellig proposed here, which was 0.681818. Olympic Cofederatios Efficiecy Score Origial Resources (R$) Reallocated Resources (R$) Athletics 1.0000 3,000,000.00 4,534,431.80 Badmito 0.4487 1,300,000.00 881,695.17 Basketball 0.3297 2,100,000.00 1,046,406.29 Boxig 0.6373 1,700,000.00 1,637,433.96 Caoeig 0.3623 2,300,000.00 1,259,564.94 Cyclig 0.2174 2,300,000.00 755,737.58 Water Sports 1.0000 3,000,000.00 4,534,431.80 Fecig 0.6818 1,100,000.00 1,133,607.65 Gymastics 0.8163 2,800,000.00 3,454,807.17 Hadball 1.0000 3,000,000.00 4,534,431.80 Horse Ridig 0.2586 2,900,000.00 1,133,609.31 Hockey o Grass 0.3846 1,300,000.00 755,737.88 Judo 1.0000 3,000,000.00 4,534,431.80 Weightliftig 0.6818 1,100,000.00 1,133,607.65 Wrestlig 0.4444 1,500,000.00 1,007,650.50 Moder Petathlo 0.5325 1,300,000.00 1,046,406.60 Oar 0.3539 1,900,000.00 1,016,338.17 Rugby 1.0000 500,000.00 755,738.63 Taekwodo 0.4861 1,200,000.00 881,694.87 Teis 0.3704 1,800,000.00 1,007,650.50 Table Teis 0.3727 2,300,000.00 1,295,552.61 Archery 0.3846 1,300,000.00 755,737.88 Sports Shootig 0.5000 2,000,000.00 1,511,477.27 Triathlo 1.0000 2,000,000.00 3,022,954.54 Sailig 1.0000 3,000,000.00 4,534,431.80 Volleyball 1.0000 3,000,000.00 4,534,431.80 TOTAL 52,700,000.00 52,700,000.00 Table 2 Efficiecy, Origial Resource ad Reallocated Resource for each DMU But it is also importat to otice that the isolated fact of wiig oe or more gold medals wo t determie that a DMU is more efficiet tha aother oe which wo o gold medals. There are several other factors ifluecig the model. A good example is the Table Teis, which despite havig wo a gold medal, achieved a lower efficiecy idex tha other Olympic sports that did ot wi gold medals, as Fecig ad Taekwodo, ad eve tha other sports that wo o medal, as Archery. This probably occurred because Table Teis received a large amout of fiacial resources, higher tha the amouts received by Fecig, Taekwodo, Archery ad may other DMUs. The fourth colum of the table represets the data obtaied by the fiacial resources reallocatio made usig a DEA-GSZ o radial approach. As metioed previously, sometimes it is ecessary to expect more tha oe iteratio whe reallocatig fuds. However, roudig the first iteratio average efficiecy up to six decimal places, the value foud E-ISSN: 2224-2678 633 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza is 1.000000. I additio, ew iteratios would produce miimal chages i the values of the iput, which i practice does ot represet sigificat chages. Therefore, the reallocatio of resources from the first iteratio, show i the fourth colum of the table, is cosidered as the oe that allows all DMUs to reach the efficiecy frotier. Comparig these data with the oes i the secod colum, the origial distributio of resources, we ca reach several importat coclusios. Firstly, the DMUs that had origially received a great amout of resources ad reached the maximum efficiecy had more tha R$ 3,000,000.00 of resources after the reallocatio. It happeed for all of DMUs with maximum efficiecy, except for the Rugby. This sport did t have a big amout of moey i the origial distributio ad it was efficiet oly because it has the lowest values of iputs. Therefore, it seems that the model recogizes that this sport does t eed much more moey to keep its efficiecy. That is why the Rugby Cofederatio did t receive much more fuds i the reallocatio, compared with how much it had already received origially. Still amog the DMUs with maximum efficiecy, those that had received exactly R$ 3,000,000.00 were trasferred the same value after the resources reallocatio: R$ 4,534,431.80. It happeed because the calculatio of the reallocated iput for each DMU is proportioal to the efficiecy of this DMU ad to its origial iput. Furthermore, all DMUs with efficiecy equal to or greater tha 0.6818 received a larger amout of fuds after the reallocatio. However, all DMUs with efficiecy equal to or less tha 0.6373 lost part of the origial amout of fuds. Therefore, accordig to the DEA model used, the greater is the DMU efficiecy reached usig the o-radial model with weight restrictios, the bigger is the amout of resources it should receive by the reallocatio with a DEA-GSZ o radial approach, i order for all DMUs to reach the maximum efficiecy. 5 Fial Commets This paper, usig Data Evelopmet Aalysis, could evaluate sports performace, based o their results at the 2011 Pa America Games ad o the fuds comig from the Agelo/Piva Law i 2011, ad could also propose a reallocatio of those fuds, allowig all DMUS to be efficiet. The results obtaied poited out may efficiet DMUs but also may others that eed urget improvemets, the oes with the lowest values of efficiecy. However, those sports eedig urget improvemets received fewer fuds with the fiacial resources reallocatio. It did t happe because the DEA-ZSG approach used iteds to be puitive, but because it iteds to reward those DMUs with best performace ad to serve as a warig sigal for those with worst performace. The DMUs with worst performace should face the results as a idicative that they have to do somethig to improve their performace. The approach used i this paper is very similar to the oe used i [14]. The major differece is that i this study the data used as outputs, represetig the umber of gold, silver ad broze medals coquered by each DMU, came from the 2011 Pa-America Games, while i the metioed paper, they came from the 2008 Olympic Games. This choice provided more robust results for this paper compared with the other oe, sice data comig Olympic Games have may ull results for Brazilia sports. Furthermore, [14] cocluded that the iclusio of the umber of gold medals offered for each sport as a iput i the model used i that study did t add ay value for the results. However, it could have bee caused, oe more time, by the coutless ull results i the data used for that study, iasmuch as i this paper the use of this iput was fudametal for the results obtaied. Also, we saw that the iclusio of this iput allow us to really take ito accout the effort for wiig a medal i a give sport. From a techical stadpoit, the models proved to be well suited to what it was iteded to do. I the evaluatio as well as i the resources reallocatio, we could reach satisfactory results, cosiderig the specificities of the study. We ca say that this study validated the use of the DEA- GSZ o radial approach for fiacial resources reallocatio o sports. We also would like to metio aother proposal of modellig this problem, which may probably brig iterestig coclusios. This proposal is quite simple ad it would use the same variables cosidered o the modellig preseted i this paper. E-ISSN: 2224-2678 634 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza The oly differece betwee them is that, while the modellig already preseted uses the umber of gold medals offered for each sport as a iput, the ew modellig would use this variable as the deomiator of the three outputs cosidered. Thus, the outputs would be the ratio of the umber of gold, silver ad broze medals wo to the umber of gold medals offered for each sport. The oly iput cosidered would be the fiacial resources allocated to each DMU. The itetio behid usig this variable is verify if the proportio of wo medals is a better way to iclude the effort i wiig a medal ad also we would have oe less variable. Research is beig doe regardig this modellig. It is very importat to otice that this study oly cosidered oe Brazilia Olympic Cofederatios fuds source: the Agelo/Piva Law. However, there are may others public ad private sources sposorig some Cofederatios studied, which were ot cosidered. Therefore, it is suggested the cosideratio of such sources for future work, i order to obtai more complete results. Eve take ito accout other fiacial assets for importat decisios [26]. Moreover, we idetified a limitatio i this preset study, which is the o-cosideratio of the maiteace costs for each sport. We believe that it is ecessary to take ito accout this cost to propose a fairer reallocatio, sice it represets a variable that, combied with the fuds available for each Cofederatio, affects the results of them. Also, we kow that some sports are more expesive tha others. Cosiderig this variable, we expect that the efficiecies obtaied with the model for each DMU will be more robust. This additio may also solve the problem of sports with high maiteace costs receivig a less amout of fuds with the fiacial resources reallocatio. Fially, it is iterestig to highlight the importace of studies like this for Brazilia sport, due to the curret situatio of the coutry: a coutry i full developmet, host of the ext FIFA World Cup ad the ext Olympic Games, with eormous iteratioal visibility, but also with serious problems ad at the same time, basic, like a poor level of educatio ad high rates of violece, which may fid its solutio with the aid of the sport. There are very few scietific studies usig DEA applied to ivestmets i sports. This is aother oe ad it serves as a icetive for future works. Refereces: [1] GLOBO-ESPORTE, Coselho de Clubes asce e ataca o COB para ter recursos da Lei Agelo/Piva [Olie]. Available: http://globoesporte.globo.com/esportes/noti cias/mais_esportes/0,,mul984796-16317,00- CONSELHO+DE+CLUBES+NASCE+E+ ATACA+O+COB+PARA+TER+RECURS OS+DA+LEI+AGNELOPIVA.html. Accessed o September 27, 2013. [2] GAZETA-DO-POVO, O COB cotra a parede [Olie]. Available: http://www.gazetadopovo.com.br/esportes/c oteudo.phtml?id=855580. Accessed o September 27, 2013. [3] CHARNES, A., COOPER, W. W. & RHODES, E., Measurig the efficiecy of decisiomakig uits, Europea Joural of Operatioal Research, 2, 1978, 429-444. [4] BANKER, R. D., CHARNES, A. & COOPER, W. W., Some models for estimatig techical scale iefficiecies i data evelopmet aalysis, Maagemet Sciece, 30, 1984, 1078-1092. [5] COOPER, W. W., SEIFORD, L. M. & TONE, K., Data evelopmet aalysis: a comprehesive text with models, applicatios, refereces ad DEA-solver software, 2007. [6] BANKER, R. D. & MOREY, R., Efficiecy aalysis for exogeously fixed iputs ad outputs, Operatios Research, 32, 1986, 513-521. [7] CAMANHO, A. S., PORTELA, M. C. & VAZ, C. B., Efficiecy aalysis accoutig for iteral ad exteral o-discretioary factors, Computers ad Operatios Research, 36, 2009, 1591-1601. [8] ALLEN, R., ATHANASSOPOULOS, A., DYSON, R. G. & THANASSOULIS, E., Weights restrictios ad value judgemets i data evelopmet aalysis: evolutio, developmet ad future directios, Aals of Operatios Research, 73, 1997, 13-34. [9] THOMPSON, R. G., LANGEMEIER, L. N., LEE, C. T., LEE, E. & THRALL, R. M., The role of multiplier bouds i efficiecy aalysis with applicatio to Kasas farmig, Joural of Ecoometrics, 46, 1990, 93-108. E-ISSN: 2224-2678 635 Issue 12, Volume 12, December 2013
WSEAS TRANSACTIONS o SYSTEMS Reato Pescarii Valério, Lidia Agulo-Meza [10] THOMPSON, R. G., SINGLETON JUNIOR, F. D., THRALL, R. M. & SMITH, B. A., Comparative evaluatio for locatig a higheergy physics lab i Texas, Iterfaces, 16, 1986, 35-49. [11] KORNBLUTH, J. S. H., Aalysig Policy Effectiveess Usig Coe Restricted Data Evelopmet Aalysis, Joural of the Operatioal Research Society, 42, 1991, 1097-1104. [12] LINS, M. P. E., GOMES, E. G., SOARES DE MELLO, J. C. C. B. & SOARES DE MELLO, A. J. R., Olympic rakig based o a zero sum gais DEA model, Europea Joural of Operatioal Research, 148, 2003, 312-322. [13] FONSECA, A. B. D. M., SOARES DE MELLO, J. C. C. B., GOMES, E. G. & ANGULO-MEZA, L., Uiformizatio of frotiers i o-radial ZSG-DEA models: A applicatio to airport reveues, Pesquisa Operacioal, 30, 2010, 175-193. [14] SANTOS, T. P., ANGULO MEZA, L. & SOARES DE MELLO, J. C. C. B. 2012. Resource allocatio usig olympic results ad dea models. I: CHARLES, V. & KUMAR, M. (eds.) Data evelopmet aalysis ad its applicatios to maagemet. Newcastle upo Tye, UK: Cambridge Scholars Publishig. [15] GOMES, E. G., SOARES DE MELLO, J. C. C. B. & ESTELLITA LINS, M. P., Busca sequecial de alvos itermediários em modelos DEA com soma de outputs costate, Ivestigação Operacioal, 23, 2003, 163-178. [16] SOARES DE MELLO, J. C. C. B., ANGULO- MEZA, L. & LACERDA, F. G., A DEA model with a o discritioary variable for Olympic evaluatio, Pesquisa Operacioal, Pre-prit, 2012. [17] SOARES DE MELLO, J. C. C. B., GOMES, E. G., ANGULO-MEZA, L. & BIONDI NETO, L., Cross Evaluatio usig Weight Restrictios i Uitary Iput DEA Models: Theoretical Aspects ad Applicatio to Olympic Games Rakig, WSEAS Trasactios o Systems, Forthcomig, 2008. [18] WU, J. & LIANG, L., Cross-efficiecy evaluatio approach to Olympic rakig ad bechmarkig: the case of Beijig 2008, Iteratioal Joural of Applied Maagemet Sciece, 2, 2010, 76-92. [19] WU, J., ZHOU, Z. & LIANG, L., Measurig the Performace of Natios at Beijig Summer Olympics Usig Iteger-Valued DEA Model, Joural of Sports Ecoomics, 11, 2010, 549-566. [20] VILLA, G. & LOZANO, S. A., Costat Sum of Outputs DEA model for Olympic Games target settig, 4th Iteratioal Symposium o DEA, 2004. [21] COB, Nota de Impresa [Olie]. Available: http://www.cob.org.br/oticias-cob/otaimpresa-026709. Accessed o September 20, 2013. [22] VALÉRIO, R. P. & ANGULO-MEZA, L., Published. A DEA Evaluatio ad Fiacial Resources Reallocatio for Brazilia Olympic Sports regardig their results i the 2011 Pa America Games, Year. 4th Iteratioal Coferece o Mathematics i Sport, 2013 Leuve, Belgium. [23] SOARES DE MELLO, J. C. C. B., GOMES, E. G., ANGULO-MEZA, L. & LETA, F. R., DEA Advaced Models for Geometric Evaluatio of used Lathes, WSEAS Trasactios o Systems, 7, 2008, 500-520. [24] SOARES DE MELLO, J. C. C. B., GOMES, E. G., ANGULO-MEZA, L., BIONDI NETO, L. & COELHO, P. H. G., A modified DEA model for olympic evaluatio, XII Cogreso Latio-Iberoamericao de Ivestigació de Operacioes y Sistemas - CLAIO 2004, 2004. [25] HAI, H. L., Usig vote-rakig ad crossevaluatio methods to assess the performace of atios at the Olympics WSEAS Trasactios o Systems, 6, 2007, 1196-1205. [26] NERI, F., Quatitative Estimatio of Market Setimet: a discussio of two alteratives, WSEAS Trasactio o Systems, 11, 2012, 691-702. E-ISSN: 2224-2678 636 Issue 12, Volume 12, December 2013