MULTIPLE SELECTIONS OF ALTERNATIVES UNDER CONSTRAINTS: CASE STUDY OF EUROPEAN COUNTRIES IN AREA OF RESEARCH AND DEVELOPMENT

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1 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse MULTIPLE SELECTIONS OF ALTERNATIVES UNDER CONSTRAINTS: CASE STUDY OF EUROPEAN COUNTRIES IN AREA OF RESEARCH AND DEVELOPMENT Adrea Furková INTRODUCTION Accordg to the Lsbo strateg for growth ad jobs the EU member states have expressed ther ambto to crease Europe s overall level of vestmet research ad developmet (R&D) to 3 % of GDP ad to rase the share of R&D fuded b busess. The polc actvtes area of R&D are sgfcat parts of ma atoal reform programs prepared b the member states as a part of Lsbo strateg. There are several reasos for govermets to take actve role stmulato vestmet R&D. R&D are geerall cosdered to be the ma ege of log-ru ecoomc growth. The objectve of R&D actvt s the geerato of ew kowledge whch ma be trasformed to commercal ovatos. Next process of ovato adopto b cosumers ad frms duces the log term postve effect of R&D actvt o ecoomc growth. Publc authortes ma cotrbute to ehace a coutr's R&D sstem b provdg the frastructure ad the sttutoal framework for supportg ovato actvt. Also The Europea Commsso s provdg more ad more resources to R&D actvtes through Commut Framework Programs whle the objectve of makg R&D actvtes more effcet s at the core of the Europea Research Area (ERA) tatve (Cote et al., 9). Ths stud provdes a multcrtera evaluato approach to the ssue of teratoal comparso of R&D dcators. We suggest a methodolog for the performace evaluato of EU member states terms of R&D effcec. Mult-attrbute decso-makg methods are used to evaluate R&D dcators of the coutres. Moreover, based o the obtaed results from the frst emprcal part, the paper also suggest a optmzato model for resources dstrbuto - subsdes for R&D ecouragemet.. MULTI-ATTRIBUTE DECISION-MAKING METHODS Multcrtera decso-makg problems ca be dvded to certa ma groups accordg to the defto of the feasble set of alteratves. The frst s the case whe we have a fte umber of crteros, but the umber of feasble alteratves s fte (the alteratves beg determed b the sstem of the requremets costrats). These problems belog to the feld of multple crtera optmzato. O the other had, the tpe of problem, whe the umber of crteros ad alteratves s fte, ad the alteratves are explctl gve, are called multattrbute decso-makg problems (MDMP). The theor of MDMP s ver well-establshed, ad the possbltes of real applcatos (evaluato of vestmet alteratves, evaluato of the credblt of bak clets, the ratg of compaes, cosumer goods evaluato ad ma others) are ver large. We kow relatvel ma dfferet methods e.g. PROMETHEE, ELECTRE, WSA, TOPSIS (see e.g. Breza, Gertler & Pekár, 6; Fuguera, Greco & Ehrgott, 5; Jabloský & Dlouhý, 4). The mult-attrbute decso-makg problem s usuall defed b a crtero matrx as s show below: X X X Y Y Y k k k k () 73 Tred v podkáí - Busess Treds /5

2 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse where X, X,...,X s the set of alteratves, Y, Y,..,Yk s the set of k crteros, j s the crtero value of the alteratve X, =,,...,, j=,,...,k. I the matrx, each colum belogs to a crtero ad each row descrbes the performace of a alteratve,.e. each elemet of the matrx j s a sgle umercal value represetg the performace of alteratve o crtero j. The essetal part of the multattrbute decso-makg problem s settg the tpe of the crtera (mmzato or maxmzato) ad assgg weghts to the crtera. The weght w reflects the relatve mportace of the crtera ad s assumed to be postve. The weghts of the crtera are usuall determed o a subjectve bass. The represet the opo of a sgle decsomaker or sthesze the opos of a group of experts usg a group decso techque as well. The ma goal of the mult-attrbute decso-makg techques ca be complete or partal rakg of alteratves. Mult-attrbute decso-makg methods are based ether o the Mult-attrbute Utlt Theor or Outrakg Methods (Fuguera, Greco & Ehrgott, 5; Jabloský & Dlouhý, 4. I ths paper, we focus o outrakg methods. These methods are based ether o par-wse outrakg assessmets (e.g. Promethee methods, Electre methods) or the dstaces to the deal soluto ad egatve deal soluto (e.g. Topss). I ths paper Topss method s used our aalss of R&D of Europea coutres ad ext obtaed results are bases for optmzato uder costrats. As our ma goal was to fd a optmal selecto of several alteratves gve a set of costrats we formulate optmzato model spred b Promethee V method. The Promethee V method exteds the PROMETHEE II method (for more detal see e.g. Fuguera, Greco & Ehrgott, 5) to ths selecto problem,.e. optmzato uder costrats. The objectve s to maxmze the total et outrakg flow value (for more detal see e.g. Fuguera, Greco & Ehrgott, 5) of the selected alteratves, at the same tme beg feasble to the costrats. Bar varables are troduced to represet whether a alteratve s selected or ot, ad teger programmg techques are appled to solve the optmzato problem (Fuguera, Greco & Ehrgott, 5). The Topss method ad Promethee V method wll be brefl outled the followg secto. The PROMETHEE V method procedure ca be summarzed as follows: Let X,,,... be the set of possble alteratves ad let us assocate the followg varables to them: f X s selected, x () f ot. The ext two followg steps are ecessar: STEP : The multcrtera problem s frst cosdered wthout costrats. The PROMETHEE II rakg s obtaed ad computed et flows X are used the ext step of the procedure. STEP : The followg model of lear programmg s the cosdered order to take to accout the addtoal costrats: max X x λ p, x x ~β p p,,...,p (3),,,..., where ~ holds for =, or. The coeffcets of the objectve fucto of the model (3) are the et outrakg flows. The hgher the et flow s the better for the alteratve. The costrats of ths model ca clude such costrats as, e.g. budget, retur, marketg, etc., ad the ca be related ether to all alteratves or to some clusters [4]. After havg solved the formulated bar lear programmg model, we obta a alteratve or a subset of alteratves satsfg the costrats ad provdg as much et flow as possble. Topss (Techque for Order Preferece b Smlart to Ideal Soluto) method s a popular approach of the mult-attrbute decso makg 74 Tred v podkáí - Busess Treds /5

3 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse methods ad has bee wdel used the lterature. Topss smultaeousl cosders the dstaces to the deal soluto ad egatve deal soluto regardg each alteratve ad selects the most relatve closeess to the deal soluto as the best alteratve. That s, the best alteratve s the earest oe to the deal soluto ad the farthest oe from the egatve deal soluto. The procedure of Topss ca be summarzed as follows:. Former crtera values j are trasformed to ormalzed value rj : j r j,,...,,,,..., k. / j j (4). Calculato of the weghted ormalzed decso matrx W=(wj) as wj=vjrj for,,...,, j,,..., k. 3. Determato of the postve deal (H, H,...,Hk) ad egatve deal soluto (D, D,...,Dk), where H max D m j w j, j,,..., k. j w j 4. Calculato of the dstace of each alteratve from the postve deal (d + ) ad egatve deal (d - ) soluto measures, usg the -dmesoal Eucldea dstace: / k j j,,...,, j d w H / (5) k d wj D j,,...,. (6) j 5. Calculato of the relatve closeess c to the deal soluto: d c,,...,. (7) d d 6. Rakg the preferece order: The closer the c s to mples the hgher prort of the alteratve.. EMPIRICAL RESULTS I the frst part of our aalss Topss method s appled order to evaluate R&D actvtes of EU member states (we excluded Cprus due to the mssg data ad cluded Norwa) through opted dcators. Our data set of 7 Europea coutres ad Norwa observed s based o statstcs of Eurostat (4). As dcators whch would sgfcatl fluece actvtes of R&D were chose: Patet applcatos (PAT) defed as patet applcatos to the Europea Patet Offce (per mllo of habtats). Ths dcator was chose due to the fact that patet applcatos are cosdered to be oe of the outputs of successful R&D. Total tramural R&D expedture (EXP) (percetage of GDP). There s ambto to crease Europe s overall level of expedture to R&D ad also to rase the share of R&D fuded b busess. Therefore we decded to volve to our aalss dcators EXP ad also EXP (defed below). Huma resources scece ad techolog (HRST) (percetage of actve populato). Ths dcator ca be perceved as huma captal that s basc assumpto of successful R&D. Emplomet kowledge-tesve actvtes (KIA) (percetage of total emplomet). Nowadas kowledgetesve dustres have sgfcat share process of ovatos. Busess eterprse R&D expedture (EXP) (percetage of GDP). 75 Tred v podkáí - Busess Treds /5

4 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse Tab. : Crtero matrx, Topss results ad optmal soluto of optmzato model MAX MAX MAX MAX MAX PAT EXP HRST KIA EXP Belgum 3,95,4 48,5 4,,5,67,743 Bulgara,53,64 3, 6,9,39,68,58 Czech Republc 7,9,88 35,5 3,9,,36,47 Demark,33,98 46,6 39,5,96,345,9 Germa 76,95,98 43,5 37,3,,97,465 Estoa 3,3,8 46,4 3,6,5,935,5377 Irelad 65,5,7 47,6 43,,,866,5499 Greece 3,53,69 33, 35,,4,635,855 Spa 33,,3 39,3 3,5,69,768,33 Frace 5,77,9 46,3 39,4,48,6549,743 Croata 6,77,75 3, 9,7,34,5,48 Ital 69,57,7 3,9 3,6,69,4,34 Latva 6,6,66 38,9 3,6,5,73,945 Lthuaa 6,9,9 43, 3,8,4,345,33 Luxembourg 33,66,46 56,7 56,6,7594,758 Hugar 9,8,3 34,4 34,,85,875,36 Malta 3,59,84 34,7 4,,5,966,83 Netherlads 63,49,6 47, 36,4,,6369,75 Austra 4,7,84 39,4 35,,95,499,985 Polad,9,9 36, 8,9,33,7,777 Portugal 7,,5 7, 3,,7,46,8 d d c (alteratv e rak) Optmal soluto,546 (6),9 (7),8389 (5),7583 (4),7977 (3),365 (4),3883 (3),84 (3),533 (8),57 (8),7 (6),56 (6),37 (),5835 (),487 (),88 (7),933 (),5336 (7),756 (5),687 (4),9698 (9) 76 Tred v podkáí - Busess Treds /5

5 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse Romaa,78,49 3,8,,9,3458, Slovea 4,6,8 4,6 34,5,6,83,797 Slovaka 9,58,8 3,4 9,8,34,38,59 Flad 69,6 3,55 48,7 37,3,44,9,566 Swede 88,67 3,4 48, 43,3,3,663,78 Uted Kgdom 79,59,7 49, 43,,9,848,5533 Norwa,6,65 49,8 39,,87,897,559 Weghts Ideal Basal,,87 3,5 4,,695 4,96,,5 8,8 6,,59 5,8 7,,738,45 4,89 (8),4958 (9),989 (5),84989 (),8849 (),39484( ),39989 () Source: EUROSTAT, 4 ad ow calculatos The umercal values of dcators are lsted tab.. All these dcators we set as maxmzato crteros ad we assumed ut weghts. The goal of the frst emprcal part was to rak coutres va topss,.e. to detf the best ad worst performers of R&D amog of EU member states. The results are provded tab., the scores of coutres were calculated accordg to equato (7) ad the raks of the coutres are lsted the brackets. As the best coutres accordg to our results were assged Swede, Flad, Germa, Demark, etc. ad o the other had as the worst performers are assged Romaa, Bulgara, Croata, Slovaka, etc. There s apparet lag of post-commust coutres ad the west coutres reached leadg postos. Therefore we also decded to formulate a optmzato model for resources dstrbuto - subsdes for R&D ecouragemet. Let us suppose stuato that The Europea Commsso (EC) s provdg through Commut Framework Programs subsdes to R&D actvtes order to ecourage R&D actvtes especall post-commust coutres. The goal s to provde e.g. 8 grats total but there are followg addtoal requremets: It s requred that at least four postcommust coutres wll be grated. The total budget s 8 mllo euro ad caot be exceeded. Facal resources must be used ol for R&D sttute establshmet. Idvdual coutres estmated facal requremets for the R&D sttute are evdet from the thrd equato of the model ( thousad euros). As suffcet sklled labour force s ecessar codto to effcet performace of R&D, t s set that overall value of HRST dcator grated coutres must be at least 3. To make a decso cocerg proper coutres selecto we emplo optmzato model (for more detals see e.g. Breza, Ččková & Reff, 4) spred b Promethee V whch eables us to take to accout the results of prevous emprcal part (preferece rakg of coutres accordg to Tops) ad, at the same tme, to take to accout defed costrats. The calculated coeffcets c (from tab. ) are used as puts the objectve 77 Tred v podkáí - Busess Treds /5

6 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse fucto of the bar lear programmg model formulated (3). Ths s cotrast to Promethee V method, where the calculated et outrakg flows are used the objectve fucto. Aother dfferece to Promethee V s that our objectve fucto s mmalzed because of specfed am to support backward coutres actvtes of R&D. Four costrats of the model are formulated based o the EC requremets ad the bar varables represet coutres. The model of bar lear programmg ca be formulated as follows: m f( x ),546x,9x,8389 x,7583 x +,7977 x +,365 x,3883x ,84x,533x,57x,7x,56x,37x,5835x ,487x,88x,933x,5336x,756x,687x,9698x ,89x,4958x,989x,84989x,8849x,39484x,39989x x x x x + x + x x x x x x x x x x x x x x x x + x x x x x x x = 8 x x x x x x x x + x x x x 5x 56 x 8 x + 9 x + 63x 7x 6x 7x 9x 66x x 59x 6x 95x 53x 66x 78x 8x 63x x+ 58x 6x3 58x4 8x5 85x6 9x7 83 x8 8 48,5x 3,x 35, 5 x 46,6 x + 43,5 x + 46,4x 47, 6x 33,x 39, 3x 46, 3x 3, x ,9x 38,9x 43,x 56,7x 34,4x 34,7x 47,x 39,4x 36 x +7 x ,8x 4,6x 3,4 x 48,7x 48,x 49, x 49,8 x Optmal soluto of the model s lsted the last colum of the tab. ad f the EC takes to accout the results of the model, t s approprate to support Bulgara, Greece, Latva, Lthuaa, Luxembourg, Polad, Slovaka ad Norwa. Surprsgl Luxembourg ad Norwa were chose however, wth regard to fulflmet of the thrd equato of the model ths ma be caused b ther hgh values of HRST dcator. CONCLUSION The purpose of ths paper was to explot a multcrtera evaluato approach to the ssue of teratoal comparso of R&D dcators. The applcato of the Topss method has provded us complete rakg of the coutres ad we were able to detf the best ad the worst performers the group. We foud out apparet lag of post-commust coutres. We also suggested ad llustrated a optmzato model for resources dstrbuto - subsdes for R&D ecouragemet whch was based o results of Topss method. We preseted multattrbute decso-makg method ad model for multple selectos of alteratves uder x ;,,,8 costrats as a cotrbuto to the dscusso about quattatve measuremet evaluato of R&D dcators. REFERENCES 78 Tred v podkáí - Busess Treds /5 3 Cote, A., et al. (9). A aalss of the effcec of publc spedg ad atoal polces the area of R&D. Europea Commsso. Avalable from: < os/publcato5847_e.pdf>. Breza, I., Ččková, Z. & Reff, M. (4). Optmzato of producto processes. I: Quattatve methods ecoomcs (multple crtera decso makg XII), (pp. 3-8). Vrt, Slovak Republk. Breza, I., Gertler, P., & Pekár, J. (6). Vackrterále vhodoce krají CEFTA metodam tred PROMETHEE prostredíctvom omálích kovergečých krtérí pr vstupe do Európskej úe. Dalóg o ekoomke a radeí, 8(4), -59. EUROSTAT (4). Avalable from: <

7 Tred v podkáí vědecký časops Fakult ekoomcké ZČU v Plz Tred v podkáí, 5() Publsher: UWB Plse ortal/scece_techolog_ovato/data/ma _tables>. Fuguera, J., Greco, S., & Ehrgott, M. (5). Multple Crtera Decso Aalss: State of the Art Surves. Bosto: Sprger. Jabloský, J. (). Multcrtera evaluato of alteratves spreadsheets. Avalable from: < Jabloský, J., & Dlouhý, M. (4). Model hodoceí efektvost produkčích jedotek. Praha: Professoal Publshg. Reff, M., Furková, A., & Kta, P. (). Retal attractveess aalss va multcrtera decso-makg methods. I: Strategc maagemet ad decso support sstems strategc maagemet: strategc maagemet ad overcomg the ecoomc ad facal crss, (pp. -7). Subotca: Palc. Author s address: Ig. Adrea Furková, PhD., Uverst of Ecoomcs Bratslava, Facult of Ecoomc Iformatcs, Departmet of Operatos Research ad Ecoometrcs, E-mal: furkova@euba.sk MULTIPLE SELECTIONS OF ALTERNATIVES UNDER CONSTRAINTS: CASE STUDY OF EUROPEAN COUNTRIES IN AREA OF RESEARCH AND DEVELOPMENT Adrea Furková Abstract Ths paper s gve over to a multcrtera evaluato approach to the ssue of teratoal comparso of research ad developmet dcators. The polc actvtes R&D (Research & Developmet) area are sgfcat parts of ma atoal programs of ma EU member states. There are several reasos for govermets to take actve role stmulato vestmet R&D. R&D are geerall cosdered to be the ma ege of log-ru ecoomc growth. Also The Europea Commsso pas more atteto to R&D actvtes ad provdes more ad more resources to these actvtes through Commut Framework Programs. We decded to explot mult-attrbute decso-makg to evaluate R&D dcators of Europea coutres. As mult-attrbute decso-makg method Topss method was appled. Tops method has provded us complete rakg of the coutres takg to accout dcators such as patet applcatos, total tramural R&D expedture, huma resources scece ad techolog, emplomet kowledge-tesve actvtes ad busess eterprse R&D expedture. Havg these results a had; we proceed to makg multple selectos of coutres uder costrats. Our ma goal was to suggest a optmzato model for resources dstrbuto - subsdes for R&D ecouragemet,.e. to fd a optmal selecto of several alteratves gve a set of costrats. To make a decso cocerg proper coutres selecto we emploed optmzato model spred b Promethee V, whch eables us to take to accout the results of prevous emprcal part ad, at the same tme, to take to accout defed costrats. Formulated bar lear programmg model could be useful support decso makg tool the process of resources dstrbuto - subsdes for R&D ecouragemet. Kewords: Mult-attrbute decso makg methods; Topss; Research ad Developmet; Promethee V JEL Classfcato: C6, M, M3 Ackowledgemets Ths work was supported b the Grat Agec of Slovak Republc - VEGA, grat o. /85/4 "Regoal modellg of the ecoomc growth of EU coutres wth cocetrato o spatal ecoometrc methods". 79 Tred v podkáí - Busess Treds /5