MULTI-CRITERIA OPTIMIZATION SOFTWARE LEVI-4.0 A TOOL TO SUPPORT DESIGN AND MANAGEMENT IN CONSTRUCTION

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1 MULTI-CRITERIA OPTIMIZATION OFTWARE LEVI-.0 A TOOL TO UPPORT DEIGN AND MANAGEMENT IN CONTRUCTION Edmudas Kazmeras Zavadskas Vlus Gedmas Techcal Uversty, auleteko av., Vlus, LT-0, Lthuaa, Emal: edmudas.zavadskas@adm.vtu.lt Fredel Peldschus Lepzg Uversty of Appled ceces, Karl-Lebkecht treet, 0 Lepzg, Germay, Emal: peldschu@fbb.htwk-lepzg.de Zeoas Tursks Vlus Gedmas Techcal Uversty, auleteko av., Vlus, LT-0, Lthuaa, Emal: zeoas.tursks@st.vgtu.lt ABTRACT Mult-crtera decso makg s used may areas of huma actvtes. Crtera ca to be qualtatve ad quattatve. They usually have dfferet uts of measuremet ad dfferet optmzato drecto. The ormalzato ams at obtag comparable scales of crtera values. I the ew program LEVI.0 verso the followg ormalzato methods are possble: vector, lear scale, o-lear ad ew logarthmc techques. Ths software cosders the ma postos of two-sded game problems. The strategc prcples are used as follows: Wald's rule, avage crtero, Hurwcz's rule, Laplace's rule, Bayes's rule, Hodges-Lehma rule. Ths program s demostrated wth a real case study volvg evaluato crtera of exteral walls of the dvdual resdetal buldgs, ow use. KEYWORD oftware, of two-sded problem, game theory, ormalzato, logarthmc, mult-crtera, a wall. INTRODUCTION A revew of stadard decsos made egeerg, maagemet ad ecoomy, has show that the evaluato of all possble actos s ot always suffcet. Each acto may lead to several, sometmes coflctg results. Therefore, mult-crtera decso makg becomes extremely mportat. Ay problem to be solved s represeted by a matrx, cotag the alteratves (rows) ad the crtera (colums). A alteratve mult-crtera evaluato s usually descrbed by quattatve ad qualtatve crtera. Usually, the crtera have dfferet dmesos. I order to avod the dffcultes caused by dfferet dmesos of the crtera, the rato to the optmal value s used. There are varous theores

2 descrbg the rato to the optmal value. However, the values are mapped ether o the terval [0; ] or the terval [0; ] by applyg the ormalzato of a decso-makg matrx. Vlus Gedmas Techcal Uversty (VGTU) ad Lepzg Uversty of Appled ceces (HTKW) have bee vestgatg the applcato of games theory prcples to cvl egeerg techology ad maagemet problems for more tha 5 years [], [], [], [], [5], [6], []. The program LEVI.0 was a result of the co-operato betwee VGTU ad HTKW. All calculatos are made wth LEVI.0 [], [], [8], [9], [0], []. The program LEVI.0 was modfed for evaluatg varous processes ecoomcs, egeerg ad maagemet. I the ew program verso LEVI.0 (Fg. ad Table ) a ew logarthmc ormalzato method [8] s mplemeted. Ths ew software allows us to fd a soluto uder the codtos of rsk ad ucertaty ad to compare the results by applyg dfferet methods.. TRUCTURE AND METHODOLOGY OF THE PROGRAM LEVI.0 I the program LEVI.0, the game theory of the dscrete optmzato problem soluto s used. Usg the Games Theory [], the two-sded questo ams at fdg the equlbrum as a result of the ratoal behavour of two partes havg the opposte terests or searchg for the equlbrum a game agast ature. Wald s rule (WA): Ths method s used to search for the best of the worst solutos []. The decso-maker acts accordg to the worst stuato occurrg a pessmstc atttude: { / maxmb } () avage crtero (A): The am s the mmzato of the loss of approprateess, whch s the dfferece betwee the greatest ad the acheved beeft []: / m maxc c ( max a ) rs ars r, () where r, m ad s,. A dsadvatage of the method les the presece of o-optmal strateges affectg the soluto. Fgure. Block-dagram of choosg the best alteratve LEVI.0 program

3 Table. Normalzato methods program LEVI.0 Normalzato method (NM) Vector (VE) 5 Wetedorf s lear [9] (WL) Jüttler s -Körth s [0], [] Peldschus et al. [] o-lear (NL) New Logarthmc (LN) [8] b Preferable max a a m a a m a b max a m a max a a b max a a b max a b l b Preferable Notes m a a The rato of the values remas costat for ths m a type of ormalzato the terval [0; ]. max a a b max a m a m a a b m a m a b a l ( ) ( a) l a a l a b The calculated values are depedet o the sze of the terval [ max a ; ma ] The applcato of ths type of ormalzato s lmted to the terval [0; ]. The values are dmshed more tha whe usg other methods The sum of ormalzed crtero values s always equal to. Hurwcz s rule (HU): A optmal strategy s based o the best ad the worst results [5]. These values, calculated from the row s mmum ad row s maxmum, are tegrated to a weghted average usg optmsm parameters: / maxh h λ maxb + 0 λ ( λ). () mb The value λ gves the most pessmstc soluto (Wald s rule). For the value λ 0 oly the maxmum values are cosdered, the greatest rsk. Laplace s rule (LA): The soluto s calculated uder the codto that all probabltes for the strateges of the oppoet are equal [6]: / max / b. () Bayes s rule (BA): Gve the probabltes for the strateges of the oppoet the maxmum for the expected value ca be used []: / max q b q. (5) Hodges-Lehma rule (HL): Accordg to ths rule, the cofdece the kowledge of the probabltes of the strateges of the oppoet ca be expressed by the parameterλ [8]: / max λ q b+ 0 λ ( λ), (6) mb where λ 0 (o cofdece) gves the soluto accordg to Wald s rule, whle λ (great cofdece) gves the soluto accordg to Bayes s rule.. A CAE TUDY OF EXTERNAL WALL ALTERNATIVE EVALUATION UING VARIOU OLUTION METHOD AND NORMALIZATION TECHNIQUE The umber of resdetal houses Lthuaa s creasg every year. Itroducto of varous thermosulato systems the cotemporary cvl egeerg practce s caused by the maor expaso

4 of eergy resource prces at the world market. For a o-sulated buldg, whch could be stuated dfferet clmate codtos, these partcular heatlosses ca vary betwee 0-0% (through floors), 5-0% (through outer walls), 5-0% (through attc slabs ad roof plates) ad 0-0% (through wdows) of the total heat-loss. Therefore, the thorough ad professoal selecto of a optmal buldg thermosulato system represets oe of the most mportat techcal ad ecoomcal goals for both the Desger ad the Ivestor. The beeft obtaed from effectvely heatg up the exteral walls could be defed by dces as show Fgure... Mult-layered exteral walls There s usually ot eough atteto pad to the fact that mult-layered facade structures are made as composte sectos of heterogeeous materals wth dfferet physcal-mechacal propertes. For multlayer walls, three basc materal cofguratos were cosdered: sulato ether sde or outsde the massve layer, ad sulato located betwee two massve layers. The results of extesve parametrc aalyss have show explctly that walls wth the sulato outsde (Fgure ) always performed better tha those wth the sulato sde... Model of problem The am of ths vestgato s to create a techque for the choce ad selecto of dfferet ad effectve versos of the costructo of exteral walls. Dfferet varats of exteral wall costructo are beg formed by usg varous materals wth thermal sulato as well as dfferet kds of decorato masory ad th daub layer. A system of dcators for wall costructo effectveess evaluato has bee establshed. These dcators defe postve ad egatve characterstcs of a obect uder vestgato. Idcator values were calculated accordg to vald stadardzg documets. The selecto of a wall costructo determes techcal, explotato, etc dcator of a buldg. Oe of the most mportat factors of a wall partto s ts aesthetc vew; however ths factor s ot a obectve oe. Log-Term Buldg Value Esurg Decrease Ar Crculato lower Premse Cool Dow Avodace of Water Vapour mprovemet of Premse Mcroclmate ICodesato Wall Protecto from Clmatc Ifluece Eergy avg Fgure. Advatage of thermal sulato of exteral walls Bearg block; Expaded polystyree; Rock wool; Fshg brck; 5 5 Outer plaster; 6 Isolato of the wd; Ier plaster; 8 Ar space (- cm) Fgure. Ma alteratves of mult-layered exteral walls The prce of parttos s calculated by cludg all the expeses of materals that a partto s composed of. The prce of a three-layer masory wall embraces the followg: slcate bearg walls, thermal ad wd sulato, decorato masory, ad grout. The prce of walls wth th daub layer cossts of: slcate bearg walls, thermal sulato ad the prce of th daub layer system. I order to establsh the mportace

5 dcators a survey has bee carred out ad 9 experts have bee questoed. These experts, basg ther aswers o ther kowledge, experece ad tuto, had to rate dcators of effectveess startg wth the most mportat. The ratg was doe o a scale from to where meat very mportat ad ot mportat at all. The mportace of dcators (e.g. ) was establshed accordg to the ratg methods [6] of these experts ad also demostrated the prortes of the user (ower). The data of the exteral walls alteratves uder vestgato are gve Table. Table. The raked alteratves Var. Descrpto of wall Fshg materal Thermal Rak v Brck Rock wool v Brck Polystyree v Th exteral Rock wool v Th exteral Polystyree There s a wde varety of exteral wall costructos whch are defed by may dfferet dcators of effectveess (A closer look at the most commoly used outer-wall buldg systems s gve fgure ). Accordg to opo of buldg experts, these alteratves of walls ca be characterzed by followg factors as show table. Effcecy of the varat was evaluated by the followg effectveess dces: estmated cost of m ( ), weght of m (kg), thermal sulato (m K/W) ad durablty of walls (cycles). The task of the selecto of dfferet versos of the effectve exteral walls costructo s solved by applyg LEVI.0 software. A specal feature of the model s the determato of attrbutes weghts []. To determe the weghts of the crtera, the expert udgmet method proposed by Kedall [] was used []. Zavadskas [6] dscussed the applcato of ths method the costructo feld. I the preset vestgato, the vector, lear, olear ad ew logarthmc methods of tal decso-makg matrx ormalzato were used. A umber of dfferet problem soluto methods, such as Wald s rule, avage crtero, also Laplace s rule, ad Bayes s rule were appled. Tables ad 5 provde the soluto results ad comparatve aalyss. Whe the crtera weghts are take to accout, the prorty order of the alteratves s preseted as v f v f v f v (mplyg that the "secod" alteratve s better tha the "frst" oe, the "frst" alteratve s better tha the "thrd" oe, the "thrd" alteratve s better tha the "secod" oe ad the "fourth" oe). A smlar set " v f v v f v s obtaed whe the crtera weghts are ot take to accout the process of alteratve assessmet. Fally alteratves raks v f v f v f v ad are preseted table 6. Uder aalyss of the problem decso results t has bee establshed, that wall wth a brck exteral layer are the most effectve. Furthermore, t s possble to ascerta, that applcato of a 5 mm layer of rock wool more effectvely tha applcato of a 00 mm layer of Polystyree.. CONCLUION It s hardly possble to evaluate the effect of varous methods of ormalzato of a decso-makg matrx o the umercal results obtaed. These problems ca be solved by applyg the program LEVI.0. ome modules of the program LEVI.0 ca be used for creatg decso-makg systems. Logarthmc ormalzato of a decso makg matrx yelds more stable results solvg multcrtera decso problems. The logarthmc ormalzato method used solvg the problems segregates more ormalzed values tha the other oes. A comparso of results obtaed by dfferet soluto methods s eeded because t s ot always possble to apply the games theory equlbrum to ecoomcs, egeerg ad maagemet. It ca be stated that:. The multple attrbute assessmet model of mult-layer exteral walls was developed.. Ths model ad soluto results has as practcal as scetfc terest. It allows to vestor to make decso evaluatg multple crtera. 5

6 . Walls wth a brck exteral layer are the most effectve.. Ths model of the exteral walls effcecy aalyss of ca be appled to the assessmet others dscrete alteratves problem costructo. REFERENCE [] Peldschus, F., Vagauskas, E. ad Zavadskas, E.K. (98). Techologsche Etscheduge be der Berückschtgug mehrerer Zehle. Bauplaug Bautechk, Vol., No. -5. [] Peldschus, F. (986). Zur Awedug der Theore der pele für Aufgabe der Bautechologe. Dss. B. Techologe. Dss. B. Techsche Hochschule Lepzg. [] Peldschus, F., Messg, D., Zavadskas, E.K., Ustovchus, L. ad Tursks, Z. (00). LEVI.0 multple crtera evaluato program uder ucertaty. Techologcal ad Ecoomc Developmet of Ecoomy, Vol. 8, No.. [] Peldschus, F. (00). The effectveess of assessmet multple crtera decsos. Iteratoal Joural of Maagemet ad Decso Makg, Vol. 8, Nos [5] Peldschus, F., ad Zavadskas, E.K. (99). Matrx games buldg techology ad maagemet. Vlus: Techka. (I Lthuaa) [6] Zavadskas, E.K. (98). Multple crtera evaluato of techologcal decsos of costructo. Dssertato of Dr. c. Moscow Cvl Egeerg Isttute, Moscow. (I Russa). [] Tursks, Z., Zavadskas, E. K., Zagorskas, J. (006). ustaable cty compactess evaluato of the bass of GI ad Bayes rule. Iteratoal Joural of trategc Property Maagemet, Vol. 0, No [8] Zavadskas, E.K., ad Tursks, Z. (008). A ew ormalzato method games theory, Iformatca, Vol. 9, Artcle press. [9] Zavadskas, E.K., Ustovchus, L., Tursks, Z., Peldschus, F. ad Messg, D. (00). LEVI.0 Multple crtera evaluato program for costructo solutos. Joural of Cvl Egeerg ad Maagemet, Vol. 8, No [0] Zavadskas, E.K., Peldschus, F., Ustovchus, L. (00). Developmet of software for multple crtera evaluato. Iformatca, Vol., No., 59-. [] Zavadskas, E.K., F. Peldschus, Ustovchus, L. ad Tursks, Z. (00). Game theory buldg techology ad maagemet. Vlus: Techka. (I Lthuaa) [] Neuma vo, J. ad Morgester, O. (9). Theory of Games ad Ecoomc Behavor. Prceto Uversty Press. [] Wald, A. (95). tatstcal decsos fuctos whch mmse the maxmum rsk. Aals of Mathematcs, Vol [] avage, L. J. (95). The Theory of tatstcal Decso. Joural of the Amerca tatstcal Assocato, Vol [5] Hurwcz, L. (95). Optmalty Crtera for Decso Makg uder Igorace. Cowles Commsso Paper, tatstcs, Vol [6] Beroull, D. (8). pecme theorae ovas de mesure sorts. Cometar Academae cetarum Iperals Petropoltaae, Vol (Traslated by ommer L. (95) Exposto of a ew theory o the measuremet of rsk, Ecoometrca, Vol. -6. [] Arrow, K.J., Blackwell, D. ad Grshck, M. A. (99). Bayes ad Mmax olutos of equetal Decso Problems. Ecoometrca, Vol. -. [8] Hodges, J.L., ad. Lehma, E.L (95). The Use of Prevous Experece Reachg tatstcal Decso. Aals of Mathematcs tudes, Vol [9] Wetedorf, D. (96). Betrag zur Optmerug der räumlche truktur ees Gebäudes. Dssertato A, Hochschule für Archtektur ud Bauwese. Wemar. [0] Jüttler, H. (966). Utersuchuge zur Frage der Operatos aforschug ud hrer Awedugsmöglchkete auf ökoomsche Problemstelluge uter besoderer Berückschtgug der peltheore, Dssertato A a der Wrtschaftswsseschaftlche Fakultät der Humboldt Uverstät, Berl. [] Körth, H. (969). Zur Berückschtgug mehrer Zelfuktoe be der Optmerug vo Produktosplae. Mathematk ud Wrtschaft, Vol [] Hwag, C.L., ad Yoo, K.P (98). Multple Attrbute Decso Makg Methods ad Applcatos. New York: prger-verlag. [] Kedall, M.G. (90). Rak correlato methods (th ed.), Lodo, Grff. [] Fsher, R.A. ad Yates, F. (96). tatstcal tables for bologcal, agrcultural ad medcal research (6th ed), Olver ad Boyd, Lodo. 6