World Appled Sceces Joural (Mathematcal Applcatos Egeerg): 38-4, 03 ISS 88-495 IDOSI Publcatos, 03 DOI: 0.589/dos.wasj.03..mae.99940 A Itegrated Modelg Based o Data Evelopmet Aalyss ad Support Vector Maches: A Case Modelg of Tehra Socal Securty Isurace Orgazato 3 4 V. Rezae, T. Ahmad, C. Daeshfard, M. Khamohammad ad S. ejata Departmet of Mathematcs, Faculty of Scece, Ibu Sa Isttute, aotechology Research Allace, Uverst Tekolog Malaysa, 830 Skuda, Johor, Malaysa Departmet of Scece, Scece ad Research Uversty, Tehra Brach, Islamc Azad Uversty, Ira 3 Departmet of Mathematcs, Faculty of scece, Islamc Azad Uversty, Islamshahr Brach, Ira 4 Departmet of Electrcal Egeerg, Yasooj Brach, Islamc Azad Uversty, Ira Abstract: Almost all sttutos ad orgazatos use Itegrated Maagemet duo to ts effcecy. Irrespectve to order or sector, they are terested to tegrate ther maagemet systems to oe ufed system wth a comprehesve set of documetato, poltczes, methods ad processes. I order to create a tegrated ad ufed commad system, modelg of the overall system s beefcal. After system modelg, orgazato ca hadle ts tegrated actvtes order to acheve ts ufed goals. I ths paper, we troduced a ew method for modellg of a system accordg to Data Evelopmet Aalyss (DEA) ad Support Vector Maches. We also offer a example of ths method. Key words: Data Evelopmet Aalyss Itegrated Maagemet Support Vector Maches ITRODUCTIO dsadvatages, for example, fdg the umber of hdde uts s stll a challegg problem eural etworks. A tegrated maagemet system s a process that Support vector mache (SVM), whch s a eural etwork, comprses sub systems of a orgazato, whch eable has sgfcat capabltes [0]. SVM solutos are the subsystems to work as a ufed ut wth a sgle characterzed by covex optmzato problems. objectve []. Itegrated system exhbts comprehesve Furthermore, the trcaces of the model, for example, the pcture of all parts of the orgazato, the effects of each hdde uts umber, meets by optmzato the covex part o other ad ther cludg rsks. There s small problem. Curretly, there s a lot of terest ths ew redudacy ad t wll be easy to oret ew subsystems mache learg. the future. I order to create a tegrated ad ufed The remder of ths paper s as follows: secto maagemet system, modellg of the system s extremely, we have a overvew o DEA. I secto 3, we have useful. a overvew o SVM ad ther potetal modellg. DEA has become a effectve method for evaluatg We gve a example of the modellg secto 4, DMUs due to the pror works of Cooper, Chares ad followed by the cocluso secto 5. Rhodes [, 3]. DEA has had a wde applcato busess [4], data aalyss of storage operatos [5], flexble Evaluatg of the DMUs Effcecy Through Adjustg maufacturg system [6], bak effcecy evaluato [7], Measure: DEA s a oparametrc method for solvg faclty layout desg problem [8] ad evaluatg evaluatg the performace of DMUs wth the same put the performace of orgazatoal eterprse ad producto terms. The DEA evaluatg methods are formato techology [9]. dvded to radal ad oradal methods. The radal eural etwork has bee a powerful modellg tool model cludes CCR ad BCC models. The oradal varous felds ad applcatos. Despte of these model cludes the addtve model, the multplcato advaces, eural etwork stll has a umber of model ad the rage-adjusted measure. I order to Correspodg Author: S. ejata, Departmet of Electrcal Egeerg, Yasooj Brach, Islamc Azad Uversty, Ira. 38
World Appl. Sc. J., (Mathematcal Applcatos Egeerg): 38-4, 03 evaluate the techcal effcecy, cosdered four codtos []. measure (RM) for evaluatg the effcecy s dffcult because of ts objectve fucto whch s a o-lear programmg problem []. Suppose that we have DMUs wth the m put ad output matrx form of X = (x j) R ad s Y = (y rj) R, wth postve put ad output data,.e., X > 0 ad Y > 0. For obtag the effectveess of DMUs by adjustg the measure we have: m Θ = j= j= m s s r= ( ) st. x x,,..., m j j j o ( ) y y, r =,..., s ( j ) ( m) ( r s) 0, =,..., 0, =,..., r m j rj r ro, =,..., r By solvg (), DMUs are dvded to Effcet ad Ieffcet categores. All DMUs wth Russel equals to oe are effectve ad all DMUs wth Russel less tha or equals to oe are effcet. For effcet DMUs, the hgher Russel the hgher rak. Accordg to (), the adjustg of the Measure s a olear model whch the effcecy s a relatve. I ths artcle, we cosder 90 braches of Socal Securty Isurace Orgazato Tehra provce. Each brach uses three puts order to produce four outputs. We have llustrated the puts ad outputs of the system Table ad the collected data of 30 braches Table. We have also llustrated the calculated effcecy ( Russel) of each brach s preseted Table 3. Support Vector Maches: Support vector maches are a ew geerato of the learg system, whch s based o recet advaces statstcal learg theory. Least square (LS) verso of support vector mache has llustrated for fucto estmato [0]. SVM s a effcet learg system, based o optmzato lmt theory, that uses the ductve prcple of mmzato structural error, whch leads to a overall optmal soluto. The SVM does ot deped o the dmesos of the problem. () Table : Labels of puts ad outputs Iput I The umber of persoel I The total umber of computers I3 The area of the brach Output O The total umber of sured perso O The umber of surace polces O3 The total umber of old age pesoers O The receved total sum (Icome) 4 Table : The Iputs ad Outputs for 30 braches of Isurace Orgazato Brach I I I3 O O O3 O4 96 86 4000 55830 30 307 45 75 88 565 36740 0.00 8385 75 3 77 85 343 38004 6588 3 4 9 93 500 35469 0 080 8 5 89 83 680 597 9 9493 0 6 0 97 3750 7054 7 7536 8 7 96 90 333 3585 47 48 54 8 85 9 500 4900 634 54 9 06 84 600 85399 43 006 79 0 07 95 75 4694 9 6608 7 94 78 90 3665 8 996 37 78 89 4433 3958 74 4 3 0 07 500 5644 30 7380 85 4 8 9 800 8776 8 630 5 5 77 9 630 500 6 047 8 6 89 85 7 4777 5 730 85 7 84 04 3400 593 5 4740 09 8 94 9 304 78550 3 4745 7 9 97 95 406 4654 3 6 9 0 8 00 340 7978 9 4473 90 7 88 393 78 0.00 9 55 0 9 075 3 5 0 3 80 00 40 389 963 56 4 87 9 3 5345 35 057 85 5 97 90 960 795 40 493 6 79 8 3375 4887 560 8 7 07 0 540 78068 6 8963 36 8 96 87 603 7743 50 876 0 9 67 8 300 38054 3 405 3 30 88 90 930 638 0 43 It has bee appled to patter recogto, regresso estmato, desty estmato problems ad lear operator equatos. 39
World Appl. Sc. J., (Mathematcal Applcatos Egeerg): 38-4, 03 Table 3: ad rakg for 30 braches Brach R( ) = L( y, f ( X, ) dp( X, y) Remp ( ) = Lyf (, ( X m, )) 0.54.0000 3 0.4987 4 0.460 5 0.48 6 0.583 7.0000 8 0.588 9.0000 0 0.358.0000 0.398 3 0.635 4.0000 5.0000 6 0.5895 7 0.398 8.0000 9 0.78 0.0000 0.000.0000 3 0.93 4.0000 5 0.600 6.0000 7 0.663 8.0000 9 0.99 30.0000 The Structural Rsk Mmzato Prcple: The goal of the best estmato of a fucto f(x, ), whch, s to mmze the dfferece betwee supervsor respose ad learer mache to the put vector X, amely: The probablty dstrbuto fucto P(x, y) s uclear, for mmzato of R ( ), expermetal rsk fucto wll be used as follows: I expermetal rsk fucto, the small amout of expermetal error does ot guaratee a small amout of the actual error. I order to tackle ths problem, Vapk suggested the Iductve prcple of structural rsk fucto Mmzato [3]. Wth probablty of - we have: () (3) for Λ ad h > R( ) R ( ) +Φ( hl,, ) emp where the s the relablty term, h s the dmeso of Vapk-Chervoeks, f(x, ) represets the capacty of ths set of fucto ad l s the umber of trag data. Mache learg based o mmzg of expermetal rsk s to fd a complex fucto wth the lowest error learg, I order to yeld loss performace. The structural rsk fucto Mmzato prcple establshes a compromse betwee the complexty of estmato fucto such that the amout of actual rsk become mmum by selectg proper f(x, ). Usg of Support Vector Maches Fuctos Estmato: The Support Vector method s a ma fucto estmato method, whch s ot depeded o the dmesos of the problem. It has bee appled patter recogto, regresso estmato ad desty estmato problems as well as to solvg lear operator equatos. The qualty of estmato s measured by the loss fucto L(y, f (x, )). SVM regresso uses a ew loss fucto called -sestve loss fucto proposed by Vapk [4]: L( y, f( X, )) = y f( X, ) 0 f y f( X, ) = y f( X, ) otherwse Ths fucto does ot cosder the rsk values whch are less tha, but for data wth dfferece more tha cosder the amout of the error equal to: = y f( X, ) By replacg of -sestve error fucto as observed rsk, support vector mache wll yelds to the followg optmzato problem: Z j j k X X j, j= maxmze W(, ) = ( + ) + ( + ) ( )( ) (, ) subject to ( ) = 0, 0, c Toobta Zˆ ( X) = ( ) k( X, X ) + b (4) (5) (6) (7) 40
World Appl. Sc. J., (Mathematcal Applcatos Egeerg): 38-4, 03 Table 4: Optmal values ad the performace of the model R RMSE MSE C 0.995 0.0383 0.0047 0.00 0.37 3 The lowest average error was acheved per optmzed parameters. The optmal obtaed values ad the performace of the model for testg data per optmal values are accordg to Table 4. As Fgure shows, wth accurate determato of parameters of the model, the of the system ca be estmated precsely. COCLUSIO Fg. : for testg data Such that ad are the Lagrage multplers ad k(x, X) s the kerel fucto. The accuracy of SVM estmato depeds o a good establshg of meta-parameters (C, ) ad the kerel parameters. Exstg software for SVM regresso usually treats SVM meta-parameters as puts defed by users. There are may algorthms for choosg the varable whch the most popular of them s cross-valdato. There are may wrtte computer codes for solvg the optmzato problems related to support vector maches. Modellg of the Example b THE SVM: For usg of support vector mache, we must determe the puts ad output of the system. I ths modellg problem, puts are the umber of persoel, total umber of computers, area of the brach, total umber of sured persos, umber of surace polces, total umber of old age pesoers ad the receved total sum (come). The output s the. The, the data of 90 braches of Tehra Socal Securty Isurace Orgazato cotag the correspodg put parameters ad output were cosdered. Amog of these vectors, we have cosdered 50 vectors for trag ad 40 vectors for testg. We have also ormalzed the put data to terval (-, ). I ths study, We use the RBF kerel fucto modellg ad estmato due to the favourable performace of t. RBF kerel fucto s as follow: k( X, X ) = exp( X X ) We use the cross-valdato method for fdg the optmzed parameters of the model. The trag data was dvded to 0 categores. We traed the mache by 9 categores ad we tested t by the oe remaed category. We repeated Ths procedure 0 tmes. (8) I ths paper, we troduced a ew method for modellg of a system accordg to Data Evelopmet Aalyss (DEA) ad Support Vector Maches. We tested the method for a practcal example. The model lears the relatoshp betwee puts ad outputs. Ths model ca apply for optmzato of system by usg optmzato method such as geetc algorthm. After system modellg, orgazato ca process ts actvtes order to acheve ts ufed goals. REFERECES. Salomoe, R., 008. Itegrated maagemet systems: expereces Itala orgazatos. Joural of Cleaer Producto, 6(6): 786-806.. Chares, A., W.W. Cooper ad E. Rhodes, 978. Measurg the effcecy of decso makg uts. Europea Joural of Operatoal Research, : 49-444. 3. Jahashahloo, G.R., F.H. Lotf, M. Khamohammad, M. Kazemmaesh ad V. Rezae, 00. Rakg of uts by postve deal DMU wth commo weghts. Expert Systems wth Applcatos, 37: 7483-7488. 4. Lu, S., 008. A fuzzy DEA/AR approach to the selecto of flexble maufacturg systems. Computers & Idustral Egeerg, 54: 66-76. 5. Mao, M., S. Hog ad I. Cho, 008. Effcecy evaluato of data warehouse operatos. Decso Support Systems, 44: 883-898. 6. Lu, J., F.Y. Dg ad V. Lall, XXXX. Usg data evelopmet aalyss to compare supplers for suppler selecto ad performace mprovemet, Supply Cha Maagemet, 5: 43-50. 7. Camaho, A.S. ad R.G. Dyso, 005. Cost effcecy measuremet wth prce ucertaty: a DEA applcato to bak brach assessmets. Europea Joural of Operatoal Research, 6: 43-446. 8. Ertay, T., D. Rua ad U. Tuzkaya, 006. Itegratg data evelopmet aalyss ad aalytc herarchy for the faclty layout desg maufacturg systems. Iformato Sceces, 76: 37-6. 4
World Appl. Sc. J., (Mathematcal Applcatos Egeerg): 38-4, 03 9. Shafer, S.M. ad T.A. Byrd, 000. A framework for. Jahashahloo, G.R., F.H. Lotf, V. Rezae ad measurg the effcecy of orgazatoal M. Khamohammad, 0. Rakg DMUs by deal vestmets formato techology usg data pots wth terval data DEA. Appled evelopmet aalyss. Omega, 8: 5-4. Mathematcal Modellg, 35: 8-9. 0. Sauders, C., A. Gammerma ad V. Vovk, XXXX. 3. Vapk, V., 998. Statstcal Learg Theory., ew Rdge Regresso Learg Algorthm Dual York, Wley. Varables. Mache Learg Proceedgs of the 4. Vapk, V., 999. The ature of Statstcal Learg Ffteeth Iteratoal Coferece (ICML 98), d Theory, Ed., Sprger. pp: 55-5.., R.R., 985. Measure of techcal effcecy. Joural of Ecoomc Theory, 35: 09-6. 4