Defining Contractor Performance Levels

Transcription

1 Defnng Contrator Performane Leels Khaled Nassar, Ph.D., AIA Assoate Professor, Ameran Unersty n Caro In many ountres, state and prate owners often ategorze ontrators nto arous groups based on ther apates as well as ther preous performane. These ategores are then used for seeral purposes nludng ontrat award and prequalfaton. A number of dfferent statstal algorthms an be used to ategorze the ontrators. No one algorthm an be used globally n all stuatons sne the performane of these algorthms depend partally on the atual data set beng used. Therefore ths paper presents a new model for groupng ontrators based on hstor data. The model deeloped here utlzes qualtate as well as quanttate measures about the ontrators performane. The model addresses the ssue of lassfyng ontrators nto arous performane ategores usng dfferent rsp and fuzzy lusterng algorthms and assesses the performane of these algorthms wth approprate aldty measures. The model was aldated usng atual data from preously reorded projet nformaton for 3 ontrators. The analyss shows that the model an be used effetely to determne the performane leel of the ontrators and to perform lusterng of ontrators nto dfferent performane groups. Keywords: Contrator Performane, Competeny, Projet Management, Buldng Construton Introduton Many owners are beomng more aware of the fat that the lowest bd does not always result n the lowest ost. Seeral owners hae been awardng ontrats based on a fnanal bd as well as a tehnal bd. Varous ealuaton methods hae been used to ealuate the tehnal bds. Ranng the ontrators for the purpose of awardng ontrats s a ery mportant proess and has obous seere mplatons for the owner and ontrator ale. When ealuatng the ontrator performane, owners often lassfy the ontrator nto dfferent performane groups based on ther hstor performane, whh s the top of ths paper. Some of the releant preous researh on the ssue nludes that of Shen et al (3) who nestgated the Contrator Key Competteness Indators, whle Wong (4) deeloped a ontrator performane predton Model for the Unted Kngdom onstruton ontrators. (Palaneeswaran and Kumaraswamy, ) foused on deelopng a model for ontrator prequalfaton and bd ealuaton n desgn/buld projets. (Sngh and Tong, 6) studed the ontrator seleton rtera for the Sngapore onstruton ndustry. (Alaro n and Mourgues, ) proposed a ontrator seleton system that norporates the ontrator s performane predton. F.Waara and J. Bröhner (6) nestgate Pre and Non-pre Crtera for Contrator Seleton. Other researh nlude that of (Hatush and Stmore 997, Holt and Olomolaye 994, Inaneh et al 997). Howeer the researh of (Sngh and Tong, 5) s more releant to ths paper sne the researhers deeloped a fuzzy deson framewor for ontrator seleton. They presented a systemat proedure based on fuzzy set theory. The proedure was ntended to ealuate the apablty of a ontrator to meet the owner s requrements n terms of ost, tme and qualty. Shapley alue was the man onept used to determne the global alue or relate mportane of eah rteron n aomplshng the oerall objete of the deson-mang proess. Howeer, no algorthm or aldaton tehnques were proposed. Ths s a major drawba sne usng dfferent rsp and fuzzy tehnques wll usually result n dfferent results. Ths s unaeptable pratally and results n a stuaton where a ontrator an be lassfed n one leel usng a spef algorthm and n a hgher or lower leel usng another algorthm. Ths paper presents a proedure arred out to ran ontrators worng n the Duba. The wor presented here was arred out on behalf of a large owner/deeloper for ranng the ontrators bddng for the deeloper. The man goal was to ategorze ontrator nto smlar ategores n terms of ther performane defned by seeral attrbutes nludng ther preous bddng performane. The deeloper, who olleted hstoral data about the ontrators t hred, was nterested n ategorzng the ontrators nto arous leels of performane and not

2 prodng a ran lst of them. The ultmate goal was that eah ontrator be assgned a ertan performane ategory and that ths ategory would be one determnant n awardng ontrats. Howeer, ths paper fouses only on the framewor for assgnng the performane ategory. The same framewor an be appled to seeral other onstruton marets. Twenty one ontrators were analyzed by mang use of ther hstoral data whh the deeloper had proded. Varous performane measures were onsdered for the analyss. Quanttate measures where alulated from a hstor database. These quanttate measures an be broen down nto 3 man ategores; shedule, ost and safety. Qualtate measures on the other hand were assessed subjetely usng the Analytal Herarhal Proess. Therefore, a data set ontanng all the performane measures ersus the ontrator was ompled. Eght performane measures were used n all: the aerage delay, the aerage number of late jobs, rato to aerage bd, Dsablng Injury Seerty Rate, the Aerage Days Charged, manageral and ustomer sere, enronment and sustanablty (the last two beng the qualtate measures). More nformaton on the alulaton and olleton of these measures an be found n Nassar 8, howeer n ths paper we wll fous on the algorthms used as desrbed n the net seton. Data Normalzaton for Clusterng Clusterng tehnques are among the unsupersed methods of data mnng whh am at lassfaton of objets based on smlartes among them. The term "smlarty" should be understood as mathematal representaton of the smlarty rtera under onsderaton. The performane of most lusterng algorthms s nfluened by the geometral propertes of the nddual lusters but also by the spatal relatons and dstanes among the lusters. Therefore arous lusterng algorthms were used n order to lassfy the ontrators nto dfferent lusters. We used the toolbo for Matlab by Balaz et al 8. Table : Normalzed Contrator Data Aerage Delay Aerage number of late jobs Shedule Measures Cost Measure Safety Measures Total lqudated damages harged ost weghed delay duraton weghed delay number of lowest bds dfferene from lowest bd rato to aerage bd Dsablng- Injury Frequeny Rate Dsablng Injury Seerty Rate Aerage Days Charged

3 Before lusterng an be arred out, the data had to be normalzed as the arous performane measure reorded was n a dfferent sale (.e. the delay may be n days, where as the weghted delay s n dollar.days). Normalzaton therefore entals settng a fed sale for all the data. Ths an be done usng by salng wth relaton to the mnmum and mamum alue of eah rteron, or alternately through normalzaton through the arane whh was the tehnque used n the analyss presented here due the relately small data sample. The followng equaton was used for normalzaton: Fgure shows three sets of harts; frst the un-normalzed raw data for the aerage delay performane measure, and seond the same data after normalzaton aordng to the mn-ma and fnally the data normalzed by arane whh was used n ths researh Fgure : The Normalzed data set One the data has been normalzed, the man goal beomes tryng to ft ontrators n arous performane ategores. Here we must frst try to determne the number of performane ategores to use and seondly determne whh of the dfferent lusterng algorthm wll produe the best results (by best we mean most onsstent). Ths means that f one were to use a ertan lusterng algorthm a spef ontrator may be assgned to one performane ategory whle the use of another algorthm may result n the same ontrator beng assgned to lower or hgher performane ategory. Ths s obously unaeptable to the owners or the ontrators who need a relable way to lassfy ontrators. Therefore a number of dfferent algorthms were used as desrbed below.

4 Fgure : The results based on C-means algorthm Clusterng Algorthms Used Consder the arous projets n the data set, as an n-dmensonal row etor = [,, n ] T. A set of N obseratons s denoted by X = { =,,,N}, where n s the number of ontrators and N are the arous performane measured onsdered. The goal s fnd a partton matr U=[µ ] The frst algorthms onsdered were two typal hard lusterng algorthms, namely K-means and K-medod. These are smple and popular, though the results are not always relable. For an N n dmensonal data (where n s the number of ontrators and N are the arous performane measured onsdered) one of lusters s alloated by mnmzng the sum of squares,.e. A l, where A s the set of data ponts n the -th luster and s the mean of those ponts. In K-medod lusterng the luster enters are the nearest objets to the mean of data n one luster V X. The results of the C-means lusterng are shown n fgure for two of the performane measures; raton to aerage bd and aerage delay. Net we onsdered the Fuzzy C-means algorthm whh s based on mnmzng an objete funton defned as

5 J N X ; U, V where, m A V,...,, R n s a etor of luster enters, whh hae to determned and D A A T A s a squared nner-produt dstane norm. The objete funton s atually a measure of the total arane of from. The mnmzaton of the - means funton represents a nonlnear optmzaton problem that an be soled by usng a arety of aalable methods, rangng from grouped oordnate mnmzaton, oer smulated annealng to genet algorthms. The most popular method, howeer, s a smple Pard teraton whh what was used n our researh. Another Fuzzy algorthm onsdered was the Gustafson and Kessel etenson of the fuzzy -means algorthm by employng an adapte dstane norm, n order to detet lusters of dfferent geometral shapes n one data set. Eah luster has ts own norm-ndung matr A, whh yelds the followng nner-produt norm: J X ; U, V, A N m D A The matres A are used as optmzaton arables n the -means funtonal, thus allowng eah luster to adapt the dstane norm to the loal topologal struture of the data. Let A denote a -tuple of the norm-ndung matres: A = (A;A; :::;A) Fgure 3: The results based on Fuzzy C-means and the Gustafson and Kessel algorthms Howeer, the objete funton annot be dretly mnmzed wth respet to A, sne t s lnear n A. Ths means that J an be made as small as desred by smply mang A less poste defnte. To obtan a feasble soluton, A must be onstraned n some way. The usual way of aomplshng ths s to onstran the determnant of A. The results of these algorthms are shown n Fgure 3. The lnes of the ontour maps mean the leel ures of the same alues of the membershp degree The last algorthm onsdered s the fuzzy mamum lelhood estmates (FMLE) lusterng algorthm, whh employs a dstane norm based on the fuzzy mamum lelhood estmates, proposed by Bezde and Dunn as: D, det F w ep ( l) T F w ( l)

6 Note that, ontrary to the GK (Gustafson and Kessel) algorthm, ths dstane norm noles an eponental term and thus dereases faster than the nner-produt norm. The membershp degrees are nterpreted as the posteror probabltes of seletng the approprate luster for eah ontrator gen the data pont Fgure 4: The results based on FMLE algorthm The queston now beomes whh of the aboe algorthm to hoose n order to lassfy the ontrators approprately. The answer s determned by ealuatng eah of the aboe algorthms aordng to arous aldty measures as desrbed net. Valdty Measures Dfferent aldty measures hae been proposed n the lterature, none of them s perfet by oneself. Therefore we used seeral ndes to ompare the arous algorthms. The frst aldty measure onsdered s the Partton Coeffent (PC): measures the amount of "oerlappng" between the lusters and s defned as: N PC ( ) j, () N j where ¹j s the membershp of data pont j n luster. The most promnent dsadantage of PC s la of dret onneton to some property of the data tself. Another measure onsdered s the lassfaton Entropy (CE) whh measures the fuzzness of the luster partton only as, N CE( ) j log j () N j The Partton Inde (SC) on the other hand s the rato of the sum of ompatness and separaton of the lusters. It s a sum of nddual luster aldty measures normalzed through dson by the fuzzy ardnalty of eah luster and s gen by, SC N m ( j j ) j ( ) (3) N j The Separaton Inde (S) uses a mnmum-dstane separaton for partton aldty.

7 N ( ) j j j S ( ) (4) N mn, j j Other measures onsdered are: the Xe and Ben's Inde (XB) whh ams to quantfy the rato of the total araton wthn lusters and the separaton of lusters, Dunn's Inde (DI) whh dentfes ompat and well separated lusters, and the Alternate Dunn Inde (ADI) whh ams at modfyng the orgnal Dunn's nde to beome more smple, when the dssmlarty funton between two lusters s rated n alue dfferently. All these aldty measures where alulated for the arous lusterng algorthms mentoned aboe and s dsplayed n Fgure 5. Fgure 5: Comparson of algorthms based on aldty measures The results show that the best performng algorthm for our data set was the Fuzzy C-means algorthm. As suh the ontrators were lassfed aordng to that algorthm whh showed lear lusters of ontrators n 4 man groups based on the lassfaton data shown n Table. Conlusons One of the man drawbas of tryng to group the arous ontrators nto dfferent performane ategores s that the numbers of the data groups hae to be deded a-pror. Ths may be a drawba sne ontrators may argue as to the aldty of the ategorzaton s-a-s the number of performane ategores used and the ratonale for dedng on a spef number of ategores (.e. a ontrator may be grouped n the seond performane ategory when ontrators are grouped nto 6 dfferent ategores, but may be grouped n the frst f only 4 ategores are seleted). Therefore ths paper presented a tehnque whh an oerome these lmtatons and possbly open the way for the wder mplementaton of ontrator lassfaton n the onstruton ndustry, whh n turn an be used for arous manageral and ontratual purposes. Referenes Balazs Balaso, Janos Abony and Balazs Fel, (8). Fuzzy Clusterng and Data Analyss Toolbo For Use wth Matlab

8 Hatush, Z., and Stmore, M. (997). Crtera for ontrator seleton. Constr. Manage. Eonom., 5, Holt, G. D., Olomolaye, P. O., and Harrs, F. C. (994). Fators nfluenng U.K. onstruton lents hoe of ontrator. Buld. Enron.,9, Huang, T., Shen, L. Y., Zhao, Z. Y., and Yam, C. H. (5). The urrent prate of managng publ setor projets n Chna. Construton Eonomy, 5, 6. Inaneh, J. M., Lorenz, P., and Snner, S. J. (997) Management qualty and ompetteness, nd ed., MGraw-Hll, New Yor. Lus Fernando Alarón and Claudo Mourgues (), Performane Modelng for Contrator Seleton, J. Mgmt. n Engrg., Volume 8, Issue, pp. 5-6 Moungnos, W., and Charoenngam, C. (3) Operatonal delay fators at mult-stages n Tha buldng onstruton. Int. Journal of Construton Management, 3, 5 3. Palaneeswaran Eambaram and Kumaraswamy Mohan M (), Contrator seleton for desgn/buld projets, Journal of onstruton engneerng and management, ol. 6, no5, pp Saaty, T. L. 98. The analyt herarhy proess, MGraw-Hll, New Yor. Shen, L. Y., Lu, W. S., Shen, Q. P., and L, H. 3. A omputer-aded deson support system for assessng a ontrator s ompetteness. Autom. Constr., 3, Sngh D. and Robert L. K. Tong (5) A Fuzzy Deson Framewor for Contrator Seleton, J. Constr. Engrg. and Mgmt., Volume 3, Issue, pp. 6-7 Sngh D. and Robert L. K. Tong (6) Contrator Seleton Crtera: Inestgaton of Opnons of Sngapore Construton Prattoners, J. Constr. Engrg. and Mgmt., Volume 3, Issue 9, pp Taylor B.N. and Kuyatt C.E. (994) Gudelnes for Ealuatng and Epressng the Unertanty of NIST Measurement Results, NIST Tehnal Note 97, Washngton DC Waara F. and J. Bröhner (6), Pre and Nonpre Crtera for Contrator Seleton, J. Constr. Engrg. and Mgmt., Volume 3, Issue 8, pp Wong Chee Hong, (4), Contrator performane predton model for the Unted Kngdom onstruton ontrator: Study of logst regresson approah, Journal of onstruton engneerng and management, 4, ol. 3, no5, pp