A Data Mining Method to Support Decision Making in Software Development Projects

A Da a Mining Me hod o Suppo Decision Making in So wa e De elopmen P ojec s J.L. ´ Al a ez and J. Ma a Dp . Ing. Elec ´onica, Sis . In o m´a icos y Au om´a ica Uni e sidad de Huel a al a ez, ma a g @uhu.es J.C. Riquelme and I. Ramos Dp . Lenguajes y Sis emas In o m´a icos Uni e sidad de Se illa iquelme, amos g @lsi.us.es Key wo ds: Knowledge Disco e y in Da a, Da a Mining, Dynamic Models, So wa e Enginee ing. Abs ac : In his pape , we p esen a s a egy o induce knowledge as suppo decision making in So wa e De elopmen P ojec s (SDP). The mo i e o his wo k is o educe he g ea quan i y o SDP do no mee he ini ial cos equi emen s, deli e y da e and he quali y o he inal p oduc . The main objec i e o his s a egy is o suppo he manage in he decision aking o es ablish he policies om managemen when beginning a so wa e p ojec . Thus, we apply a da a mining ool, called ELLIPSES, on da abases o SDP. The da abases a e gene a ed by means o he simula ion o a dynamic model o he managemen o SDP. ELLIPSES ool is a new me hod o ien ed o disco e knowledge acco ding o he expe ’s needs, by he de ec ion o he mos signi ican egions. The me hod essence is ound in an e olu iona y algo i hm ha inds hese egions one a e ano he . The expe decides which egions a e signi ican and de e mines he s op c i e ion. The ex ac ed knowledge is o e ed h ough wo ypes o ules: quan i a i e and quali a i e models. The ool also o e s a isualiza ion o each ule by pa allel coo dina e sys ems. In o de o p esen his s a egy, ELLIPSES is applied o a da abase which has al eady been ob ained by means o he simula ion o a dynamic model on a p ojec concluded. 1 INTRODUCTION Cu en ly, many So wa e De elopmen P ojec s (SDP) do no mee he ini ial cos equi emen s, de- li e y da e and he quali y o he inal p oduc . The eason o his si ua ion is he g ea quan i y o a - ibu es ha in luence on he de elopmen p ocess, whose alues should be es ablished by he manage o he p ojec . These alues depend on he di e en managemen policies as well as he ma u i y le el o he o ganiza ion o de elopmen . In he adi ional me hod, he manage akes a de- cision o he alues o hese a ibu es acco ding o his expe ience, he ini ial a ailable esou ces and he equi emen s o he p ojec . This decision is a e y di icul ask because i is necessa y o decide each a - ibu e indi idually and u he mo e o bea in mind he a ibu es al oge he . The simula ion o dynamic models o he manage- men o SDP (Abdel-Hamid and Madnick, 1991) p o- duces an imp o emen as opposi e o adi ional s a ic models. The dynamic models allow o analyze, be- o e beginning hede elopmen , he esul o he man- age ’s decision. Howe e , i he manage has unce - ain y abou many a ibu es hen many simula ions will be necessa y and he canno make an exhaus i e analysis o he p ocess. Da a mining me hod can be used o sol e his p ob- lem (Aguila e al., 2001). Da a mining is a machine lea ning p ocess ha induce pa e ns om da abases (Chen e al., 1996; Fayyad e al., 1996). Thus, a da abase can be gene a e h ough he sim- ula ion o a dynamic model o he de elopmen p o- cess. Each ins ance o he da abase is composedo he a ibu es (pa ame e s) used on he simula ion and he a ibu es ( a iables) ob ained om he simula ion. A da a mining me hod can be applied o his da abase. In his pape , we p esen an o e iew o his p o- cess. Thus, we o e he esul s a e applying ou da a mining ool, called ELLIPSES ( ´ Al a ez e al., 2002), on a da abase. This da abase has been gene a ed us- ing he dynamic model o he managemen o SDP desc ibed in (Ramos and Riquelme, 1999). The emaining pa o he pape is o ganized as ol- lows. In sec ion 2, a b ie desc ip ion o he use o he dynamic model on SDP is in oduced. In sec ion 3, he s a egy o apply da a mining me hods on SDP is gi en. In sec ion 4, he ELLIPSES ool is desc ibed. 1 ICEIS 2003 - The case s udy and expe imen al esul s a e desc ibed in sec ion 5 and he pape is conclude in sec ion 6. 2 DYNAMIC MODELS AND SOFTWARE ENGINEERING A he beginning o he 90’s a signi ican e en ook place in so wa e enginee ing ield: he use o he i s dynamic model (Abdel-Hamid and Madnick, 1991) applied o SDP. In he las yea s, new dynamic models o SDP and powe ul simula ion en i on- men s (S ella, Vensim, iThink, Powe Sim, e c.) ha e s ongly suppo ed he complex p ocess o decision making. The po en ial o he simula ion o he dy- namic models o he o ma ion and aining o he manage o p ojec s has been p o ed in (Ruiz e al., 2001; Dhiel, 1991; G aham e al., 1992). These sys- ems o e o he manage , wi hou isks, he impac ha can ha e on a p ojec he applica ion o manage- men policies. Thus, he simula ion o so wa e p ojec s by dy- namic models can be used o accomplish: A p io i analysis: he simula ion o he p ojec is made be o ebeginning he de elopmen . This anal- ysis gua an ees he li e cycle o he p ojec apply- ing he analyzed policies. Moni o ing analysis: he simula ion o he p ojec is made du ing he de elopmen p ocess. This analy- sis pe mi s o compa e he eal s a e p ojec wi h he esul s o he simula ion. Pos -mo em analysis: he simula ion is made a e he de elopmen p ocess. This analysis helps o im- p o e he esul s on u u e p ojec s. Ob iously, he g ea quan i y o si ua ion ha he manage needs o simula e in a p ojec p e en s o make an analy ical exhaus i e. Thus, he manage only will be able o accomplish some simula ions. In he nex sec ion, a solu ion o his p oblem is gi en. 3 DATA MINING AND SOFTWARE ENGINEERING Da a Mining me hods ha e been on many ields o - e ing excellen esul s. Howe e , he e a e no many esea che s using hese me hods on he so wa e en- ginee ing ield. A possible con ibu ion o he da a mining on he so wa e enginee ing is he imp o e- men o he de elopmen p ocess. Thus, da a mining algo i hms analyze de elopmen p ocess da abases o induce a se o managemen ules. This s a egy has an incon enience: he e a e no many eal da abases o de elopmen p ocess. This Figu e 1: P ocess o induce managemen ules om so - wa e de elopmen p ojec s. p oblem can be sol ed using a simula ion en i on- men wi h a dynamic model o he managemen SDP. Thus, he a ibu es wi h ce ain unce ain y le el a e selec ed by he manage acco ding o his expe- ience, he equi emen s o he p ojec and he man- agemen policies. Fo each one o hem, he manage chooses a ange, since he do no know ha he alue o a a ibu e will be 37, bu know ha will be be- ween 30 and 40. The simula ion en i onmen will choose a andomly alue o hese a ibu es and will simula e he p ojec gene a ing he esul s o cos , de- li e y da e and quali y o he inal p oduc . This p o- cess is epea ed un il he da abase has he necessa y ins ances. Figu e 1 shows he sequence o his p oce- du e. Finally, a da a mining algo i hm is applied on his da abase ob aining a se o managemen ules. The manage can be use he in e es ing knowledge ha hese ules o e . The e a e some c i e ia in o de o choose he ules:  To choose he ules ha co e mo e ins ances.  To choose he ules wi h less a ibu es.  I i is a pos -mo em analysis, o choose he ules o hose he ange o each a ibu e con ains he ini ial alue.  I i is a p io i analysis, o choose he ules whose a ibu es can be con olled easily.  To choose he ules ha o e he bes esul s. 3.1 Adjus men o he s a egy The desc ibed s a egy p e iously has a p oblem i we wan o apply ou ool. A da abase gene a ed ac- co ding o he p e ious p ocedu e is composed by a - ibu es: pa ame e s (inpu a ibu es) and a iables (ou pu a ibu es), whose alues a e all con inuous. Howe e , ELLISPES ool needs a aining se whose a ibu es a e con inuous alues, bu he class is a ca - ego ical alue. In o de o sol e his p oblem, he con inuous a i- ables should be ans o med in only one ca ego ical a ibu e using he expe ience o he p ojec manage . This way, he manage needs o es ablish he max- imum alues o each ou pu a ibu e (cos , deli e y da e and quali y), in such a way ha i hese alues 2 A Da a Mining Me hod o Suppo Decision Making in So wa e De elopmen P ojec s Figu e 2: G aphical ep esen a ion o an hipe ellipse a) wo b) h ee dimen ional. a e su passed he p ojec is conside ed as no accep - able. In o wa d, each se o maximum alues o he a iables will be deno ed ”cu ing sec ion”. Thus, each ”cu ing sec ion” p oduces a di e en aining se on he gene a ed da abase, whe e he in- s ances whose ou pu a ibu es su pass hose alues a e conside ed as ”good”, and he ins ances whose ou pu a ibu es main ain hose alues a e conside ed as ”no good”. The ”good” ins ances a e labelled wi h ”G” and he ”no good” ins ances a e labelled wi h ”N”. The new aining se s a e composed o he inpu a ibu es and he new class. 4 ELLIPSES TOOL ELLIPSES ool is a da a mining me hod o induce in e es ing egions in da abases. The co e o he al- go i hm is a e olu iona y p ocess (Goldbe g, 1989; Holland, 1975; Michalewicz, 1999) whose indi idu- als a e ellip ical su ace in he sea ch space. The esul s a e shown by quan i a i e and quali a- i e ules, and a isualiza ion by pa allel coo dina es sys ems is also shown. In he nex sec ions, he p elimina y de ails, a b ie desc ip ion o he algo i hm and he isualiza ion a e desc ibed. 4.1 P elimina ies Ou me hod uses conical egions o ind he mos sig- ni ican ules. These egions con ain he ea u es o each class. This sec ion o e s he basic de ini ions o he models o ules used in ou ool. An hype ellipse ( he w appe ) is equal o an el- lipse o ci cum e ence in a wo-dimensional space R 2 . An hype ellipsoid ( he w apped olume) is equal o an ellipsoid o ci cle in a wo-dimensional space R 2 . Figu e 2 o e s a g aphical ep esen a iono hese concep s. Figu e 2a) ep esen s an ellipse o cen e (  1 ;  2 ) , g ea e axis a 1 and smalle axis a 2 o wo a ibu es x 1 and x 2 ( wo-dimensional space R 2 ) and igu e 2b) shows an hype ellipse o h ee a ibu es x 1 , x 2 and x 3 ( h ee-dimensional space R 3 ). ( x 1   1 ) 2 a 2 1 + ( x 2   2 ) 2 a 2 2 = 1 (1) ( x 1   1 ) 2 a 2 1 + ( x 2   2 ) 2 a 2 2  1 (2) ( x 1   1 ) 2 a 2 1 + ( x 2   2 ) 2 a 2 2 + ::: + ( x d   d ) 2 a 2 d  1 (3) The equa ion o he ellipse in R 2 is shownin 1. The equa ion o an ellipsoid is shown in 2. This equa ion is ob ained changing = by  in he equa ion o he associa ed ellipses. Gene alizing, in R d , he equa ion o an hype ellipsoid is shown in 3. I x 1 (  1 ; a 1 ) and ::: and x d (  d ; a d ) ) C i (4) h ( x i ; a i ) = 8 > > > < > > > : L a g e i a i > 40% A x ML a g e i 25% A x < a i  40% A x M edium i 15% A x < a i  25% A x MS ho i 5% A x < a i  15% A x S ho i a i  5% A x (5) I x 1 (  1 ; E 1 ) and ::: and x d (  d ; E n ) ) C i (6) The models o he ules (quan i a i e and quali a- i e)used in ou ool a ebased on 1, 2 and 3. Thus, he quan i a i e model is ob ained di ec ly by he equa- ion o he ellipse. This model is shown in 4 and i o e s he cen al  i alue and he ex en (wid h) a i o each a ibu e, and he associa ed class C i . The quali- a i e model uses i e labels o speci y he ex en . Fo each a ibu e x i , a E j label is gene a ed by h ( x i ; a i ) unc ion, acco ding o 5, whe e A x is x iM  x im , x iM is he maximum and x im he minimum o x i a ibu e. The quali a i e model is shown in 6. The in e p e a ion o hese models o ule is e y in ui i e because he ule does no di e om he ypical clas- si ica ion ules. Thus, le be : ( y 1 ; y 2 ; :::; y n ) , i y i 2 [ x i  a i ; x i + a i ℄ 8 i hen he i em is associa ed wi h he class C i , acco ding o 4. In he quali a i e model, he label es ablishes he di e ence be ween y i and x i . The C i o an hype ellipsoid is assigned as ollows. Le be : ( x 1 ; x 2 ; :::; x d ; C i ) i em, i i sa is ies he equa ion 3 hen he i em is wi hin he olume o he hype ellipsoid. Thus, he majo i y class wi hin he hype ellipse is he associa ed class o i . 4.2 E olu iona y P ocess The main objec i e o ou ool is o induce he e- gions o he sea ch space wi h a g ea e numbe o 3 ICEIS 2003 - ELIPSES Algo i hm 1. T Read T aining se 2. Repea 3. i e i e + 1 4. P i Ini ialize popula ion on T 5. Repea 6. E alua e P i on T 7. Selec he bes in P i o P i +1 8. Selec 10% in P i o P i +1 9. C osso e P i indi iduals o P i +1 10. Mu a e P i +1 11. P i +1 is P i 12. Un il numbe gene a ions 13. Selec he bes o P i 14. i alpha( ) > ALPHA THEN add(R, ) 15. Un il (i e =ITER o be a( ) > BETA) 16. Show R ules 17. Visualiza ion R by Pa allel Coo dina es END. Figu e 3: ELLIPSES Algo i hm. he ins ances belonging o he same class and o pe - mi he human-expe in e ac ion in o de o es ablish some c i e ia o he sea ch p ocess. The inal esul shows a educed and easie in e p e able se o ules. ELLIPSES is based on E olu iona y Algo i hm (EA). EA a e a heu is ic sea ch echnique ha has demon- s a ed o be obus o a a ie y o complex sea ch space. Figu e 3 shows he ELLIPSES algo i hm. I e a- i ely, he EA inds he bes hype ellipse based on he numbe o posi i e and nega i e i ems in he hy- pe ellipsoid. Le be al pha ( ) he pe cen age o he same class i ems in , i al pha ( ) is g ea e han he p ede ined human-expe pe cen age ALP H A , hen egion is conside ed. This p ocess is epea ed un il eaching a p ede ined human-expe numbe o ules o p ede ined human-expe pe cen age B E T A , whe e be a ( ) is he numbe o co e ed cases. Fi- nally, he ules a e shown acco ding o 4 and 6 (quan- i a i e and quali a i e models), and hey a e shown by pa allel coo dina e sys ems. 4.2.1 Rep esen a ion An indi idual (a easible solu ion) is a se I =  1 ,...,  d , a 1 ,..., a d g whe e d is he numbe o a ibu es and  i ; a i 2 < a e, espec i ely, he cen e and ex en o he x i a ibu e and hey ep esen he equa ion o an hype ellipsoid acco ding o 3. Figu e 4 shows a g aphical ep esen a ion o he indi iduals. In p ac ice, an indi idual ep esen s a sea ch space egion. Each egion will be associa ed o a class ha will be deduced by he majo i yclass o he da a i ems Figu e 4: Rep esen a ion o an indi idual in he ELLIPSES e olu iona y algo i hm. in he hype ellipsoid. 4.2.2 Fi ness unc ion The i ness (o me i as a solu ion) o an indi idual is ob ained by aining se i em analysis. An i em can be in o ou o he hype ellipse. The ou i ems a e igno ed. The di e en classes o he i ems in he hy- pe ellipse a e coun ed and he associa ed class o he indi idual is he majo i y class. Thus, he i ems wi h he same class a e posi i e cases and he i ems wi h di e en classes a e nega i e cases. Fu he mo e, nex i e a ion mus di ec he e olu- iona y p ocess o o he egions. Thus, he posi i e cases co e ed by disco e ed ules a e conside ed co - e ed cases. Finally, ou me hod needs o ob ain he g ea es egion. Thus, he ampli ude o he hype - ellipse is he hype ellipse olume di ide by sea ch spaces olume. ( i ) = P os ( i )  N eg ( i )  C o e ( i )  F C + Ampl ( i ) (7) Ou algo i hm maximizes he i ness unc ion o each indi idual i . The i ness unc ion is gi en in 7, whe e P os ( i ) and N eg ( i ) a e he posi i e and nega- i e cases in he hype elipsoid ha ep esen he in- di idual i, C o e ( i ) a e he co e ed cases by p e- ious hype ellipses, F C is he co e u e ac o and Ampl ( i ) is he hype ellipse ampli ude. Co e u e ac o ( F C ) is a alue in he in e al [0 :: 1℄ , and i o - e s he possibili y o elaxing he co e ed cases, so, i F C is closed o 1, hen he co e ed cases a e con- side ed nega i e cases, and i F C is closed o 0, hen he co e ed cases a e igno ed. 4.2.3 Gene ic Ope a o s The e a e ee gene ic ope a o s: selec ion, c osso e and mu a ion. To o m a new popula ion ( he nex gene a ion), he indi iduals a e selec ed acco ding o hei i ness by he selec ion ope a o . Many selec ion p ocedu es a e cu en ly in use, ou algo i hm uses oule e wheel p ocedu e, whe e indi iduals a e se- lec ed wi h a p opo ional p obabili y o hei ela i e i ness. This ensu es ha an indi idual is chosen in a expec ed numbe o imes app oxima elyp opo ional o i s ela i e pe o mance in he popula ion. Thus, high- i ness (good) indi iduals s and a be e chance 4 A Da a Mining Me hod o Suppo Decision Making in So wa e De elopmen P ojec s Figu e 5: The middle poin c osso e ope a o in he EL- LIPSES e olu iona y algo i hm. Figu e 6: The uni o m poin c osso e ope a o in he EL- LIPSES e olu iona y algo i hm. o selec ing, while low- i ness indi iduals a e mo e likely o disappea . Selec ion canno in oduce any new indi iduals in o he popula ion. These indi iduals a e gene a ed h ough c oss-o e and mu a ion ope a o s. C osso e ope a o is pe o med by selec ing wo indi iduals called pa en s, and gene a ing new indi iduals called o sp ing. Inou algo i hm, he c osso e ope a o has wo componen s: he middle poin c osso e and he uni o m c osso e . They a e pe o med wi h a p ob- abili y p  oss ha chooses be ween he middle poin c osso e and he uni o m c osso e . The middle poin c osso e andomly spli s he indi iduals in wo pa s. Then he agmen s a e exchanged gene a ing wo new indi iduals. Figu e 5 g aphically shows his p ocess. The uni o m c osso e decides , indepen- den ly o each coe icien o an indi idual, whe he i con ibu e o no o he new indi idual. An example o his p ocedu e is shown in igu e 6. ij = ij  Quan  P e M u  ij (8) Finally, he mu a ion ope a o is in oduced o p e- en p ema u e con e gence o local op imum by an- domly sampling newpoin s in he sea ch space. Th ee a ian s a e implemen ed: cen e mu a ion, ampli- ude mu a ion and ex eme mu a ion. Mu a ion is pe - o med wi h p obabili y p mu on an indi idual. When an indi idual mus be mu a ed, a p obabili y chooses be ween he di e en ope a o s. The cen e and am- pli ude mu a ion ope a o s al e he cen e (  1 ; :::;  d ) and he ex en ( a 1 ; :::; a d ) o he hype ellipse, espec- i ely, acco ding o 8, whe e ij is he ac o o al- e , Quan and P e M u ake hei alues om[0..1], Quan is he andom quan i y ha ij is al e ed and P e M u is he pe cen age o mu a ion ha de e - mines how he mu a ion in luence on ij . The ex- eme mu a ion ope a o al e s bo h cen e (  i ) and ex en ( a i ) o an a ibu e ( x i ). Thus, he mu a ion le he middle alue o x iM  x im o  i and le x iM  x im 2 o a i . The objec i e o his ope a o is o co e he a ibu e. Figu e 7: ELLIPSES Pa allel Coo dina e Sys ems. 4.3 Pa allel Coo dina e Sys ems Al hough ou ool o e s wo models o ules and he quali a i e model is easily in e p e ed, some imes i is necessa y o p o ide he in o ma ion using ano he philosophy. Thus, a isualiza ion o he ela ionships among he a ibu es o e s a good suppo o he ex- pe . The isualiza ion echnique used in ou algo- i hm is shown in his sec ion. This echnique o e s he ela ionships among a ibu es by pa allel coo di- na es (Inselbe g, 1985). A pa allel coo dina e sys em is composed by a se o pa allel axes sepa a ed by a ixed dis ance. Each axis co esponds wi h an a ibu e and hey a e esca- la ed on he ange o he a ibu e. Thus, d axes a e necessa y o ep esen d a ibu es. In his sys em, a line ep esen s each da a i em. This line in e sec s wi h each axis on he alue o he i em o ha a - ibu e. Figu e 7a) shows he adi ional pa allel coo - dina e sys em. In ou me hod, each egion is ep esen ed on a pa - allel coo dina e sys em. Bu , all da a i ems in a e- gion a e no ep esen ed on pa allel coo dina e sys- em. Thus, only he minimal alue and he maximal alue, o each a ibu e, a e ep esen ed on each axis and hese alues a e joined by illed polygonal. Fig- u e 7b) o e s an example o his me hod. The in e nal lines a e elimina ed. The objec i e o his a ian is o o e a clea e and compac ision o he ela ionships be ween he a ibu es. 5 CASE STUDY In his case s udy, we will analyze he in luence o he policieso pe sonnelmanagemen on he a iables o a SDP wi h es ic ions in he deli e y ime. Thus, he used a ibu es on his s udy a e: he a - e age delay o he new echnicians’ adap a ion ha has inco po a ed o he p ojec ( echnicians’ in eg a- ion), he a e age delay o he echnicians’ exi o he p ojec ( echnicians’ discha ge), he a e age delay o he new echnicians’ inco po a ion in he p ojec ( echnicians’ ec ui ing) and he maximum delay on he deli e y ime. Table 1 shows mo e in o ma ion 5 ICEIS 2003 - Table 1: SDP a ibu es A ibu es Desc ip ion uni ini ial alue ange inpu s ASIMDY (A) The a e age delay o he new echnicians’ adap a ion ha has inco po- a ed o he p ojec days 20 [5,15] HIREDY (H) The a e age delay o he new echnicians’ inco po a ion in he p ojec days 30 [5,10] MXSCDX (M) The maximum delay on he deli e y ime % 1.16 [1, 1.2] TRNSDY (T) The a e age delay o he echnicians’ exi o he p ojec days 10 [5,10] ou pu s JBSZMD Necessa y e o o ca y ou he p ojec echnicians-days 1111 - SCHCDT De elopmen ime days 320 - ANERPT Final p oduc quali y e o s/ asks 0 - Table 2: ”Cu ing sec ion” on CRCCRT da abase CRCCRT JBSZMD SCHCDT ANERPT Cu ing sec ion 1 -  352 (10%)  0 : 45 (0.45%) Cu ing sec ion 2 -  352 (10%)  0 : 35 (0.35%) abou hese a ibu es. Fu he mo e, his able shows he a iables ha will be analyzed: deli e y ime, cos and quali y o he inal p oduc . The da abase, ha we will call CRCCRT, has been gene a ed using a quick ec ui ing wi h e- s ic ion on he deli e y ime s a egy1. Thus, he a ibu es ela ed wi h pe sonnel managemen (ASIMDY, HIREDY and TRNSDY) ake alue inside he in e al conside ed as quick and he a ibu e e- la ed wi h he deli e y ime managemen (MXSCDX) akes alues inside he in e als o ixed e m and mode a e e m. In his s udy has been analyzed wo ”cu ing sec- ions” o he CRCCRT da abase. The alues o he a iables o each ”cu ing sec ion” a e shown in a- ble 2. The objec i es o each ”cu ing sec ion” a e di e en acco ding o he used alues. Thus, he ob- jec i e o he cu ing sec ion 1 is o induce manage- men ules whe e he deli e y ime canno o e come a he es ima ed (320 days) in mo e han 10% (352 days) and quali y o he p ojec canno g ea e han 0.45 e o s/ asks. The objec i e o he cu ing sec ion 2 is equal conce ning deli e y ime, bu he e a e e- s ic ions s onge conce ning quali y. Tha is o say, he inal p oduc quali y canno g ea e han 0.35 e - o s/ ask. This new es ic ion will educe he numbe o ins ances and, consequen ly, he eliabili y o he induced knowledge, bu , howe e , he quali y o he inal p oduc will be g ea e han in he p e ious cu - ing sec ion. 1A quick ec ui ing s a egy has been analyzed since some esea ches (Ramos and Ruiz, 1998) ha e shown ha he ul illmen o he deli e y ime is a o ed by hese poli- cies hough he cos could be inc eased. Figu e 8: Visualiza ion by pa allel coo dina es o he man- agemen ules induced om cu ing sec ion 1. 5.1 Cu ing sec ion 1: es ic ions o ime and quali y I a da a mining me hod, e.g. ELLIPSES, is applied o he aining se gene a ed by he cu ing sec ion 1, hen a se o ules o he managemen o SDP can be ob ained. These ules will o e in o ma ion on he policy o pe sonnel managemen (ASIMDY, HIREDY, TRNSDY) and he maximum pos pone- men o he deli e y ime o he p ojec (MXSCDX) when he objec i e is o ob ain a inal p oduc wi h a deli e y ime (SCHCDT) less han 352 days and a quali y (ANERPT) less han 0.45 e o / asks; ega d- less o he cos o he necessa y e o o ca y ou he p ojec ( able 2, cu ing sec ion 1). The ules induced by ELLIPSES, labelled as ”good”, on his aining se a e: R1: A(11.9,3.14) & H(7.9,1.57) & M(1.185,0.015) R2: A(13.4,1.65) & H(9.3,1.53) & M(1.160,0.018) R3: A(13.6,1.01) & M(1.178,0.021) & T(8.6,1.17) The quali a i e models o hese ules a e2: R1: A(11.9,ML) & H(7.9,ML) & M(1.185,MS) R2: A(13.4,M) & H(9.3,ML) & M(1.160,MS) R3: A(13.6,MS) & M(1.178,MS) & T(8.6,M) The isualiza ion o g aphical ep esen a ionby pa - allel coo dina es o hese ules a e shown in igu e 8. The in e p e a ion o his knowledge would be: 2(L) La ge, (ML) Medium La ge, (M) Medium, (MS) Medium Sho and (S) Sho . 6 A Da a Mining Me hod o Suppo Decision Making in So wa e De elopmen P ojec s  Figu e 8R1): Asimdy, de ined in he in e al [5, 15], akes middle high alues (wi h cen e 11.9 and a ma gin o  3.14), Hi edy, de ined in [5,10], akes middle high alues, bu wi hou eaching he ex eme alues (cen e 7.9 wi h ma gin o  1.57) and Mxscdx, de ined in [1,1.2], akes e yhigh al- ues (cen e 1.185 and ma gin o  0.015), p ac i- cally, o he ex eme.  Figu e 8R2): Asimdy akes high alues (cen e 13.4 wi h a ma gin o  1.65), Hi edy akes high alues (cen e 9.3 and ma gin o  1.53) and Mxscdx akes middle high alues (cen e 1.160 and wi h a ma gin o  0.018).  Figu e 8R3): Asimdy akes high alues, bu wi h- ou eaching he ex eme alues (cen e 13.6 wi h ma gin o  1.01), Mxscdx akes high alues, bu wi hou eaching he ex eme alues (cen e 1.178 and ma gin o  0.021) and T nsdy, de ined in he in e al [5,10], akes middle and high alues, bu wi hou eaching he ex eme alues(cen e 8.6 and wi h a ma gin o  1.17). 5.2 Cu ing sec ion 2: es ic ions o ime and g ea e le el quali y The se o ules o he managemen o SDP ha can be ob ained om he aining se gene a edby he cu - ing sec ion 2 o e in o ma ion on he policy o pe - sonnel managemen (ASIMDY, HIREDY, TRNSDY) and he maximum pos ponemen o he deli e y ime o he p ojec (MXSCDX) when he objec i e is o ob ain a inal p oduc wi h a deli e y ime (SCHCDT) less han 352 days and he quali y o he inal p oduc (ANERPT) is less han 0.35 e o / asks; ega dless o he cos o he necessa y e o o ca y ou he p ojec ( able 2, cu ing sec ion 2). Thus, he cu ing sec ion 2 es ablishes a g ea e le el o quali y ha he cu ing sec ion 1. The ules induced by ELLIPSES, labelled as ”good”, on he aining se ob ained by cu ing sec- ion 2 om CRCCRT da abase a e: R1: A(13.5,1.57) & H(8.7,0.28) R2: A(12.4,2.04) & M(1.175,0.006) & T(6.9,1.19) R3: A(14.8,0.74) & H(9.9,1.20) & M(1.095,0.055) The quali a i e models o hese ules a e 2 : R1: A(13.5,M) & H(8.7,S) R2: A(12.4,M) & M(1.175,S) & T(6.9,M) R3: A(14.8,MS) & H(9.9,M) & M(1.095,ML) The isualiza ion o he ob ained ules by EL- LIPSES on his aining se is shown in Figu e 9. The in e p e a ion o his knowledge would be:  Figu e 9R1): Asimdy akes high alues (cen e 13.5 wi h a ma gin o  1.57) and Hi edy akes high alues, bu wi hou eaching he ex eme al- ues (cen e 8.7 wi h a ma gin o  0.28). Figu e 9: Visualiza ion by pa allel coo dina es o he man- agemen ules induced om cu ing sec ion 2.  Figu e 9R2): Asimdy akes high alues, bu wi h- ou eaching he ex eme alues (cen e 12.4 wi h a ma gin o  2.04), Mxscdx akes high alues, bu wi hou eaching he ex eme alues (cen e 1.175 and ma gin o  0.006) and T nsdy akes low and middle alues (cen e 6.9 wi h a ma gin o  1.19).  Figu e 9R3): Asimdy akes e y high alues (cen- e 14.8 wi h a ma gin o  0.74), Hi edy akes high alues (cen e 9.9 and ma gin o  1.20) and Mxscdx low and middle alues, bu wi hou each- ing he ex eme alues (cen e 1.095 wi h a ma gin o  0.055). 5.3 Analysis o he induced knowledge The manage can choose he managemen ule ha he wan s o apply, when he ules ha e been induced. This decision mus ake in o conside a ion o he s ea- u es o he p ojec : he ini ial a ailable esou ces, he equi emen s o he p ojec , he managemen policies as well as he ma u i y le el o he o ganiza ion o de- elopmen . Tha is o say, all induced ules canno apply di ec ly. Analyzing he ob ained esul s o bo h cu ing sec- ion, he bes ule o apply is R1 o he cu ing sec ion 2 acco ding o he c i e ia in o de o choose he ules es ablished in sec ion 3. The ule R1 is e y easy o apply, because he manage only mus supe ise wo a ibu es (ASIMDY and HIREDY) in o de o ob- ained an accep able le el o quali y. Bu his ule has an incon enience wi h ega d o o he induced ules: he in e als o ASIMDY and HIREDY a e less wide han in o he ules. Thus, he manage does no ha e a lo o ma gin when his ule is applied. Figu e 10 shows he e olu ion o he p ojec i he ules R1 and R3 o he cu ing sec ion 2 a e applied. Analyzing his igu e, we can see ha he deli e y ime is simila in bo h ules (350 and 351 days, e- spec i ely), bu he necessa y e o o ca y ou he p ojec in R1 (2615 echnicians/days) is lowe han he e o in R2 (2769 echnicians/days). Summa iz- ing, he wo ules ob ain simila esul s o deli e y ime and quali y, bu R1 educes he cos o he p ojec 7 ICEIS 2003 - Figu e 10: Resul s o he p ojec simula ion wi h he ules R1 and R3 o he cu ing sec ion 2. diminishing he necessa y e o o de elopmen . 6 CONCLUSION In his pape , wep esen a s a egy o induce knowl- edge in da abases o so wa e de elopmen p ojec s. The da abases a e gene a ed by simula ions o dy- namic models o he managemen p ojec s. A da a mining ool analyzes hese da a inducing he new knowledge. This s a egy can be used o make h ee analysis: a p io i analysis, moni o ing analysis and pos -mo em analysis We uphold he use o his new s a egy as opposed o adi ional s a ic model o simple dynamic models. Acknowledgmen s This wo k has been suppo ed by Spanish Resea ch Agency CICYT unde g an TIC2001-1143-C03-02. REFERENCES Abdel-Hamid, T. and Madnick, S. (1991). So wa e P ojec Dynamics: an In eg a ed App oach. P en ice-Hall. Aguila , J., Ramos, I., Riquelme, J., and To o, M. 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