Estimating Productivity of Software Development Using the Total Factor Productivity Approach

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1 Inernaonal Journal of Engneerng Busness anagemen ARICLE Esmang roducv of Sofare Develomen Usng he oal Facor roducv Aroach Regular aer achek Ondre 1* Hnlca Jr 2 and Heda Jan 3 1 Unvers of Economcs rague Dearmen of Busness Economcs Facul of Busness Admnsraon 2 Unvers of Economcs rague Dearmen of Busness Economcs Facul of Busness Admnsraon 3 Czech echncal Unvers n rague Dearmen of Bomedcal echnolog Facul of Bomedcal Engneerng * Corresondng auhor E-mal: ondre.machek@vse.cz Receved 2 Jul 2012; Acceed 27 Augus 2012 DOI : / achek e al.; lcensee Inech. hs s an oen access arcle dsrbued under he erms of he Creave Commons Arbuon Lcense (h://creavecommons.org/lcenses/b/3.0) hch erms unresrced use dsrbuo and reroducon n an medu rovded he orgnal ork s roerl ced. Absrac he desg conrol and omzaon of sofare engneerng rocesses generall requre he deermnaon of erformance measures such as effcenc or roducv. Hoever he defnon and measuremen of roducv s ofen naccurae and dffers from one mehod o anoher. On he oher hand economc heor offers a ell grounded ool of roducv measuremen. In hs arcle e roose a model of rocess roducv measuremen based on he oal facor roducv (F) aroach commonl used n economcs. In he frs ar of he arcle e defne roducv and s measuremen. We also dscuss he maor daa ssues hch have o be aken no consderaon. Consequenl e al he F aroach n he doman of sofare engneerng and e roose a F model of roducv assessmen. Keords oal facor roducv sofare develomen roducv roducv of rocesses 1. Inroducon In economcs a roducer s defned as an agen ransformng a se of nus no a se of ouus and he roducon rocess s defned b he roducon funcon. A smlar conce s used n engneerng here a rocess s defned as a se of nerrelaed asks ha ogeher ransform nus no ouus [1]. he desg conrol and omzaon of engneerng rocesses generall requre deermnaon of erformance measures such as effcenc or roducv. Hoever man models of measurng rocess erformance have usuall been derved from emrcal observaons and have found o be naccurae. Le s ake sofare develomen rocesses as an eamle. Several as sudes such as [2] [3] or [4] confrmed a farl large magnude of relave errors of he esmaes of he models. In he meanhle he smlar beeen engneerng rocesses and economc roducon rocesses has been noced b some researchers. Hu lan and Herz [5] roosed a model for sofare cos.nechoen.com In.. achek eng. bus. Ondre manag. Hnlca 2012 Jr Vol. and 4 Heda 34:2012 Jan: Esmang roducv of Sofare Develomen Usng he oal Facor roducv Aroach 1

2 esmaon based on he economc roducon heor hch roved o be more accurae han radonal COCOO [6] or SLI [7] cos esmaon models. easurng roducv goes beond cos esmaon snce caures no onl coss bu also revenues. oal facor roducv (F) s a mehod of measurng overall roducv of economes ndusres or ndvdual frms. Hoever snce roducv s no a roer hch s lmed o aggregaed enes F could also be used on a loer level of absraco n busness or engneerng rocesses hch conss of a seres of acves. he am of hs arcle s o roose he use of oal facor roducv mehods n he roducv evaluaon of sofare develomen rocesses. In he frs ar of he arcle e defne roducv and s measuremen and e nroduce oal facor roducv and ndees commonl used n measurng F changes. We also dscuss he maor daa ssues n he F aroach. Consequenl e al hs aroach on he rocess of sofare develomen. In he fnal ar e sugges a F model of sofare develomen roducv analss. 2. oal facor roducv and s measuremen radonall roducv s defned as a rao of ouu over nu. he oal facor roducv (F) aroach akes no accoun all ouus and nus of he evaluaed frm. herefore s necessar o aggregae he se of ouus and ouus so ha roducv becomes a scalar value. In racce F change s measured b roducv ndees or roducv ndcaors. Indees have mullcave for hereas ndcaors have addve form. F nde numbers can be based eher on dsance funcon or on rce aggregaon. Among measures based on dsance funco e can ce he almqus roducv nde [8] and he Hcks oorseen roducv nde [9]. he mos common F measures hch are based on rce aggregaon are he örnqvs roducv nde [10] and he Fsher roducv nde [11]. he ndees based on dsance funcons are raher heorecal and requre larger ses of cross seconal daa. B conras he cos based ndees are que sraghforard o calculae and necessae a mnmum of onl o observaons. Indees are a common ool n economcs o measure rce or quan changes beeen o erods he mos knon eamles beng he consumer rce nde (CI) or Do Jones sock nde. Snce n F calculaons e deal h he rao of ouu and nu quanes e ll use quan ndees. he calculaon s based on observed or esmaed quanes and rces of nu and ouu facors. In he follong e le = (12 ) denoe he nu quanes le = (12 ) denoe he ouu quanes = (12 ) s he vecor of nu rces = (12 ) s he vecor of ouu rces he number of nus and he number of ouus. Le us frs nroduce he Fsher nde of roducv [11]. I s a geomerc average of he Laseres and aasche ndees. he Laseres nde eghs he quanes h he rces of he basc erod. We can secf he Laseres ouu quan nde or nu quan nde resecvel as L n n res. 1 n 1 1 L m (1) 1 m 1 m m 1 he aasche nde eghs he quanes h he rces of he curren erod. he aasche ouu (nu) quan nde can be secfed as n n n 1 1 res. m (2) 1 m 1 1 m m 1 1 Snce roducv s defned as a rao of ouu over nu s ossble o defne he Fsher nde as he rao of geomerc averages of Laseres and aasche ouu and nu ndees so L F F (3) F L he örnqvs nde of roducv [10] s defned as a rao of ouu quan nde and nu quan nde. I s a eghed geomerc average of quan relaves. Usuall he o quan ndees are secfed n her logarhmc form as ln ln n ln 1 1 ln Fnall he örnqvs nde of roducv can be secfed as (4) 1 ln ln e (5) m 2 In.. eng. bus. manag Vol. 4 34:2012.nechoen.com

3 If he rces are no drecl observable s ossble o aromae hem usng eer esmaes or economerc mehods such as non lnear regresson. Fsher and örnqvs ndees have several neresng roeres because of hch he are classfed as eac and suerlave ndees (more on hs subec n [12]). If he roducon s reresened b a ranslog funco he örnqvs nde aromaes he deal almqus nde and smlarl f he roducon s reresened b quadrac funco he Fsher nde aromaes he deal almqus nde. Accdenall a sud [13] found ha ranslog and quadrac cos funcons are more suable for reresenaon of sofare roducon rocesses han he radonall consdered lnear or Cobb Douglas funconal forms. he above defned ndees are suable for measurng and analsng roducv of a sngle sofare develomen rocess. When comarng roducv across mulle subecs or rocesses he ndees have o sasf he roer of ransv. Hoever he Fsher and örnqvs ndees hemselves are no ransve. An eamle of rocedures of he converson of non ransve ndees no ransve ndees s he rocedure roosed b Caves Chrsensen and Deer (CCD) [8] and s ell descrbed n [14]. If I denoes he number of comared rocesses and I denoes he örnqvs nde for ar hen he ransve ndees can be obaned as I CCD I k 1 k 3. Daa ssues n measurng F changes 1/ I k I I (6) he measuremen of roducv usng he F aroach nvolves several daa ssues hch subsanall affec he resuls. 3.1 easuremen of Ouus he defnon and measuremen of ouus and her rces s one of he challengng asks. Ouus should reresen he comlee baske of servces and roducs rovded b he ransformaon rocess. he should reflec ho much s beng roduced h ha effor and he should no om he qual of servce. he defnon of he qual asec s arcularl challengng. oreover one of he man concerns s ha f he se of ouus s oo large one ma encouner he roblem of degrees of freedom and he analss becomes comlcaed. In hs case ma be suable o aggregae he ouus no smaller caegores n hch case he socalled Hcks Leonef condons for aggregaon should be reseced ([15] [16]). he rces of ouus should also be reaed carefull and rce level changes should no be omed. If he rces are no drecl observable s necessar o aromae her eghs n he oal revenue and derve he rces numercall. hese eghs are calculaed from he share of each ouu n he oal revenue of he rocess. hs aroach nvolves eher arbrar udgmens abou he relave morance or economerc esmaon of cos funcon (see e.g. [17]). here s an academc debae over hch of hese aroaches erforms he bes. Hoever hen rces of ouus are no drecl observable some degree of naccurac s raccall nevable. 3.2 easuremen of Inus Anoher challengng ask s o defne and measure accurael he nus and her rces. radonall he economc heor akes no accoun a leas he follong caegores of nu facors: labour (L) caal (K) and maerals (). Somemes hn maerals energ (E) and servces (S) are also consdered and all hese facors ogeher are referred o as KLES. Labour (L) s mos ofen measured b he number of emloees or man hours hch should be correced snce ousourcng of acves can dsor he resuls. oreover s referable o dsngush among he eole accordng o her sklls educaon and eerence snce more sklled emloees conrbue o he roducv groh o a greaer een. Because of hese dffcules labour s somemes ncororaed no oerang eendures (OE) hch are aken ogeher as an aggregae measure of labour and maerals. Hoever labour coss ofen reresen he maor oron of oal nu coss and herefore hs nu should be reaed carefull n order o oban relable F esmaes. Wage deflaors can be aken no consderaon o caure he effecs of ages nflaon. Hoever he mos conenous nu facor s he measuremen of caal (K). he caal nu should reflec he oal servce flo from caal asses used n he rocess. he asses can be of a angble or nangble naure such as comuers sofare n I chemcal reacors n chemsr roducon rocesses ransor equme heav machner ec. Of course he se of asses ll var a lo across ndusres and even coman dearmens. he caal can be measured drecl n hscal uns or ndrecl n mone value. Boh aroaches have her advanages and dsadvanages; he are dscussed n deal n [17]. he roducve caal sock can be measured b he ereual nvenor mehod roosed b OECD [18]. If e denoe he roducve caal sock b K hen.nechoen.com achek Ondre Hnlca Jr and Heda Jan: Esmang roducv of Sofare Develomen Usng he oal Facor roducv Aroach 3

4 K 0 I F (7) q 0 here h s an age effcenc rofle racng he loss n roducve effcenc as an asse ages akng values beeen 1 (hen an asses s ne) and 0 (hen has los s enre roducve caac). F s a reremen funcon ha quanfes he share of asses of age τ ha are sll n servce. hs funcon s declnng and akes values beeen 1 (hen all asses are n esence) and 0 (hen all asses have been rered). I s he nomnal nvesmen eendure on he asse a me τ hch s deflaed b an nvesmen rce nde q 0 here subscrs ndcae a rce nde for he asse of age zero (a ne asse) n ear τ. Follong he same manual he cos of caal (renal rce) can be deermned usng he follong formula: h q r d ) ( q q ) (8) ( 1 here q s he marke rce of a ne asse d s he derecaon rae and r s some measure of he cos of fnancal caal such as he marke rae of neres. Hoever s ossble o aromae he cos of caal nus usng regresson mehods follong [17]. 4. roducv n engneerng alcaons: sofare roec managemen Sofare develomen s clearl an eamle of rocess ransformng a se of nus no a se of ouus. Hoever some as sudes such as [19] found hs rocess o be noorous due o cos overruns and me delas. an scenss have red o measure roducv of sofare develomen roecs. In conform h he radonal defnon of roducv he varous mehods comare he rao of ouus and nus. Generall hoever he mehods do no ake no accoun all he ouus and all he nus hch are nvolved n he analsed rocess as requred b he oal facor roducv aroach. Recenl a sud [20] summarzed he mehods of measurng sofare develomen eam roducv. os of he auhors ([21] [22] [23] [24]) consdered onl ver smlsc measures of ouus and nus. For nsance he ouu s radonall reresened b lnes of code (LOC) or funcon ons (F). Bu hs smle measure does no caure eher qual or oher ossble ouus such as reusabl of he roduced code s comle ec. hch are no evden a frs sgh. Smlarl he se of nus s ofen reduced o man hours of labour. Such a measure s nohng less han a smle labour roducv a aral roducv measure; furhermore hese man hours are call no dfferenaed accordng o he knoledge and sklls of develomen eam members. In addo caal maerals and servces are generall omed from he roducv analss bu develomen sofare a cal nangble asse hch s subec o amorzaon reresens an moran nu of he rocess; he choce of rogrammng language as ell as rogrammng echnques clearl affec no onl he number of LOC or F bu also her qual. Usuall derecaon of hardare resources and oher maerals such as energ are consdered o be neglgble. We beleve ha hese facors could reresen a source of naccurac of he measuremen; he neglgence of qual of ouus as ell as mnor nus ossbl bases he roducv esmaes. he oal facor roducv aroach akes no accoun all ouus and all nus. Some more recen mehods descrbed n [20] ake no consderaon more sohscaed ses of ouus and nus. Besdes mahemacal models based on regresson echnques (see for eamle [25]) n her more recen orks (.e. [26] [27] or [28]) he auhors have ncluded he qual asec as ell as ools and oher resources. 5. F model of sofare develomen roecs F ndees can easl be esmaed usng common comung ools such as S Ecel or ALAB. In hs seco e roose a model of sofare develomen roec roducv measuremen based on he F aroach. 5.1 Ouu Defnons radonall he ouus of sofare develomen are measured b lnes of code (LOC) or funcon ons (F). hese o measures are hghl correlaed bu addonall he F aroach akes no accoun he comle (see e.g. [29]). o ncororae boh he quan and qual asecs e roose consderng code reuse comle funconal and lengh follong [28]. Reuse s measured b he esmaed ercenage of reused obec ons; comle s measured usng he bg O noaon famlar n comuer scence funconal b he funcon ons coun and lengh b akng no consderaon he dens of commens. Besdes hese measures of code e roose ncororang oher ouus: daa documenaon and ranng as roosed b [27]. o sum u e roose he follong se of ouus: 1: Reuse (ercenage of reused obec ons) 2: Comle (delvered source nsrucons) 3: Funconal (funcon ons coun) 4 In.. eng. bus. manag Vol. 4 34:2012.nechoen.com

5 4: Lengh (LOC correced h resec o he dens of commens) 5: Daa (lnes of roduced useful daa) 6: Documenaon (lnes of roduced documenaon) 7: ranng (number of raned ersons) 5.2 Inu Defnons os of he esng aroaches ake no accoun onl he labour nu. Hoever s desrable o dfferenae he saff accordng o her sklls. Follong [27] e can consder a leas four caegores of labour engneerng esng managemen and suor. o avod a smle labour roducv calculao s necessar o nclude oher nu facors. One ma consder he roducve caal sock (hardare sofare and lcences) and maerals and servces hch can be aggregaed ogeher snce he reresen onl a mnor oron of sofare develomen coss. o summarze e roose he follong se of nus: 1: Engneerng labour (man hours) 2: esng labour (man hours) 3: anagemen labour (man hours) 4: Suor labour (man hours) 5: aerals and servces (deflaed value) 6: angble caal sock (deflaed value) 7: Inangble caal sock (deflaed value) 8: Oher caal (deflaed value) 5.3 Ouu and Inu rces Deermnaon he rces of nus and ouus are lkel no o be drecl observable. In hs case s necessar o esmae hem. As menoned before he esmaon nvolves eher arbrar udgmen or economerc mehods. In our model e follo [17] and use boh mehodologes. he rces of nus can be esmaed usng he former aroach. Labour coss maerals and servce value are usuall eas o measure as ell as he oal revenue of he roec. he nu egh gven o labour s sml he rao of he labour coss o oal revenue of he roec as ell as he maerals and servces rao. he aggregae egh of he res of nus s gven b one mnus labour share mnus maerals and servces share. hs aggregae egh s hen dvded b he aromae shares of he caal caegores n he oal value of he asses. he oal roec coss are hen dvded accordng o he eghs o he nu caegores. B dvdng he caegor coss b he number of arorae uns of nu e deermne he vecor of coss of nus. Once he coss of nus are calculaed s ossble o esmae he coss of ouus usng regresson mehods. Follong [17] e use he Leonef mul ouu cos funcon hch akes he form a 1 b C( ) (9) here denoes he number of nus denoes he number of ouus s an nu rce s an ouu quan and s a me rend reresenng echnologcal change (he number of ear). Usng he Shehard s lemma knon n economcs e can derve he nu demand equaons 1 2 a b 1 (10) B alng a sandard non lnear regresson o hese equaons e oban he nu ouu coeffcens a and he coeffcens b. o e can esmae he ouu eghs as 2 a 1 b 1 h (11) 2 a 1 b 1 1 B dvdng he oal revenue accordng o he eghs and number of ouus e deermne he coss of ouus. 5.4 oal Facor roducv Calculaons Once e have defned and measured he ouus nus and her coss and e can easl calculae he Fsher or örnqvs roducv ndees as descrbed n he revous secons. hese ndees can be used o assess and evaluae roducv changes and her sources. In he case of mullaeral comarsons.e. hen comarng among mulle roecs or enes s desrable o conver he ndees no her ransve for for eamle usng he mehod descrbed n [14]. 6. Concluson Relable esmaon of he roducv of sofare develomen rocess s an moran ask for sofare engneerng raconers and academcs. he oal facor roducv aroach s a ell grounded and esablshed mehodolog frequenl used n economcs. I s mos ofen used a he aggregae level; hoever F s no lmed o hole economes or ndusres bu can also be used n assessng roducv of comanes dearmens and busness rocesses. In hs arcle e roosed a model of sofare develomen roec roducv measuremen based on he F aroach. In he frs ar of he arcle e defned oal facor roducv and s measuremen. We suggesed he use of he örnqvs and Fsher quan ndees o measure.nechoen.com achek Ondre Hnlca Jr and Heda Jan: Esmang roducv of Sofare Develomen Usng he oal Facor roducv Aroach 5

6 he F changes across me erods. When comarng mulle sofare develomen rocesses he ransve versons of he ndees should be used. In he follong seco e deal h he maor daa ssues hch have o be aken no consderaon hen measurng nus ouus and her rces. Consequenl e dscussed he ssues of measurng roducv n engneerng alcaons n arcular n sofare roec managemen. We found ou ha mos of he currenl used mehods are n fac smle labour roducv measures and do no nclude all nus and ouus ha arcae n he develomen rocess. In he fnal ar e suggesed a F model of sofare develomen roducv analss. In order o caure all he relevan ouus and he qual e roosed ncludng he rae of code reuse he code comle funconal and lengh. Furhermore e suggesed consderng oher ouus of he sofare develomen rocess namel daa roduced documenaon and ranng of ersons. Concernng he nus e roosed o dfferenae he labour nu accordng o he funcon of he develomen eam funcons: a leas engneerng esng managemen and suor labour force should be ncluded n he analss. Besdes labour e refer o consder oher nu facors: maerals and servces angble and nangble asses and oher caal. All hese facors ogeher reflec he comlee se of classcal nu facors consdered n economc heor. Fnall e descrbed he rocess of he deermnaon of nu and ouu rces n case he are no drecl observable. Boh eer esmaes and regresson mehods can be used. An accurae esmaon of roducv changes could hel sofare engneers denf srenghs and eaknesses of develomen rocesses and mrove he useful ouu of he rocess hch n ur could be accomlshed h less effor. Hoever emrcal evdence s needed hch could be he focus of he fuure research on hs subec. 7. Acknoledgmens hs arcle as ren h fnancal suor from he Inernal Gran Agenc of he Unvers of Economcs n rague roec no. F3/22/2011 ʺRegulaon of energ ules n Cenral Euroe and he ossbles for mrovemen.ʺ 8. References [1] echamerca (1999) ASI EIA 632 Sandard: rocesses for Engneerng a Ssem. echamerca. [2] ohan S (1981) Sofare cos esmaon: resen and fuure. Sofare: racce and Eerence 11: [3] Kemerer C.E (1987) An emrcal valdaon of sofare cos esmaon models. Communcaons of he AC 30: [4] Jorgensen (1995) Eerence h he accurac of sofare manenance ask effor redcon models. IEEE ransacons on Sofare Engneerng 21. [5] Hu Q lan R. Herz D.B (1998) Sofare cos esmaon usng economc roducon models. Journal of anagemen Informaon Ssem 15: [6] Boehm B.W (1981) Sofare Engneerng Economcs. e ork: rence Hall. [7] unam L.H (1992) easures for Ecellence: Relable Sofare on me hn Budge. e ork: ourdon ress. [8] Caves D Chrsensen L Deer W.E (1982) ullaeral comarsons of ouu nu and roducv usng suerlave nde numbers. Economc Journal 92: [9] Deer W.E (1992) Fsher deal ouu nu and roducv ndees revsed. Journal of roducv Analss 3: [10] örnqvs L (1936) he bank of Fnlandʹs consumon rce nde. Bank of Fnland onhl Bullen 10: 1 8. [11] Fsher I (1922) he akng of Inde umbers. Boson: Houghon ffln. [12] Deer W.E (1976) Eac and suerlave nde numbers. Journal of Economercs 4: [13] Hu Q (1997) Evaluang alernave sofare roducon funcons. IEEE ransacons of Sofare Engneerng 23. [14] Coell.J rasada Rao D.S O Donnell C. J Baese G.E (2005) An nroducon o Effcenc and roducv Analss. e ork. Srnger. [15] Leonef W (1936) Comose commodes and he roblem of nde numbers. Economerca 4: [16] Hcks J (1939) Value and Caal. Oford: Clarendon ress. [17] Larence D Deer W.E (2006) Regulang elecrc neorks: he ABC of seng n e Zealand. In: Coell Larence D. edors. erformance easuremen and Regulaon of eork Ules. orhamon: Edard Elgar [18] OECD (2001) easuremen of aggregae and ndusr level roducv groh. ars: OECD. [19] Jenkns A. aumann J.D Weherbe J.C (1984) Emrcal nvesgaon of ssems develomen racces and resuls. Informaon and anagemen 7. 6 In.. eng. bus. manag Vol. 4 34:2012.nechoen.com

7 [20] Sudhakar G. Farooq A anak S (2012) easurng roducv of sofare develomen eam. Serban Journal of anagemen 7: [21] ausorhe R.C (1982) Saffng mlcaons of sofare roducv models. roc. 7h Annual Sofare Engneerng Worksho ASA/Goddard Greenbel. [22] Banker R.D Daar S. Kemerer C.F (1991) A model o evaluae varables macng he roducv of sofare manenance roecs. anagemen Scence 37. [23] ook.e Vouk.A. (1999) A model of correlaed eam behavor n a sofare develomen envronmen. roceedngs of IEEE Smosum on Alcaon secfc Ssems and Sofare Engneerng and echnolog ASSE 99 Rchardson. [24] Blackburn J.D Lare.A Van Wassenhove L. (2002) Brooks la revsed: Imrovng sofare roducv b managng comle. Vanderbl Unvers Workng aer. [25] ocke S (2000) he effec of eam sze on eam roducv and roec cos. Lecure noes of sofare roec manageme CSSE 515 Seale Unvers. [26] Krshnan.S Krebel C.H Kekre S ukhoadha (2000) An emrcal analss of roducv and qual n sofare roducs. anagemen Scence 46: [27] Card D. (2006) he Challenge of roducv easuremen. roceedng of acfc orhes Sofare Qual Conference orland. [28] elh E Amadn I.F (2008) odelng sofare reuse n radonal roducv model. Asan Journal of Informaon echnolog 7: [29] Caers J (1994) Funcon ons: A ne a of lookng a ools. Comuer 27: nechoen.com achek Ondre Hnlca Jr and Heda Jan: Esmang roducv of Sofare Develomen Usng he oal Facor roducv Aroach 7