A New Schedule Estimation Technique for Construction Projects

Transcription

1 A New Schedule Esimaion Technique for Consrucion Projecs Roger D. H. Warburon Deparmen of Adminisraive Sciences, Meropolian College Boson, MA hp://people.bu.edu/rwarb DOI /omcj Research paper Keywords Schedule esimaion, Schedule performance index, Earned schedule, Consrucion labor profile Allen sudied hundreds of consrucion projecs and developed an accu-rae, pracically useful model of heir labor profiles. We combine Al-len s labor profile wih sandard Earned Value Managemen (EVM) echniques and derive a simple, pracical formula ha esimaes he fi-nal schedule from early projec daa. The schedule esimaion formula is exac; i requires no approximaions. The esimae is also surprisingly accurae and available early enough in he projec for he projec manager o be able o ake appropriae acions. We use one of Allen s real-world consrucion daa ses o calibrae and validae our heorei-cal model. Early esimaes of he final schedule are remarkably accu-rae, and available early enough o be used o effec managemen changes. We also explain why a curren schedule esimaion mehod, Earned Schedule (ES), has a poor heoreical foundaion and show ha our model is superior o ES in predicing consrucion schedule delays. The model should provide warning of schedule delays early enough for projec managers o ake correcive acions. roger d. h. warburon a new schedule esimaion echnique for consrucion projecs pp

2 INTRODUCTION Earned Value Managemen (EVM) has been successful in providing projec manag-ers wih early warning signals of projec rouble and such signals were found o be re-liable as early as 15% ino a projec (Chrisensen 1993, Chrisensen & Templin 2002). The Pracice Sandard for EVM (PMI 2005) defines he basic elemens and suggess ha EVM can play a crucial role in esimaing coss (Chrisensen 1993, Chrisensen & Templin 2002). Hisorically, before i was re-engineered as Earned Value Managemen, he ideas were par of he Program Evaluaion and Review (PERT) echnique and laer became he Cos and Schedule Conrol Sysems (CSSC) ool (Fleming and Koppelman 1999). However, he applicaion of EVM o schedule deerminaion is problemaic because he key schedule indicaor, he schedule performance index (SPI), is ime-dependen (Kerzner 2006, Lipke 2003). Therefore, while he SPI indicaes a delay, i canno be used o predic he lengh of a schedule delay (Meredih & Manel Jr. 2011). Three schedule forecasing mehods have emerged o address his deficiency: Planned Value (Anbari 2003), Earned Duraion (Jacob 2003), and Earned Schedule (Lipke 2003). There is saisical suppor for he idea ha all mehods seem o work in pracice (Vanhoucke & Vandevoorde 2007, Vanhoucke & Vandevoorde 2006, Lipke, Zwikael & Anbari 2009). However, all schedule esimaion formulae appear o be based on a consan labor rae, so ha he cumulaive labor profile is linear in ime. Why should a model based on linear cumulaive profiles for planned and earned value apply o projecs whose labor curves are S-shaped? One can consider a linear profile o be an approximaion of an acual S-curve. Wha is needed is a simple and effecive mehod for esimaing a projec s final schedule ha is based on a sound heoreical model ha has been calibraed by real-world daa. In his paper, we provide such a heory for schedule esimaion for he consrucion indusry. The objecive is o provide a formally grounded heory and o derive a reliable, pracical schedule esimaion mehod. We begin by characerizing he labor rae curve proposed for he consrucion in-dusry by Allen (1979). We develop an equaion ha describes Allen's labor rae curve, as well as he corresponding cumulaive labor S-curve. From early projec daa, we derive he heoreical formula ha allows us o accuraely esimae he acual final schedule. The expression for he schedule is sraigh forward and exac. I requires no ap-proximaions and so he errors in he final schedule esimae should be solely due o he degree o which he projec daa follows he proposed labor rae profile. Allen used hundreds of real-world daa ses o calibrae his profile and demon-sraed ha i provides a remarkably accurae descripion of consrucion projecs. One of Allen's examples concerns a projec planned o be compleed in 20 weeks, bu ha acually ook 40 weeks. From ha Allen daa se, we obain a surprisingly accurae esimae of he final schedule ha can be made quie early in he projec, a resul ha adds pracical credibiliy o he heory. We conclude wih a discussion of he wid-er projec managemen implicaions. Lieraure Earned Value Managemen (EVM) is designed o measure a projec's acual progress agains is plan (Fleming & Koppelman 2005). There are many merics ha work well in he forecas of a projec s final cos (Chrisensen 1993). However, here are significan issues when using EVM o esimae he schedule (Lipke 2003, Lipke e al. 2009, Meredih & Manel Jr. 2011). Three mehods have been proposed o address his shorcoming in schedule esimaion: Planned Value, Earned Duraion, and Earned Schedule. The Planned Value mehod calculaes a planned value rae as PVRae = BAC/ PD (Anbari 2003). This mehod uses averages, and so is predicions will be accurae o he exen ha he averages represen acual, ime-dependen quaniies. In he Earned Duraion mehod he performance needed o finish wihin he planned duraion is represened by a quaniy denoed as he To-Complee SPI, TCSPI (Jacob 2003). For each ime uni spen on he remaining work, TCSPI ime unis are required o be earned in order o finish according o he plan. Lipke (2003) defined earned schedule (ES) wih a phenomenological consrucion and explained i furher in his book (Lipke 2010). Sraon (2007) provided one of he firs formal definiions for ES, which is illusraed in Figure 3. The ES mehod has been shown o ouperform oher forecasing mehods (Vanhoucke & Vandevoorde 2007, Vanhoucke & Vandevoorde 2006). Jacob & Kane (2004) argued ha EVM can only be used o measure performance when SPI merics are used a he aciviy level, and no a higher WBS levels. Their simple example leads o misleading resuls, because delayed aciviies ha are no on he criical pah should no conribue o schedule merics. According o Vanhoucke & Vandevoorde (2006), all forecasing mehods yield similar resuls. This has also been observed by Jacob & Kane (2004), who aribue he high correlaion of all mehods o he fac ha hey apply he same basic parameers. More imporanly, and somewha underappreciaed, is ha he heory of all mehods is based on he lineariy of he cumulaive labor profile. Unforunaely, mos projecs seem o follow a non-linear, S-shaped, cumulaive labor curve and, so, he lineariy as-sumpion makes he accuracy of he schedule 1076 organizaion, echnology and managemen in consrucion an inernaional journal 6(3)2014

3 predicion formulae quesionable, a leas from a heoreical perspecive. Recenly, Lipke e al. (2009) sudied 12 projecs and esimaes of he final cos and he duraion were claimed o be sufficienly relia-ble for general applicaion of he ES forecasing mehod. While he saisical suppor is conclusive, no heoreical underpinning for ES was provided and, so, we are lef wih he quesion of precisely where he model is applicable. In general, he validiy of S-curves in consrucion was esablished by Chrisian & Kallouris (1991). Allen formalized he shape of he S-curve by proposing ha a rap-ezoidal hisogram accuraely describes he labor rae on consrucion conracs (Allen 1994) and applies o enire projecs, sub-conracs, and even individual rade work. Using labor profiles has proved successful for esimaing and racking projecs in oher indusries. Cioffi (2006a) showed how a labor profile curve ofen used in popu-laion dynamics can be applied o projec S-curves, and gave a fascinaing example of is applicaion o he developmen of he Oxford English Dicionary, a projec span-ning many decades (Cioffi 2006b). One of he firs heoreical models for including ime dependence ino EVM was proposed by Warburon (2011), who derived ime-dependen expressions for he planned value, earned value, and acual cos, along wih he cos and schedule per-formance indices. The model was buil on he well-esablished Punam-Norden-Rayleigh (PNR) labor rae profile and accuraely prediced boh he cos and he schedule early in he projec. Warburon also applied he model o a well-known sofware daa se, esimaing he projec's final cos and schedule from early projec daa, which converged faser o he correc answer wih less variabiliy han he sandard Esimae-a-Compleion (EAC) formula. ALLEN S CONSTRUCTION LABOR RATE PROFILE Allen s managemen perspecive is suppored by he fac ha on well run con-srucion projecs, he labor rae profile arises from managemen applying resources a he appropriae ime. The firs sage of he projec is a linear build up from zero as work becomes progressively more available. Planning, ordering maerials and under-sanding of he local condiions requires fewer, bu criical, people and more supervi-sion. These key people recrui local crews as more asks become available o work on. In he second sage, which is abou 50% hrough he schedule, a consan level of ef-for is reached where condiions are opimal. Too many crews would over-crowd he area, while oo few would reduce produciviy. In sage hree, he labor is gradually reduced as crews run ou of work. Allen validaed his labor profile on a wide range of projecs and subconracor effors. In one paricularly impressive analysis, Allen summarized he S-curves for 40 differen elecrical conracors on 54 building projecs in 32 ciies. Remarkably, he en-ire variaion in heir ime-scales is less han 10%. The inescapable conclusion is ha Allen's profile is an excellen fi o a wide variey of consrucion projec daa. 100% 80% Figure 1: Allen s consrucion projec daa and he associaed rapezoidal labor rae profile. people on sie 60% 40% 20% 0% weeks roger d. h. warburon a new schedule esimaion echnique for consrucion projecs pp

4 Allen's labor rae profile for a paricular consrucion projec is shown in Figure 1. The verical bars show he acual number of workers on sie each week. The acual la-bor rae can be accuraely represened by a rapezoid. In he firs phase, he labor increases linearly o a peak, which occurs abou half way hrough he projec. The la-bor remains consan a his peak value unil he 75% compleion poin. The labor is hen reduced linearly o zero a he end of he projec. Since he rapezoidal labor rae profile displays he acual number of people on sie, i is direcly proporional o he acual labor cos, ac(). We use lower case leers o indicae insananeous (weekly) quaniies, while capial leers are used for cumula-ive quaniies. The end of he projec is denoed as Te. The linear ramp up spans 50% of he schedule, [0, Te/2]. The second sage lass from 50% o 75% of he projec, [Te/2, 3Te/4]. In he hird sage, he labor rae is reduced linearly o zero, [3Te/4, Te]. The peak value of he labor rae curve is a he value, Pa. Thus, he equaion for he rape-zoidal acual labor rae profile, applicable o consrucion, is: { 2Pa T e ac() = Pa 4Pa 1 T e ( ) This equaion is ploed in Figure 1, where i can be seen ha he agreemen be-ween heory and pracice is excellen. Allen had access o hundreds of real-world da-a ses, which esablishes (1) as an accurae descripion of consrucion projecs. he planned labor rae also has a rapezoidal shape, an assumpion ha is well verified by Allen's daa ses. The planned compleion ime for he projec is Tp and he peak in he planned la-bor rae curve is denoed as Pp. Therefore, he expression for he planned value, pv(), has he same form as (1) wih Pp replacing Pa and Tp replacing Te. The weekly planned value, pv(), is ploed in Figure 2. The cumulaive Planned Value, PV (), is defined as he cumulaive sum of he weekly planned values, so: PV () = 0 pv () d. Eq. (2) generaes a non-linear S-curve. The cumulaive planned value, PV (), is ploed in Figure 3 and shows he ypical S-curve. The oal labor, L, is given by he area under he labor rae curve, which is easily calculaed as he sum of he wo riangles and he quadrilaeral: 5 L = PV T e* 8 0 < < T e / 2 T e < < 3T e / 4 2 3T e < < T e. 4 The oal planned labor is he budge for he projec, which is also given by he fi-nal value of he S-curve, i.e., PV (Te): 5 L = PV (T e) = ( ) P e* 8 This is Allen's Rule, which says ha he Peak Labor is approximaely 1.6 imes he Average Labor. While i appears ha Allen derived his rule from empirical observa-ion, we deduced i here as an inheren propery of he rapezoidal labor rae profile. We now derive an expression for he earned value. We assume ha he projec s acual execuion does no necessarily follow is planned execuion. The projec was planned o end a Tp, bu i is delayed and ends a ime, Te > Tp. The key assumpion is ha while he earned value labor rae curve is delayed relaive o he planned value labor rae curve, hey boh have a rapezoidal shape. The oal planned labor equals he oal earned value labor, so he earned value has a smaller value for he peak, which we denoe as Pe < Pp. Therefore, he expression for he earned value, ev(), has he same form as (2) wih Pe replacing Pp and Te replacing Tp. Finally, we assume he acual labor is proporional o he earned value (as op-posed o he plan). This assumpion is reasonable because earned value accumulaes as deliverables are compleed and i is reasonable o assume ha he earned ex-pendiures acually follow he deliverables. Therefore, we wrie: ac() = (1+c)ev(), where c represens a cos overrun facor. In his paper, we are more ineresed in schedule han cos, so he cos formula is no paricularly imporan in wha follows, bu i does allow us o complee he model, and in a reasonable and sraighforward man-ner. The weekly planned, earned and acual daa are shown in Figure 2. Consrucion EVM In EVM parlance, he weekly rae a which aciviies are planned o be compleed is called he planned value, pv(). Following Allen, we assume ha We can rearrange (4) as follows: 5 P = 8 Toal Labor T e = 1.6 x Average Labor organizaion, echnology and managemen in consrucion an inernaional journal 6(3)2014

5 140% 120% PV 100% 80% AC people on sie 60% 40% EV 20% 0% weeks Figure 2 Weekly planned value, earned value, and acual cos for he consrucion labor profile AC 1500 Figure 3 Cumulaive planned value, earned value, and acual cos for he consrucion labor profile. All hree are non-linear S-curves PV EV 500 δ roger d. h. warburon a new schedule esimaion echnique for consrucion projecs pp

6 CPI Subsiuing for Pp/Pe from (9) ino (8), gives: T SPI = 2 p T 2 e Therefore, he new esimae of he schedule is deermined from: T SPI = 2 p T 2 e T e = T p SPI As i was for he planned value, he cumulaive versions are defined as he sum of he weekly planned values, so: EV () = 0 ev (s) ds AC () = 0 ac (s) ds These equaions for he cumulaive earned value and acual cos for he Allen pro-file are S-curves, and are shown in Figure 3. As a specific example, we have used he daa from Figure 2. The projec ha was supposed o be complee afer 20 weeks, bu was delayed and, acually, finished afer 40 weeks. There is a cos overrun, which is indicaed by he AC() curve rising above he PV () curve. Esimaing The Final Schedule In he previous secion, we deermined ha he projec was significanly delayed. I is of ineres, herefore, o ask how early in he projec could one deec he delay and a wha poin could one accuraely esimae he new schedule? SPI Figure 4 CPI() and SPI() for he consrucion projec labor rae profile. In he early phase of he projec (up o Te/2), he PV(), EV() and AC() are given by: PV () = EV () = AC () = (1 + c) EV (). 2 T p 2 Te Therefore, he SPI and CPI are given by: EV () SPI = CPI = PV () EV () AC () A he end of he projec, all of he planned labor has been earned and, so, he oal planned value equals he oal earned value. Using (4) for he oal labor gives: L = 5 8 Pp Tp = 5 8 Pe Te Early in he projec, where he linear expressions for he planned and earned val-ue labor raes are valid, he SPI is a consan. Therefore, if we measure he SPI early on, an esimae of he final schedule is available from (10). Therefore, early in he projec, a value can be deermined for he SPI, and he fi-nal schedule can be accuraely esimaed. This is shown in Figure 5, where (10) was used o esimae he final schedule. Afer only 4-5 weeks, he esimae of he final schedule is quie good and i shows ha he schedule has doubled. We emphasize ha he esimae for he final schedule from (10) is exac, no ap-proximaions were required. Eq. (10) only depends only on he assumpion ha he planned and earned value raes are described by rapezoidal funcions. Even hough he SPI is a funcion of ime, he esimae in equaion (10) is a consan because he ime cancels from (8). The resul hen simply follows from he applicaion of sandard EVM definiions. Comparison Wih Earned Schedule The Earned Schedule a ime,, is denoed as, ES(), and is defined as he ime of he inersecion of he cumulaive earned value curve a ime,, projeced back o he planned value curve (Lipke 2010). This consrucion is shown in Figure 3. Mahemaical-ly, he earned schedule inersecion is defined as: EV() = P ( - δ), where δ is defined as he schedule delay. In he early sages, EV () and PV () are given by (7), so: 1080 organizaion, echnology and managemen in consrucion an inernaional journal 6(3)2014

7 schedule esimae ACTUAL PLAN consrucion case o esimae he final schedule. The imporan conclusion is ha we have a simple, exac expression for he sched-ule esimae for he consrucion labor profile, which is based on a sound heoreical model. Early in he projec, we can esimae he final schedule using he sandard SPI, which should lead o improved projec planning and racking. References 10 Allen, W. (1979). Developing he projec plan. Engineering Insiue of Canada Annu-al Congress Workshop, Torono, weeks Figure 5 Early esimaes of he final schedule. Allen, W. (1994). A pragmaic approach o using resource loading, producion and learning curves on consrucion projecs. Canadian Journal of Civil Engineering 21, Anbari, Frank T. (2003). Earned Value Projec Managemen: Mehod and exensions. Projec Managemen Journal 34(4), 12. Early on, he expression for δ() is a linear funcion of ime. Since he earned schedule is ES() = - δ(), we have: Te δ() = ( 1 ) Tp Te ES() = ( ) Tp The earned schedule is also a funcion of ime. However, since his funcion is only good up in he linear region of he rapezoid (Tp < 10), we do no have an expression for ES(Tp), and, herefore, canno deermine Te. Therefore, while here may be a saisical jusificaion for using ES (Lipke e al. 2009), he above equaions do no provide a heoreical jusificaion o suppor is use. Therefore, from a heoreical perspecive, we canno conclude wheher ES is valid when applied o consrucion projecs. Conclusions We derived an analyical expression for he labor profile for consrucion conracs and showed how early values of he SPI can be used o esimae he revised schedule. The final schedule formula for is exac, no approximaions were required. We demonsraed he model s applicaion by analyzing a consrucion projec whose planned schedule was 20 weeks and afer only 5-6 weeks, we were able o quie accuraely predic he evenual, acual compleion dae of 40 weeks, and wihin abou 10%. Afer 10 weeks, he final schedule was esimaed o wihin 5%. A sand-ard SPI calculaion would have indicaed a delay, bu i would no have allowed us o esimae he final schedule. We compared our model o he earned schedule (ES) approach. While he growh in ES can be measured, here is no heoreical formula ha relaes i o he final sched-ule. Therefore, i canno be used in he Chrisensen, D. S. (1993). The esimae a compleion problem: A review of hree sudies. Projec Managemen Journal 24(1), Chrisensen, D. S. & C. Templin (2002). EAC evaluaion mehods: Do hey sill work? Acquisiion Review Quarerly pp Chrisian, J. & G. Kallouris (1991). An exper sysem for predicing he cos-ime pro-files of building aciviies. Canadian Journal of Civil Engineering 18, 814. Cioffi, D. F. (2006a). Subjec experise, managemen effeciveness, and he newness of a projec: The creaion of he Oxford English Dicionary. Projec Managemen Insiue Research Conference, Monreal, Projec Managemen Insiue. Cioffi, Denis F. (2006b). Compleing projecs according o plans: An Earned-Value improvemen index. Journal of he Operaional Research Sociey 57, Fleming, Q. W. & J. M. Koppelman (2005). Earned Value Projec Managemen 3rd edn, Projec Managemen Insiue, Newown Square, PA. Fleming, Q. W. & J. M. Koppelman (1999). The Earned Value Body of Knowledge Seminar roger d. h. warburon a new schedule esimaion echnique for consrucion projecs pp

8 and Symposium, Projec Managemen Insiue, Newown Square, PA, January. Jacob, D.S. (2003). Forecasing projec schedule compleion wih earned value merics. The Measurable News 1(11), 7-9. Jacob, D.S. & M. Kane (2004). Forecasing schedule compleion using earned value merics revisied. The Measurable News 1(11). Kerzner, H. (2006). Projec Managemen: A Sysems Approach o Planning, Scheduling, and Conrolling, 9h ed., John Wiley & Sons, New York, NY. Lipke, W. (2003). Schedule is differen. The Measurable News Lipke, W. (2010). Earned Schedule, Lulu (R) Publishing, Lexingon, KY. Lipke, W, O. Zwikael, Henderson K. & F. Anbari (2009). Predicion of projec ou-come. The applicaion of saisical mehods o Earned Value Managemen and Earned Schedule performance indexes', Inernaional Journal of Projec Man-agemen 27, Managemen: A Managerial Approach, 8h edn, John Wiley & Sons. PMI (2005), Pracice Sandard for Earned Value Managemen, Projec Managemen Insiue, Newown Square, PA. Sraon, Ray (2007). Applying earned schedule analysis o EVM daa for esimaing compleion dae. AACE Inernaional Transacions pp Vanhoucke, M. & S. Vandevoorde (2006). A comparison of differen projec duraion forecasing mehods using Earned Value merics. Inernaional Journal of Pro-jec Managemen 24, Vanhoucke, M. & S. Vandevoorde (2007). A simulaion and evaluaion of Earned Value Merics o forecas he projec duraion', Journal of he Operaional Re-search Sociey 58, Warburon, R. D. H. (2011). A ime-dependen Earned Value model for sofware pro-jecs. Inernaional Journal of Projec Managemen 29, Meredih, J. R. & S. J. Manel Jr. (2011). Projec 1082 organizaion, echnology and managemen in consrucion an inernaional journal 6(3)2014