Project lfe cycle and resource usage Phases Project Management Project Phases the S curve Eng. Gorgo Locatell RATE OF RESOURCE ES Conceptual Defnton Realzaton Release TIME Cumulated resource usage and the S curves Sgmod Functon Why ths form? RATE OF TIME Phase of ntal acceleraton Few qualfed resources Operatve conductons and means moblzaton progressve defnton Learnng curve Central phase Resources moblzaton Hgh and constant usage rates Phase of fnal deceleraton Constrants from work already done, physcal mpedments and procedures Draggng effect 3 4 Connecton between project progress and resource usage Project s progress measure RATE OF PRODUCTIVITY RATE Realzed physcal quanttes Equvalent n man-hours for the realzed work Total sunk cost (accountng progress) 5
Project s macro-phases progress Objectves for the project and macro-phases analytc representaton through the S curve % of progress reserved" for supply 9 8 Electromechancal assemblng start 7 Assembles completon buldng yard start 5 engneerng 4 Constructon/assembles 3 3 4 5 7 8 9 Project duraton 7 Resources cumul lated usage % % 9% 8% 7% - Plannng % 5% 4% 3% Tme now % % - Control % % % % 3% 4% 5% % 7% 8% 9% % Progressve Tme % 3- Redevelop 8 S Curves Use durng the plannng phase The S curves are a tool used durng the project plannng phase at aggregate level to: assess the tme/cost objectves feasblty f the reference ponts o Contractual mlestones o Schedule mlestones plan the resources usage and assess the congruence wth the progress rates study the correlatons among the macro project phases S Curves Use durng the control and redevelopment phase The S curve are useful durng the project realzaton phase to: run an ntegrated tme/cost analyss (C/S and CS methodology) make a comparson budget vs. fnal statement (C/S and CS methodology) assess the feasblty of respectng the project tme/cost objectves perform an (eventual) tme/cost estmate at competton redevelop the project schedule consderng the tme-now stuaton to acheve the orgnal (or new) tme/cost objectves redevelop the necessary resources and to assess ther avalablty 9 S Curves analytc representaton Formal requrements The S Curve s normalzed wth: n abscssa the tme passed, epressed lke percentage of the overall project duraton n ordnate the cumulated progress n terms of work done compared to hs the total amount ; y ; passng through (,) and (,) Monotonc curve not decreasng (dervatve always postve) Upward concavty plus nflecton pont, downward concavty (that s frst dervatve ncreases, mamum, frst dervatve decreases) S Curves analytc representaton Substantal requrements Fleblty to ft to the dfferent projects progress typologes (e. g. front/back loaded) Connecton wth the operatve nformaton o Contractual or schedule mlestones o Mamum progress rate on the mean value Easy to mplement and manpulate (e.g. mplementaton n a spreadsheet)
Classfcaton of the model proposed n lterature and used n practce. Lnear/trapezodal appromaton Progress rate and relatve cumulated curve. Theoretcal functons Gauss s ntegral Gompertz Gamma Logstc curve 3. Emprcal curves Polynomal of degree 5 Lnear combnaton of lne and transcendent functon We are gong to consder: Trapezodal appromaton Logstc curve Hermte polynomals Splne curves 4. Curve nterpolaton Hermte polynomal Splne curve 3 growng computatonal costs for growng accuracy levels 4 Trapezodal appromaton Trapezodal appromaton Analytc epresson for the cumulated progress curve,,9,8,7 [%],,5,4,3,,, RATE 3 4 5 7 8 9 3 4 5 7 8 9 k Month n,7,,5,4,3,,, [%]/month 5 R k kr y R R ( n ) n begnnng of the fnal deceleratons part k end of the ntal acceleraton part R R n + n R R( n,k) + n k ( kn + k) ( n ) for k for k n for n Trapezodal appromaton: Eercse Consder a project wth the followng characterstcs: At the % of the total progress t s acheved the nomnal progress rate (%/month) The deceleraton phase starts at the 9% of the total progress. The progress rate has a trapezodal form Determne: the project duraton the progress analytcal functon Assume that at the 5 th month the effectve progress s 5% less than the planned progress. Determnate: How much s necessary to ncrement the nomnal progress rate to conclude the project on tme (wthout changng the duraton of the deceleraton phase) Wth the hypothess of mantan the same nomnal progress rate calculate how ncrease the project duraton (wthout changng the duraton of the deceleraton phase) 7 Trapezodal appromaton: Soluton Eercse Project duraton PD DAP + DCP + DDP PD Project Duraton DAP Duraton of the Acceleraton Phase DCP Duraton of the Central Phase DDP Duraton of the Deceleraton Phase DAP,, DFA 3,35 months DCP,,8 DCP 3,3 months DDP,, DDP 3,35 months DP months 8
Trapezodal appromaton: Soluton Eercse Determnate the analytcal functon descrbng the cumulated project s progress 3,35,5 k,7; n,83 R R ( n,k ), +,83,7 3, y,, 3,57 + 7,4,57 for,7 for,7,83 for,83 Trapezodal appromaton: Soluton Eercse 3 Progress planned for the month #5:,C Progress really acheved at the end of the month #5:,5 Delay at the end of the month #5:,5 Delay at the project concluson:,5/,,85 months Remanng duraton for the central phase,5 5,5 Progress already planned n the remanng part of the central phase:,9,,7 Progress rate n the remanng part of the central phase: (,5 +,7)/,5,4 (+7%) 9 Use of the logstc curve dy( ) a y( ) b y( ) d y F( ) + β e a saturaton level b β, where y y curvatureparameter > s the ordnateat the orgn β > > ( + β) y( ) Use of the logstc curve ln( β) DERIVATIVES STUDY F( ) e + β e β + e β β e F' '( ) β + e LIMITS AND Y-INTERCEPT lm F( ) + lm F( ) F( ) ( ) + β ( β + e ) F ma β ' ( ) 3 ln( β ) ( ) nflecton > for ln( β) ; y ma 4 ; y nflecton Use of the logstc curve Eercse Use of the logstc curve Eercse - Soluton The progress acheved n a certan project at t s the 4,7% It s hyphotzed that the mamal slope for the progress curve can be %, 8% or % Usng the logstc curve estmate the month, called T, when the project s completed (consder a project completed when t s acheved the 99% of progress) accordng to the 3 hypothess Determnate the month, called tf, havng the nflecton pont for the 3 curve For the curve havng a mamal slope equal to %, determnate the cumulated progress foreseen for the th month 3 The logstc curve epresson s: Consderng: F () + β,47 F(t) lnβ t F F(t ) F + β e t β ma F'(t), 47, 4 + β 4,4 F(t) C C,99 T ln,4t + e β T 9 tf (ln ) / 4 7,5 months 4
Splne functons theory The man dea s to appromate an f () functon by polynomal functons n peces (Splne functons), made by the approach of polynomal of degree k ntersectng the orgnal functon n same ponts. f ( ) C [ a,b ] Cubc Splne Functons a < < <... < N b A Cubc splne functons In each part: ( ) Ay + By+ + Cy'' + Dy' ' S + 3 + ( A A)( ) + C + S( ) C [ a, b ] It s a 3 rd degree polynomal peces wth: B A + D 3 ( B B)( ) + S( ) y f ( ) Contnuous dervatve n the 5 y d Cubc splne functons Frst dervatve n each part + + y 3A 3B ( + ) y'' + ( + ) y' ' + Frst dervatve contnuty before the boundary n each part (N lnear equatons n the N unknowns y ) d d + Assumed well-known the frst dervatve at the boundary of the nterval ( lnear equatons n the N unknowns y ) d a nota d b nota Cubc splne functons Plannng phase Passage through the pont of project begnnng, scheduled and/or contractual mlestones, pont of project end Compatblty assessment among the mlestones postons Redevelopment phase Passage through the ponts of project begnnng, tme-now, eventually ntermedate mlestones and pont of project end (as an alternatve) passage through the tme-now, ntermedate mlestones and pont of project end N.B. In each case t s necessary a fnal assessment to check the outlne of the progress rate obtaned 7 8