SOFTWARE FOR PROJECT RELIABILITY ESTIMATION AND RISK EVALUATION

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1 17 th Internatonal Conference on the Applcatons of Computer Scence and Mathematcs n Archtecture and Cvl Engneerng K. Gürlebec and C. Köne (eds.) Wemar, Germany, July 26 SOFTWARE FOR PROJECT RELIABILITY ESTIMATION AND RISK EVALUATION V.BERAN *, E. HROMADA * CTU Prague, Faculty of Cvl Engneerng Tháurova 7, Prague 6 E-mal:beran@fsv.cvut.cz Keywords: Smulaton, Tme schedulng, Cost schedulng, Relablty and Rs, Multdmensonal Analyss, Correlaton. Abstract. The contrbuton presents a model that s able to smulate constructon duraton and cost for a buldng project. Ths model predcts set of expected project costs and duraton schedule dependng on nput parameters such as producton speed, scope of wor, tme schedule, bondng condtons, maxmum and mnmum devatons from scope of wor and producton speed. Constructon cost and tme models are, n many ways, useful tools n project management. Clents are able to mae proper decsons about the tme and cost schedules of ther nvestments. Consequently, buldng contractors are able to schedule predcted project cost and duraton before any decson s fnalzed.

2 1 INTRODUCTION The smulaton of the constructon process (constructon actvtes on the bass of producton speed) maes t possble to montor the relablty of expected tme schedule and total cost dependng on such nput parameters as producton speed, scope of wor, tme schedule, bondng condtons, maxmum and mnmum devatons from scope of wor and producton speed. 2 FIELD OF APPLICATIONS The smulaton model s useful at many levels of project management. The possble felds of applcaton are shown n the table 1. Tab. 1 Felds of applcaton. Project phase User Feld of applcaton Clent Decsons about realzaton of ntentons. Preparaton phase Compettor Cost assessment and nference of bd prce. Submtter Buldng contractor Comparatve base. Dynamc schedule. Detaled calculaton of cost and tme schedule of constructon actvtes. Constructon phase Optmzaton of constructon process. Decrease of the number of clams among buldng contractor, buldng subcontractors and submtter. Buldng contractor & submtter Informaton source usable n realzaton of future projects. 3 METHODOLOGICAL AND CONCEPTUAL APPROACH The applcaton software carres out on the bass of producton speed, analyss of duraton and cost smulatons of constructon actvtes. On the bass of a statstcal evaluaton of enacted smulatons a program algorthm calculates the assumed cost and tme frames of partcular constructon actvtes. CONSTRUCTION DURATION + CONSTRUCTION COST + RISK OF CONSTRUCTION DURATION RISK OF CONSTRUCTION COST (CONTRACTOR, SUBCONTRACTOR) Fg. 1 Interactons between constructon duraton and constructon cost. 2

3 It s a general prncple that the nteractons between tme and cost create a postve dependence. Lengthenng or shortenng of constructon duraton leads to the ncreases of total constructon cost. The graphc n Fgure 1 llustrates the above statement. However there exst a lot of problems n applyng the determnaton of constructon duraton. There s a possble appearance of rss whch affect termnaton date of a buldng project, for example shortenng or lengthenng of constructon duraton ncurred by clmatc nfluences, dsorder n supples of materals and components, nadequaces ascertaned on acceptance of nput materals, etc. Seemngly elementary and transparent stuatons are further complcated n many practcal cases by the fact, that the bndngs between llustrated elements (Tme duraton, Cost) are able to change polarty over tme. It s lely to see a change to negatve ln from postve ln between elements Tme duraton and Cost. Hgher cost could objectvely negatvely affect constructon duraton. It deals wth a stuaton, n whch these s used a cost-expensve component wth a shorter tme schedule of wors on a buldng ste (prefabrcaton, n advance ready fabrcaton wors, etc.). In respect of the fact, that the mentoned stuaton s possble n all wors, the calculaton s very hghly burdened by these nfluences, whch are dffcult to manage by common calculaton methods (Beran, 22; Haas, 1981). 4 GENERAL PROBLEM FORMULATION The ntaton of the buldng project smulaton t s necessary to formulate the problem as such. The applcaton receves nput data through Module of nput data (see Table 6, 7, 8, 9), whch defnes partcular constructon actvtes (1), volume Q of these partcular constructon Tab. 2 Dynamc progress chart of buldng project. Actvty Scope Producton of wor speed Tme duraton Start End Ground wors Water connecton Sewerage connecton Electrcty connecton Bottom constructon Dumpng place Day Overhead constructon Roof Insde parget Facade renderng Completng wors Demands of sources through tme Q'(t) Total demands of sources through tme Q(t) Key: Noncrtcal actvty Crtcal actvty Total reserve Watng for actvty Watng for actvty - on crtcal way actvtes n physcal or fnancal unts, ts producton speed v and bondng condtons D connecton actvtes lnng partcular actvtes. TAB project characterzes the calculaton as a 3

4 meta problem called Dynamc Harmonogram (flow-sheet). N characterzes generally sequental networs N (Beran, 22). The set expresson s gven as TAB project = {N [D = f (Q rs, v rs, D connecton actvtes)], = 1,.. } (1) where are partal processes and D s as set of actvty duratons, rs nfluence s condtoned externalty (see Fg. 1). The notaton s completed wth condtonalty of breach of supposed nput parameters of scope of wor and producton speed. The Module of nput data s llustrated n the subchapter 8 SW support. A practcal soluton of the calculaton accordng to the dynamc progress chart (1) s based on the nput of wor volume, producton speed and a tme schedule of partcular actvtes. Tme duraton n the dynamc progress chart s calculated as the quotent of quanttes Q a v or more precsely D = Q /v. Input data ncluded n Module of nput data n sheet Connecton actvtes defne bondng condtons among partcular producton actvtes. The sheets called Devatons of project parameters 1 and 2 contan nput data about mnmum / maxmum devatons of scope of wor and producton speed of partcular actvtes based on expected parameters of the buldng process. 5 SOLUTION AND EXAMPLE On the bass of an ordnary Excel VBA applcaton the algorthm maes t possble to calculate an nstant dynamc progress chart of the buldng project that ncludes a tme schedule of resources. The dynamc progress chart s n terms of notaton (1) completed by Thousand EUR Tme duraton (worng days) Thousand EUR Tme duraton (worng days) Fg. 2 Requred cash flow of captal needed from the start to the end of constructon and cumulatve need of captal. 4

means of dfferences calculated on the bass of a common progress chart. Calculaton s based on producton speeds and ndvdual actvtes, whch are descrbed n columns Start and End (Tab.

5 means of dfferences calculated on the bass of a common progress chart. Calculaton s based on producton speeds and ndvdual actvtes, whch are descrbed n columns Start and End (Tab. 2), whch represent bndngs between ndvdual actvtes. It factually represents relatons between declared functon f(q rs, v rs, D connecton actvtes) from notaton (1) and composton of tas as a consecutve process on the base of tme duraton of ndvdual processes N [D] (Beran, 25); (Beran, 22); (Heralová, 22). The dynamc progress chart creates a comprehensve methodcally unform model. Among the model s outputs belong nformaton about the start and end terms of producton actvtes and nformaton about cost schedules. The applcaton creates graphc vsualzaton of resources demand n tme see Fg. 2. The queston of contnuty of project realzaton s nterconnected wth cost-cuttng management measures of constructon cost. The varyng constructon speed evoes changes n constructon costs. The flow of constructon costs are a sgnfcant ndcator of economy of captal employment. Fg. 3 Example of 3D probablty bar chart as expresson on the bass of (1). 5

6 The descrbed calculaton and software applcaton s useful for evaluaton of bd proposals of nvestment projects. The approach carres out two dmensonal smulaton. The projects descrbed n propostons tme and costs, wll be labeled as a predefned project. The dscrete probablstc varables (T; C) obtan values (t ; c j ). We wll wrte P(T= t ; C= c j ) = p j. Fg. 4 Probablty 3D bar chart for constructon project wth fxed cost scope C. On ths bass of predefned projects data the addtve nput nformaton about mnmum and maxmum devatons (see subchapeter 8. Software Support). SW applcaton carres out smulaton of the presumed development of the examned constructon phase, the constructon project as a whole, or just to a set of constructon actvtes. It s possble to dentfy the effects of changes, read management changes, on the scope of partcular jobs (constructon actvtes) and ther probablty (relablty) of proposed (read contracted) fnshng deadlne t fn and proposed contractng lmt of cost c fn. In general we are loong for acceptable F(t fn ; c fn ) = t c P(T < tfn; C < c fn ) for chosen project actvtes A (2) or ther actvty sets A, A l, A x, functonalty-desgned nto networ. The results of partcular smulatons P(T; C) = P(smTAB project (T; C)) for example mentoned further s T <45;89> and C <2411;3131>. Smulaton data are contnuously recorded on the bass of (1), (Beran, 22). The smulaton s based on the tme schedule gven n Table 2. Obtanable s the rangng of 5 smulatons nto 3x3 categores. When a smulaton s fnshed, the recorded data serve as a bass for statstcal analyss of constructon processes. Data fle serves for fnal analyss and nter ala s the bass (2a) 6

7 for modfed 3D vsualzaton smlar to Fg. 3. The calculaton of expected or fxed probablty starts, ends and reserves gven are the results n Fg. 4 and Fg. 5. In Tab. 3 are structured data of the comprehensve smulaton example. The partcular ponts ate calculated as a constructon bd proposal descrbed underneath by smulaton study shows, how far the ntended fnshng date and cost are actually compettve and realstc. Fg. 5 Probablty 3D bar chart for constructon project wth fxed tme duraton T. P(T (45,89) ; C (2411,3131) ) = P(smTAB project (T; C)) = P (sm{n [D = f (Q rs, v rs, D connecton actvtes)], for subprojects or sub actvtes = 1,.. } ) (2b). The constructon project (Tománová, 23) s proposed n tme schedule and scope of wor as gven n 3D bar chart. The ellpse n Table 3 shows the shft of probablty n tme and costs. Usng ths approach t s possble to specfy more exactly the results of smulatons. Occurrence frequences of partcular scenaros of buldng project bd are comparable. The hghest values of smulaton frequences n 3D bar graph lead to probabltes of potental success scenaros for the constructon project. In ths case the buldng project wll be realzed wth satsfed commercal probablty wthn the range of 57 to 59 days and ts constructon cost s gven n the range of to thousand EUR. Wthn the framewor of smulaton of buldng project t s common that the calculaton fnds out the unque regular soluton. The example of 3D probablty bar chart wth unque regular soluton s shown n Fgure 3. 7

In case of complcated bondng condtons and other addtonal nterdependences among partcular actvtes, the soluton of the smulaton may not be unque. Tab.

8 In case of complcated bondng condtons and other addtonal nterdependences among partcular actvtes, the soluton of the smulaton may not be unque. Tab. 3 The example of 3D bar chart, that llustrates the result of 5 smulatons. The Fgure 6 and the Fgure 6a present the buldng project; n whch nput parameters contan specfc nterdependence wthn the frst actvty (ground wors). Compare these results to Fg. 3. In the event that the frst actvty should tae more than 25 days, the buldng,9,8,7,6 Probablty,5,4,3,2,1, Tme duraton (Worng days) Constructon cost (Thousand EUR) Fg. 6 Example of 3D probablty bar chart wth heterogeneous solutons. 8

ground machnes must be wthout delay dslocated on another major actvty (another buldng project). Ths stuaton causes slppage of dates wthn the range of 21 days.

9 ground machnes must be wthout delay dslocated on another major actvty (another buldng project). Ths stuaton causes slppage of dates wthn the range of 21 days. After that perod ground wors could be resumed. Ths specfc condton s the cause of heterogeneous soluton of the smulaton. It s dffcult to fnd the soluton of ths buldng project by usng standard statstcal methods. It s convenent to tae advantage of vsualzaton technques and partcular smulaton calculatons. Fg. 6a Example of graph wth nterdependences among tme duraton and constructon cost. Important nformaton regardng the proposal of a future project tme schedule s specfed by tests of potental scenaros of the project development wth current fxng of certan parameters of the buldng organzatonal model. It s possble to obtan mportant nformaton about crtcal parameters of the planned project, for example by fxng of devatons wor of scope of wor of partcular actvtes see Q n notaton (1). It s common practce to present the probablty of the total constructon tme of a buldng project wthout a cost vewpont (Fg. 5). A better expressed project cost s presented as a respected fxed value that wll be stable and ndependent of project duraton. Addressng ths noton the proposed approach of smulaton of nterrelated values tme and cost n Fg. 4 s more comprehensble and complex as nformaton n Fg. 5 where T or as for calculaton wth fxed scope of wor T P(a T b) = F(t b ) - F(t a ) (3) P(45 T 89) = P(smTAB project (T) ) (3a). 9

10 A smlar stuaton develops f we fx alternaton of tme schedules for the project. Scope of wor gven as C s specfed as C P(x C y) = F(c y ) - F(c x ) for data smulated n Tab. 3 we dsplay n Fgure 6. C P(2411 C 3131) = P(smTAB project (C) ), for calculaton wth fxed tme raton (3c). In Fg. 6 we may follow changes of project cost for fxed on duraton of observed project. The expected tme duraton of total constructon project s gven by ts mean value E[T project C = const.] = t P( T = t ) = t (4) T Accordngly t s possble to quantfy expected scope of wor of total constructon project by ts mean value E[C project T = const.] = c P( C = c ) = c (5) C (3b) 6 THE SEARCH FOR RELIABLE CONSTRUCTION COST AND TIME DURATION The smulaton model s able to calculate, on the bass of nput level of probablty, the adequate constructon cost and tme duraton of a project. The recprocal vew attends to fndng out the adequate level of probablty for constructon cost and actvty duratons. There are two ways that lead to the calculaton of adequate level of probablty. The frst way conssts n fxaton of one varable parameter and nvestgaton of changes n remanng parameter. The second way conssts n smultaneous nvestgaton of devatons of both parameters. The approach used n ths paper s based on expresson (1) and Table 4 (dscreet probablty densty table) enables on data of Table 3 calculate the level of probablty as cumulatve densty functon F(T; C) = ( = t ; C = T C P T c ) (6), where t a c runs through the set of all possble values of T and C and T C P ( T = t ; C = c ) = 1 (6a). The Fg. 6b shows extracted data from expresson (6) or Table 4 as hstogram. On closer nvestgaton of results of partcular smulatons there was found a dependence between level of probablty and constructon cost and tme duraton. In the followng fgures are shown blateral nteractons of mentoned project parameters. 1

11 Tab. 4 Example of calculaton of level of Dscrete Probablty Dstrbuton (DPD).,12,1,8,6 Probablty,4, Scope of wor (Thousand EUR) Tme duraton (Worng days), Fg. 6b Bar chart 3D for DPD on level of probablty F(T; C) =,

12 7 PRESUMED DYNAMIC PROGRESS CHART Among nterpretve outputs of the applcaton software belongs the complaton of a presumed dynamc progress chart. Ths progress chart represents the expected scenaro of development of a buldng project wth the mappng of potental tme dslocatons for partcular actvtes. The calculaton of a presumed dynamc progress chart s based on an algorthm, whch calculates mean values as a partal result of the smulated buldng project. Tab. 5 Presumed dynamc progress chart of buldng project. Actvty Scope of wor Producton speed Tme Start End duraton Ground wors Water connecton Sewerage connecton Electrcty connecton Bottom constructon Dumpng place Overhead constructon Day , , Roof Insde parget Facade renderng Completng wors Demands of sources through tme Q'(t) Total demands of sources through tme Q(t) Key: Noncrtcal actvty Crtcal actvty Total reserve Watng for actvty Watng for actvty - on crtcal way Possble progresson of actvty The progress charts of buldng project are based on calculaton of mean values of start and end of project actvtes E(T; C) = E(45 T 89; 2411 C 3131). However the nformaton of start-rs and end-rs represents substantal nformaton calculated as followng varances where tt s correlaton ndex, 2 2 D(T) = tt = σ = ( t t ) P( T = ) t T t 2 2 D(C) = cc = σ = ( c c) P( C = ) c C c where cc s correlaton ndex. Further the correlaton ndex tc s generally gven as (7) (8) j n = when j = j (9) n n n3 1n 3n nn 12

13 For our example the correlaton ndex tc s gven as tt tc tc = = ct cc In the Tab. 5 are characterstcs of dsperson nterrelated to chart actvtes. More extensve explanatons are gven n Fgure 5a. 1,2 Tab. 5a Presumed dynamc progress chart of buldng project.,2 1 (1) The earlest possble start term of the project t 1 = 1 The probable start term of the project t 1 = 2 The probable end term of the frst actvty t 1 = 7 Actvty Scope of wor Producton speed Tme Start End duraton Ground wors Water connecton Sewerage connecton Electrcty connecton Bottom constructon Dumpng place Overhead constructon Day , ,7 The latest possble end term of the frst actvty t 1 = Roof Insde parget Facade renderng Completng wors The mean value of the sxth actvty E(; C) = E(2; 55) Demands of sources through tme Q'(t) Total demands of sources through tme Q(t) There are extensve possbltes of calculaton of correlatons of T and C calculated as normalzed values as j r j = (11). D T ] D[ C ] [ j 8 SOFTWARE SUPPORT Tab. 6 1 shows example of Module of nput data. The Basc page, Project parameters, Connecton actvtes, Devatons of project parameters. 9 CONCLUSION Ths model maes t possble to predct an expected project cost and duraton schedule dependng on nput parameters such as producton speed, scope of wor, tme schedule, bondng condtons, maxmum and mnmum devatons from scope of wor and producton speed. The useful results are rs evaluaton for the projects or for the project actvtes. 13

14 Tab. 6 Module of nput data Basc page Tab. 7 Module of nput data - Project parameters 14

15 Tab. 8 Module of nput data - Connecton actvtes Tab. 9 Module of nput data - Devatons of project parameters 15

16 REFERENCES [1] Beran V., Dlas P.: Management udržtelného rozvoje, Academa, Praha, 25. [2] Beran, V., Dlas, P., Heralová, R., Bera, V.: Dynamcý harmonogram, rozvrhování výroby do času, 1. vyd. Praha: Academa, s. ISBN [3] Dlas, P., Beran, V.: MDM 24 - teoretcá příruča, 1. vyd. Praha: Vydavatelství ČVUT, s. ISBN [4] Haas Š., Háje Vl.: Systémové plánování a řízení ve stavebnctví. SNTL Praha, [5] Heralová, R. - Frová, J. - Tománová, J.: Decson Mang and Bds n Constructon Industry. Integrated Rs Management. Berln: Humbolt Unverstät Berln, 22. [6] Tománová, J.: Plannng n Project Management. Proceedngs of Worshop 23. Prague: CTU, 23, vol. B, 1194 s. ISBN

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