Improvement of the Model of Minimization of the Costs in a Time Overrun Context Case of Construction Projects

8/11/2019 Improvement of the Model of Minimization of the Costs in a Time Overrun Context Case of Construction Projects

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 6308 (Print),ISSN 0976 6316(Online), Volume 5, Issue 9, September (2014), pp. 114-134 IAEME

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IMPROVEMENT OF THE MODEL OF MINIMIZATION OF THE COSTS INA TIME-OVERRUN CONTEXT: CASE OF CONSTRUCTION PROJECTS

Paul Louzolo-Kimbembe 1, BenotRomaric Mampika-Bathy 2 1Department of the Exact Sciences, Ecole Normale Suprieure (ENS),

Marien Ngouabi University, p.o. box 237, Brazzaville, Republic of Congo2Department of Civil Engineering, cole Nationale Suprieure Polytechnique,

Marien Ngouabi University, p.o. box 69, Brazzaville, Republic of Congo

ABSTRACT

In the field of construction time-overruns are recurring. The construction cost optimizatiomodel in time-overrun context (CCOMTOC) was developed to generate a new optimal schedule th

could allow minimizing the total cost of a construction project subject to penalties for delay. Thoriginal CCOMTOC is based on the assumption that the delay on the whole project is envisagebefore the beginning of the works. In practice, the delay can be noticed either before startup, oduring the realization of a task. It is this reality that is reflected in the improvement of the originCCOMTOC. The comparison between the improved and the original model shows a greatereduction of the cost-overrun after skidding for the duration of the tasks.

Keywords: Cost-Overrun, Time-Overrun, Delay Penalties, Optimization, Linear ProgrammingConstruction Project.

1. INTRODUCTION

Companies working in the field of building and civil engineering frequently encountedifficulties in organizing construction projects, where from the recurring phenomenon of exceedinof costs and deadlines.

Numerous studies have been conducted to explain the causes of delay in the constructionindustry, particularly in Developing countries [Koushki et al, 2005; Singh, 2009; Assaf et al, 200Aibinu et al, 2002; Chalabi et al, 1984; Al-Momani, 2000; Al-Khalil, 1999]. It appears from thestudies that the fact of not complying with the performance criteria of construction projectsdo ncontributes to the reduction of additional costs.Mansfield et al (1994) attribute the problems to a popractice of the management of the projects, economic factors and the natural environmenta

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ISSN 0976 6308 (Print)ISSN 0976 6316(Online)Volume 5, Issue 9, September (2014), pp. 114-134 IAEME: www.iaeme.com/Ijciet.aspJournal Impact Factor (2014): 7.9290 (Calculated by GISI)www.jifactor.com

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conditions. Frimpong et al (2003) think that the main causes of delay and cost-overrun oconstruction projects come from the difficulties of payment by agencies, bad management by thcontractor, of the supply problem in materials and poor technical performance.

Several authors have proposed different methods to analyze the impact of the factors causinthe delay in construction. In this connection, an interesting review of literature was made by Sheboet al (2012) in an article where they develop a new methodology to analyze and quantify the impaof the delay factors affecting construction projects.

However, the purpose of this study is not to deal with the actual causes of delay, but to takplace in a context where we admit that delays in the completion of a construction project woubecome inevitable. If the execution of the works continued with the current pace, withouacceleration of the tasks, the consequences will be non-compliance of the provisional deadline of tconstruction project and the additional costs related to the penalties for delay and the other inducecharges.The question that arises then is to know how best to limit the subsequent cost-overruns.

Indeed, when a construction company is located in a time-overrun context in the execution oa project, very often, three immediate consequences ensue from it:

The change of the initial schedule, which entails ipso-facto an extension of the date ocompletion of the works or the injection of new resources to catch up at best the delay [Tse eal, 2003];

The increase in the total cost of the works, on the one hand, due to the injection of newresources (or by the overtime work), and secondly by the weight of penalties and othercharges that accumulate as the project is delayed within the new deadline;

The prolonged or definitive abandonmentof the project. This is a very remarkable situation iDeveloping countries.

The optimal reduction of the additional costs incurred in this time-overrun context is adifficult problem to solve for most companies, because many of them use only empirical, generalineffective and inadequate methods in such situations. Also it is noticed dysfunctionswithin thesentities, especially from the managerial point of view.

This is how Louzolo (2007) led to propose a model of minimization of the costs ofconstruction projects responding to thecontext of exceeding the deadline. This is called CCOMTOacronym meaning "construction cost optimization model in time overrun context". This model based on the time-cost compression called Time-Cost Trade-off (TCT). The TCT aims to reduce thinitial duration of a project planned following the method of critical path (CPM) in order to findspecific completion date corresponding to a lower cost. In other words, TCT focuses on minimizinthe cost of the construction project by maintaining the desired duration.

We note that in the specialized literature, very abundant, studies do focus on the compressioof tasks in a project (project crashing),where the problem concerns especially the acceleration

anestablished program by advancing the initial date of completion of the project. We yet know ththe biggest problem usually encountered in the conduct of construction projects lies just beyond thnormal date of completion of the project.

The CCOMTOC was developed to take account of the perspective of passing of the deadlinfor completion of the construction project in order to anticipate the reorganization of the schedule the work with the cost as low as possible. However, it appears that the CCOMTOC applies only fotasks that have not yet begun as we anticipate a possible delay in their execution. In reality, happens that tasks already know a beginning of execution before falling through a situation of delaIt is this aspect that should be considered to improve the original CCOMTOC.


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2. METHODOLOGY

The following methodology is adopted in this study:

Brief presentation of the original CCOMTOC.

Development to the existing model in order to improve it.

The comparison between the original CCOMTOC and the improved CCOMTOC based on concrete case study. The objective is to demonstrate that with the new model the additionacosts engendered by the delay are lower than projected in the original model.

3. PRESENTATION OF CCOMTOC

It is known that the cost and time are closely related in cases of skid of deadline in the field othe construction. Where from it is required good coordination of tasks and regular monitoring of thproject.

The CCOMTOC allows us to adjust certain parameters to minimize the additional costinduced by the exceeding of deadlines. This mathematical model is essentially based on lineaprogramming. The decsion-making variable is the time parameter. The CCOMTOC is a tool thfacilitates the decision-making support in construction projects suffering from a problem of delay.

Having anticipated the skid of the deadline for completion of the project and the additionacost that it will engender, we will have to reduce the foreseeable delay to lesser and reasonablproportions, with a fair knowledge of the possible lowest cost that this will bring. We will ensure ththe operating time of the tasks (slabs, posts, beams, etc) that require special monitoring are noshortcuts despite the noticed skid.

To process an optimization problem in a time-overrun context, we can glimpse twoantagonistic evolutions of charges on the project [Louzolo et al., 2007]:

The penalties and the other charges that accumulate from the exceeding of deadlineplannefor the completion of the work. The corresponding expenses will be all thehigher as the delawill be important. We will therefore have an increasing curve of the cost of penalties.

The compression of tasks to minimize the delay which corresponds to an increase in theicost.

We will have the corresponding graphical situation shown in figure 1.


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Legend:

Pij = cost of the activity Aij

xij = duration of the activity Aij

Dij = normal duration of the activity Aij

ij = accelerated duration of the activity Aijto catch up the delay at the best

ij = skidded duration (maximum delay expected)

C1ij = maximum additional cost of the activityAij due to the penalties.

C2ij = additional costs expected in the absence of any acceleration of the activity Aij C2 ij= maximum additional cost resulting from the acceleration of the activityAijto the catch up the

delay.

The mathematical formulation of the CCOMTOC is given by the linear program below[Louzolo et al, 2007]:

)

C 2 ij

P ij

C 2 i

C 1 ij

0 D ij ij ijxij

Figure (1): Curves representing the penalty costs (C1), and the costs resultingfromthe compression (C2), for the activity Aij.


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+=U ji

ijU ji

ijt xC xC C Minimize),(

2),(

1 )()( (1)

)()(1 ijijij D xW xC = (2)

)()1()( 22 ijijij

Dij x D

C C xC ij

ij

+= (3)

Subject to the constraints:

iiji j S j xT T ,0 (4)

ijijij x D (5)

n ji

ij T x

= ),(

(6)

=nT (7)nn D (8)

niji T xT p+ (9)

Legend:

(i, j) = arc from the summit i (step Ei) to the summit j (step E j);CDij = normal cost of the activity Aij Dn = initial deadline of the projectn = maximum delay for the whole project = new deadline fixed for the completion of the construction project = sub-setof the activities on the criticalpathSi = set of the successors of the stageEi Ti, T j = the earliest dates of the start of the steps Ei andEj respectively.Tn = total minimum duration imposed after skidding of the construction project;U = set of arcs constituting the graph of the program (set of activities).

n

D

D

C W n= : daily cost of the construction project.

We define the following expressions:(1): minimum total cost;(2): cost of penalties in which (attenuation factor) indicates a fraction fixed during the signature

of the contract, with 0.01 0.75, [Al-Tabtabai et al, 1998; D'alpaos et al, 2009;Louzolo et al,2013];

(3): cost due to compression of tasks in which (compression factor)designates a multiple of theinitial resource reflecting the additional cost;

(4): constraints expressing the dependency relationships in the program, i.e. the link between tasks

( )


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(5): constraints indicating the limitation of the duration of each activity, in other words, theindicate the deadlines of activities.

(6): constraints indicating that the total duration of tasks being on the critical path must be equal Tn;

(7): constraints meaning that the date of completion of the project shall not exceed a clearldetermined deadline. This date is imposed by the parameter ;(8): constraint meaning that the parameter must be limited between the normal deadlineDn and theskidded durationn.

(9): constraints indicating that the starting-up dates for tasks should not exceed the date ocompletion of the project.

The decision variables are represented by xij and are non-negative (xij 0).The CCOMTOC assumes that the parameters CDij and are constants. In reality, these are

estimators based on predictions of future conditions. Therefore, the resulting calculations argenerally used to starting point to support subsequent analyses of the problem [Djila, 2009].

4. IMPROVEMENT OF THE CCOMTOC : INITIATING OF A TASK BEFORE THENORMAL DEADLINE

If the delay in the progress of the work is envisaged after having realized a part of the task Aij in timeij


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Legend:

ij = duration already carried out for the execution of the activity AijC1(xij)= new penalties costC2(xij)= new cost resulting from the compression

The improvement of CCOMTOC concerns essentially the coefficientij,the daily cost Wij andthe introduction of the duration of initiatingij relative to the task Aij.

Also the improved CCOMTOCcan be written:

)

C 2 ij

P ij

C 2 i

C 1 i

0 D ijD ij+ ij ij ij- ij ijxij

)

Figure (2): Consideration of the initiating of the task Aij before the exceedingof the deadline Dij


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,, (1)

(13)

(14)

Subject to the constraints: iiji j S j xT T ,0 (4)

(15) (16)

n ji

ij T x

= ),(

(6)

=nT (7)nn D (8)niji T xT p+ (9)

It should be noted that the original model (I) is replaced by the improved model (II). Thmodification of the original model concerns the equations (13) and (14), as well as the constrain(15) and (16).

Thus, the reduction of the additional costs induced by the skid of the duration is possible witthe CCOMTOC, starting from the following assumptions:

The delay on the whole construction project is foreseen before the launch of the workscausing a skid of the duration of the tasks, it is the original CCOMTOC (I).

The delay on the whole constructionproject is perceived after the completion and theinitiating of certain tasks, which leads to the improved CCOMTOC (II).

Now, we will compare the original model (I) to the improved model (II) by taking asillustration a project for the rehabilitation of thepremises of a site.

5. COMPARATIVE STUDY OF THE IMPROVED CCOMTOC AND THE ORIGINALCCOMTOC : APPLICATION TO THE CASE OF A PROJECT FOR THEREHABILITATION OF THE PREMISES OF A SITE

The project which is the subject of our case study concerns the rehabilitation of the premiseof a site on a ground of 18,000 m2, in which we find:

Six (06) buildings (3 buildings of 3 bedrooms, living room, kitchen, two bathrooms and 3buildings of 2 bedrooms, living room, kitchen and a bathroom).

A technical building (containing an electrical room, water room, and electric engineerinlocal);

A multi-purpose hall under construction; A basketball court; Two tennis courts; A playground of badminton; Drilling in water; Two sentry boxes.

( )


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Criticalpath

The designation and allocation of cost by tasks are given in Appendix A. We determined thoperating duration of each task with the aimof planning different activities by the PERT method.The initial duration plannedfor the whole works is 7.5 months that is 195 working days.The initial overall cost of the works is estimated to 1,614,449,750 F CFA1.

Our goal is to minimize the overall cost of a construction project in the context of exceedinof initial deadline. We assumed exceeded the cost and the deadline of the works, after starting up the project. This skid suggests us to proceed to theoptimization of the total cost of the project throuthe improved CCOMTOC.

The normal work schedule (Figure 3: PERT chart) indicates the initial date of completion othe project to the 195th day.

Figure (3): PERT chart of construction project

Let us suppose that for any causes, this deadline cannot be any more observed. A pessimistiestimation of the duration then allows us to assign to each operation a maximum delay that causethe skid of the normal operating duration of the activity Aij. This problem of skid will result ipsofacto an additional cost of the activity Aij, for which we have to try to minimize.In our study, two cases are distinguished: the partial time-overrun context with tasks not initiate(original CCOMTOC) and the partial time-overrun contextwith tasks initiated (improveCCOMTOC).

5.1. ORIGINAL CCOMTOC : THE PARTIAL TIME-OVERRUN CONTEXT WITH NOTINITIATED TASKS

We assume our project to take lagging during the execution of the works, that is, a number otasks are affected by the delay and that others have been totally executed within the time limits. Athe delayed tasks do not yet know a start of execution. In this case the optimization will concern on

1 1 55. 5 1$ 500


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the tasks that will be performed after the whole construction project has fell overto a situation odelay.

The start of works took place on the scheduled date. After the normal execution of the taskA, B, C, D, E, F and J, and for any reasons (delay due to funding, the unavailability of materials, loof the workforce or change of supervision, etc.), the remaining tasks of the project undergo a delaythe starting up causing a lengthening of their deadlines. In the present case, the optimization of thcost of the construction project is required to avoid significant cost-overrun due to the delay penaltiand other charges (including rental charges).

In our analysis, we consider firstly the tasks situatedon the critical path (Figure 3), thoswhich are directly concerned by the delay and on which penalties are applied.The new deadline for the completion of the project passes now from 195 to 255 days. Anticipateskid is thus of 60 days over the initial deadline, that is an exceeding of time of 31%. The cost of tconstruction project, without penalties, passes from 1,614,449,750 F CFA to 1,967,142,970 F CFA(Appendix B).

On the other hand, in time-overrun context, the optimized total cost due to the compression otasks amounts to 2,086,980,000 F CFA, while the optimized total cost of delay penalties i102,301,000 F CFA (Appendix C, = 0.70). The optimized total cost of the whole constructionproject amounts now to 2,189,280,000 F CFA after 255 days, an increase of the total cost of 35.6%According to our estimations, to complete this project in the 255th day may result in enormoufinancial losses within the company, because this has not been first expected in the planning of thproject management structure in charge of the realization of the works. Under these conditions, should be advisable to readjust this skid so that the total duration of the works is reduced to 215 daywhile remaining rigorous in the performance of the works and the compliance with technicstandards, as well as measures and safety instructions in the building and public works industr(construction).

The simulation is performed thanks to the specialized language of linear programmingsoftware Visual Xpress-MP. An illustration of this simulation is presented in Appendix B, for planned deadline of completion of 215 days.

If the skid of the deadline for completion of the project is reduced from 255 to 215 days, thoptimized total cost will then be 2,177,780,000F CFA (Appendix B, = 0.70). It now represents alittle lower overrun of the initial total cost, equal to 34.9%. This shortening of the deadline ocompletion, decided to minimize the total cost, led to a reduction of the additional cost of 0.7%, antherefore an apparent gain of 11,500,000 F CFA.

This deadline fixed in 215 days gives us a new work schedule (Appendix B) fixing thoptimal duration of each activity, as well as the corresponding optimal cost. We can notice that in toptimized schedule, the optimal duration of an activity is generally always chosen so as to impothe initial normal duration, except for the activities D1 and E1where the skidded duration isnecessary, and especially the activity B1which takes a random duration generated by the calculationprogram and contained between D9,10 and9,10.

The extension of the simulation to various deadlinesof completion of the construction projec

gave the results reported in Appendix C. The different values of costs, in relation to the deadlines completion, allowed us to plot cost-time curves (TCT: Time-Cost-Trade-off) illustrated in figure 4.


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The two curves of figure 4 have the same shape. They are characteristic of the TCT curves ia time-overrun context [Louzolo, 2005; Louzolo, 2014]. These curves are symmetrical to the TCcurves obtained in the usual context where the construction project must be delivered before thinitial date of completion [Leu et al., 1999; Beasley, 2003]. Under normal circumstances, delapenalties are not taken into account.

The TCT curve with = 0.70 is above that with = 0.60 (Figure 4). This shows that thepenalties attenuation coefficient significantly influences the total cost of the project in a time-overrun context, which confirms the results already found by Louzolo (2007).

5.2. IMPROVED CCOMTOC : THE PARTIAL TIME-OVERRUN CONTEXT WITHINITIATED TASKS

We consider that our project is in situation of delay. Some tasks are already completed, whilsome of those that are initiated are delayed. In this case the delay will concern the begun tasks anthose whose execution has not yet started.

The starting up of the works took place on the scheduled date. But, for the same reasons athose pointed out in the first case, some tasks undergo an extension of the duration of executionNote that tasks A, B, C, D, E, F and J were realized in due time, and that there was initiating of tasG, K, L, U, W and H1. Apart from the completed tasks, all other tasks are subject to delay.Consequently, the optimization of the cost of the construction project is needed for tasks nocompleted to avoid significant financial losses.

We illustrate in Appendix D (= 215 days, = 0.70) the results of the simulation of aminimization of construction project cost in a partial time-overrun context with initiatedtasks.

The optimal solution wishedfor = 215 days indicates a minimum cost of 2,128,180,000 F CFA(Appendix D, = 0.70). This represents more than an exceedingof the initial total cost of 31.82%,while for = 255 days the cost-overrun is 32.35%. Thus the reduction of the cost-overrun will be0.53% if we shorten the deadline of completion from 255 to 215 days that is a gain of abou8,560,000 F CFA.

2.1

2.1 0

2.1 3

2.1

2.1

2.1 2

2.1 5

2.1

2.1 1

215 220 225 230 235 240 245 250 255

( 1 0

)

( )

0.

0.

Figure (4): Curves TCT ( = 0.60 and = 0.70) for the whole construction project,in a partial time-overrun context with tasks not initiated; original CCOMTOC


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The calculation program generated values of operating durations other than Dij or ij for thetasks G, K, L, U, W and H1, thus offering a new optimized schedule for = 215 days. Note that thesetasks are other than those who have been initiated.

The optimal solutions of construction costs resulting from the simulation, with values ocoefficients ofattenuationof penalties fixed to 0.6 and 0.7 are given in Appendix E.Curves TCT (Figure 5) show a more gradual change cost between 215 and 230 days for = 0.60,while for = 0.70 the cost varies slowly between 215 and 225 days. Beyond these deadlines, the cosvaries very quickly that the delay increases.

5.3. COMPARISON OF THE IMPROVED CCOMTOC WITH THE ORIGINAL CCOMTOC We place two-two on the same graphic the curves TCT of figure 4 (original CCOMTOC) an

those of figure 5 (improved CCOMTOC), respectively for = 0.60 and = 0.70.

Figure (5): Curves TCT ( = 0.60 and = 0.70) for the wholeconstruction project,in a artial time-overrun context with initiated tasks; im rovedCCOMTOC

2.11

2.120

2.123

2.12

2.12

2.132

2.135

2.13

215 220 225 230 235 240 245 250 255

( 1 0

)

( )

' 0.

' 0.

2.115

2.125

2.135

2.145

2.155

2.1 5

2.1 5

215 220 225 230 235 240 245 250 255

0.

' 0.

Figure (6): Comparison of curves Ct (original CCOMTOC) and Ct(improved CCOMTOC), for = 0.60


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with two models, according to the duration of the construction project. We note that this rate increastrongly for a rising delay.

6. CONCLUSION

The problem of time-overrun is a scourge that several companies knowall around the worldThey are regularly victims by lack of effective managerialpractice, since the design phase of thproject up to its implementation. For this purpose, the recourse of an optimal organization of projecbecomes an essential factor for the success of the construction companies confronted with a situatiof time-overrun. The improvement of the original CCOMTOC aims to approachat best of thpractical realities for the treatment of this type of problem. The illustration through a case studallowed showing that the improved CCOMTOC provides a more significant reduction of the totcost of a construction project in situation of delay than does the original CCOMTOC. The differenis even greater that the delay becomes more important.

The time-overrun context is actually only a consequence resulting from a violation of certai

parameters of the project by the actors who are involved there. The improved CCOMTOCtries tgive the best possible answers on how projects suffering from an exceeding of provisional deadlinof execution must be planned and managed optimally to minimize the cost-overruns induced by thdelay.

Note, however, that the improved CCOMTOC is limited by the restriction placed upon thvalue of the duration of initiating of a task ( ij), which may not exceed half of the differencebetweenskidded duration and normal duration for a task, that is the quantity (ij - Dij) / 2.Thus, thismodel remains to perfect in order to take into account most important durations of initiating.

2.2

2.30

2.33

2.3

2.3

2.42

215 220 225 230 235 240 245 250 255

( % )

( )

/ (%)

Figure (8): Rate of variation of the construction cost ,

with , depending on the duration of the construction project ( = 0.70)


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7. REFERENCES

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APPENDIX

Appendix - A: Designation and allocation of costs and durations by task

ShareCode

of tasks Overview of tasksTask durations

Dij (day)Costs of tasksCDij

(F CFA)

N 1 :

P a t

h a n

d V a r

i o u s n e

t w o r

k s

C i v i l e n g i n e e r

i g

A Installation construction site 06 4,220,000B Removal of the openings of the ducts 08 100,000C Trenchand the openings of the ducts 20 13,346,500D Laying pipe 10 70,710,000E Network adduction and networks 15 10,380,000F Heavy work 25 22,745,250G Roof 10 1,680,000

H Metalwork and painting 15 5,780,000I Tiles 30 5,085,000

N 2 : R e v a m p i n g - K

i t c h e n

J Removal and modification kitchens 10 28,210,000K Manufacturing 70 48,000,000L Plumbing and electricity 35 90,792,000M Tiles 30 36,960,000N Laying and partition 45 23,400,000O Painting/Coating 22 19,550,000

N 3 :

C a r p e n t e r y P Carpenterywood and aluminium 30 156,900,000

Q Glaziery and mosquito nets 30 13,575,000

N 4 :

P l u m

b i n g

R Removal 15 9,000,000

S Network and equipment 35 20,400,000

T Suppressor 15 37,050,000


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130

Share Codeof tasks

Overview of tasksTask

durations

Dij

Costs of tasksCDij (F CFA)

N 5 : E

l e c t r i c a

l c o m p l

i a n c e

U Removalelectrical installation 20 4,700,000

V quipotential 20 1,900,000W High-voltage transformer and celles 26 67,050,000X Circuit breaker connectionand electrical 16 19,480,000

cupboardsY Pathways 20 10,360,000Z Local equipments 17 17,890,000A1 Connections and building equipments 20 38,740,000

B1 lectricityLowcurrents 15 600,000C1 Firedetection 10 830,000

N 6 : E

l e c t r i c a

l

e n g i n e e r

i n g

T a n

k

d i e s e l

f u e l

D1 Electrical engineering material removal andequipotential

08 8,530,000

E1 Generators 10 111,500,000

F1 Tank diesel fuel and elctricity 22 34,425,000

N 7 : T e l e c o m

n e t w o r

k

a n d h o u s e h o l

d

e l e c

t r i c a l a p p l

i a n c e s

G1 Telecom network and television 35 162,560,500

H1 Household electrical appliances purchase andimported furnishingspurchase

79 420,000,500

I1 Localfurnishingspurchase 60 98,000,000

Total 1,614,449,750

Dn: Initial deadline; n: Skidded total duration; Tn: Imposed total durationNote that the compression factor of tasks is found by calculating the ratio .


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Appendix -B: Simulation of reduction of cost-overruns and reorganization of the schedule of theworks in a partial time-overrun context with not initiated tasks ( = 215 days; = 0.70); original

CCOMTOC

T a s

k s

P r e v i o u s

s t a g e s

S u b s e q u e n

t

s t a g e s

o r m a

d u r a

t i o n

( d a y

) e

d u r a

t i o n

( d a y

)

N o r m a l c o s

t

( 1 0 3 F C F A )

S k i d d e d

c o s t s

w i t h o u t

p e n a

l t i e s

( 1 0 3

F C F A )

C o m p r e s s i o

n f a c t o r Optimal solutionEarliest

newstartingup date

Optimalduration

(day)

Optimalcost

(103 F CFA)i j Dij ij CDij C2ij ij xij C(xij)

A 1 2 6 6 4,220 4,220.00 1.00 0 6 4,220B 2 13 8 8 100 100.00 1.00 6e 8 100C 2 3 20 20 13,346.5 13,346.50 1.00 6e 20 13,346.5D 13 4 10 10 70,710 70,710.00 1.00 26e 10 91,923E 3 4 15 15 10,380 10,380.00 1.00 26e 15 10,380F 3 17 25 25 22,745.25 22,745.25 1.00 26e 25 22,745.3G 17 18 10 13 1,680 2,184.00 1.30 51e 10 2,335.2

H 18 19 15 21 5,780 8,092.00 1.40 61e 15 9,016.8I 19 20 30 38 5,085 6,441.00 1.28 76e 30 6,820.68J 2 21 10 10 28,210 28,210.00 1.00 6e 10 28,210K 21 23 70 75 48,000 51 ,428.57 1.07 16e 70 51,668.6L 21 22 35 40 90,792 103,762.29 1.15 16e 35 105,708M 22 23 30 40 36,960 49,280.00 1.34 51e 30 53,468.8N 22 9 45 55 23,400 28,600.00 1.23 51e 45 29,796O 23 20 22 27 19,550 23,993.18 1.23 86e 22 25,015.1P 14 15 30 35 156,900 183,050.00 1.17 46e 30 187,496Q 15 16 30 40 13,575 18,100.00 1.34 175e 30 19,638.5R 8 24 15 19 9,000 11,400.00 1.27 120e 15 12,048S 24 25 35 40 20,400 23,314.29 1.15 135e 35 23,751.4T 25 27 15 20 37,050 49,400.00 1.34 170e 15 53,599U 13 14 20 33 4,700 7,755.00 1.65 26e 20 47,470V 14 5 20 33 1,900 3,135.00 1.65 46e 20 3,937.75W 4 5 26 35 67,050 90,259.62 1.35 41e 26 98,383X 5 6 16 25 19,480 30,437.50 1.56 67e 16 36,573.7Y 6 7 20 25 10,360 12,950.00 1.25 83e 20 13,597.5Z 7 8 17 25 17,890 26,308.82 1.47 103e 17 30,265.7A1 8 9 20 30 38,740 58,110.00 1.50 120e 20 67,795B1 9 10 15 23 600 920.00 1.53 140e 20 1,123.6C1 16 27 10 11 830 913.00 1.10 205e 10 921.3D1 10 11 8 15 8,530 15,993.75 1.88 160e 15 21,218.4E1 11 12 10 18 111,500 200,700.00 1.80 175e 18 263,140F1 12 27 22 29 34,425 45,378.41 1.32 193e 22 48,883.5

G1 22 27 35 38 162,560.5 176,494.26 1.10 51e 35 177,888H1 1 26 79 90 420,000.5 478 ,481.58 1.14 0 79 486,669I1 26 27 60 75 98,000 122,500.00 1.25 79e 60 128,625

Dn (day)

n (day)

Total(103 F CFA)

Total(103 F CFA)

Tn Imposed

totalduration

(day)

Minimumtotal cost

(103 FCFA)

195 255 1,614,449.75 1,967,142.97 215 2,177,780


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Appendix - C: Synthetic results of the simulation for values of attenuationcoefficient ofpenaltiesfixed to = 0.60 and = 0.70, case of the time-overrun context with not initiated

tasks; original CCOMTOC

V a l u e o f

t h e

a t t e n u a t

i o n

c o e f

f i c i e n

t

P r o

j e c t

i n i t i a l

d e a d

l i n e

( d a y

)

D n

Optimal solution

I m p o s e

d

d e a d

l i n e a f

t e r

s k i d d i n g

( d a y

)

=

T n

O p t

i m i z e d

t o t a l

c o s t o f p e n a

l t i e s

C t 1

( 1 0 3 F C F A )

O p t

i m i z e d

t o t a l

c o s t

f r o m

c o m p r e s s i o n

C t 2

( 1 0 3 F C F A )

O p t

i m i z e d

t o t a l

c o s t o f

t h e

p r o j e c

t

C t (

1 0 3 F C F A )

0.60 195

215 60,938.3 2,106,920 2,167,860220 62,471.3 2,105,490 2,167,960225 66,123.8 2,102,080 2,168,210230 69,479 2,099,230 2,168,710

235 72,636 2,096,760 2,169,400240 74,190 2,096,110 2,170,300245 80,001 2,091,270 2,171,270250 85,812 2,086,430 2,172,240255 107,649 2,066,640 2,174,290

0.70 195

215 67,804.6 2,109,970 2,177,780220 69,593.1 2,108,550 2,178,140225 73,854.4 2,105,140 2,178,990230 76,646.7 2,103,380 2,180,030235 79,581.8 2,101,640 2,181,220240 83,265.1 2,099,170 2,182,430245 90,044.6 2,094,330 2,184,370250 96,824.1 2,089,480 2,186,310255 102,301 2,086,980 2,189,280


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133

Dn: Initial deadline; n: Skidded total duration; Tn: Imposed total duration;

Appendix -D: Simulation of reduction of cost-overruns and reorganization of the schedule of theworks in a partial time-overrun context with initiated tasks ( = 215 days; = 0.70); improved

CCOMTOC

T a s

k s

P r e v

i o u s

s t a g e s

S u b s e q u e n t

s t a g e s

o r m a

d u r a

t i o n

( d a y ) e

d u r a

t i o n

( d a y )

D u r a t

i o n o f

i n i t i a t i n g

( d a y )

N o r m a l c o s

t

( 1 0 3 F C F A )

S k i d d e d

c o s t s w

i t h o u

t

p e n a

l t i e s

( 1 0 3

F C F A )

C o m p r e s s

i o n

f a c t o r

Optimal solution

Earliestnew

startingup date

Optimalduration

(day)

Optimal cost(103 F CFA)

i j Dij ij ij CDij C2ij ij xij C'(xij)

A 1 2 6 6 0 4,220 4,220.00 1.00 0 6 4,220B 2 13 8 8 0 100 100.00 1.00 6e 8 100C 2 3 20 20 0 13,346.5 13,346.50 1.00 6e 20 13,346.5D 13 4 10 10 0 70,710 70,710.00 1.00 26e 10 91,923E 3 4 15 15 0 10,380 10,380.00 1.00 26e 15 10,380F 3 17 25 25 0 22,745.25 22,745.25 1.00 26e 25 22,745.3G 17 18 10 13 1 1,680 2,184.00 1.30 51e 11 2,234.4H 18 19 15 21 0 5,780 8,092.00 1.40 62e 15 9,016.8

I 19 20 30 38 0 5,085 6,441.00 1.28 77e 30 6,820.68J 2 21 10 10 0 28,210 28,210.00 1.00 6e 10 28,210K 21 23 70 75 2 48,000 51,428.57 1.07 16e 72 51,476.6L 21 22 35 40 2 90,792 103,762.29 1.15 16e 37 104,151M 22 23 30 40 0 36,960 49,280.00 1.34 53e 30 53,468.8N 22 9 45 55 0 23,400 28,600.00 1.23 53e 45 29,796O 23 20 22 27 0 19,550 23,993.18 1.23 88e 22 25,015.1P 14 15 30 35 0 156,900 183,050.00 1.17 52e 30 187,496Q 15 16 30 40 0 13,575 18,100.00 1.34 175e 30 19,638.6R 8 24 15 19 0 9,000 11,400.00 1.27 125e 15 12,048S 24 25 35 40 0 20,400 23,314.29 1.15 140e 35 23,751.4T 25 27 15 20 0 37,050 49,400.00 1.34 175e 15 53,599

U 13 14 20 33 6 4,700 7,755.00 1.65 26e 26 10,810V 14 5 20 33 0 1,900 3,135.00 1.65 52e 20 3,937.75W 4 5 26 35 3 67,050 90,259.62 1.35 41e 31 94,772.6X 5 6 16 25 0 19,480 30,437.50 1.56 72e 16 36,573.7Y 6 7 20 25 0 10,360 12,950.00 1.25 88e 20 13,597.5Z 7 8 17 25 0 17,890 26,308.82 1.47 108e 17 30,265.7A1 8 9 20 30 0 38,740 58,110.00 1.50 125e 20 67,795B1 9 10 15 23 0 600 920.00 1.53 145e 15 1,089.6C1 16 27 10 11 0 830 913.00 1.10 205e 10 921.3D1 10 11 8 15 0 8,530 15,993.75 1.88 160e 15 21,218.4E1 11 12 10 18 0 111,500 200,700.00 1.80 175e 18 263,140F1 12 27 22 29 0 34,425 45,378.41 1.32 193e 22 48,883.5G1 22 27 35 38 0 162,560.5 176,494.26 1.10 53e 35 177,888

H1 1 26 79 90 5 420,000.5 478,481.58 1.14 0 84 479,226I1 26 27 60 75 0 98,000 122,500.00 1.25 84e 60 128,625

Dn (jour)

n (jour)

Total(103 F CFA)

Total(103 F CFA)

Tn Imposed

totalduration

(day)

Minimum totalcost

(103 FCFA)

195 255 1,614,449.75 1,967,142.97 215 2,128,180


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134

Appendix - E: Synthetic results of the simulation for values of penaltiescoefficient of attenuation fixed to = 0.60 and = 0.70, case of the time-

overrun context with initiated tasks; improvedCCOMTOC

V a l u e o f

t h e a t

t e n u a t

i o n

c o e f

f i c i e n

t

P r o

j e c t

i n i t i a l d e a

d l i n e

( d a y

)

D n

Optimal solution

I m p o s e

d d e a d

l i n e a f

t e r

s k i d d i n g

( d a y

)

=

T n

O p t

i m i z e d

t o t a l c o s

t o f

p e n a

l t i e s

C t 1

( 1 0 3 F C F A )

O p t

i m i z e d

t o t a l c o s

t

f r o m

c o m p r e s s i o n

C t 2

( 1 0 3 F C F A )

O p t

i m i z e d

t o t a l c o s

t o f

t h e p r o j e c

t

C t ( 1

0 3 F C F A )

0.60 195

215 61,092.9 2,056,910 2,118,000220 61,212.9 2,056,800 2,118,010

225 62,745.9 2,055,370 2,118,120230 66,398.4 2,051,960 2,118,360

235 69,753.6 2,049,120 2,118,870

240 72,910.7 2,046,640 2,119,550

245 74,464.7 2,046,000 2,120,460

250 80,275.7 2,041,150 2,121,430

255 86,086.7 2,036,310 2,122,400

0.70 195

215 71,275 2,056,910 2,128,180220 71,415 2,056,800 2,128,210

225 73,203.5 2,055,370 2,128,580230 77,464.8 2,051,960 2,129,430

235 80,257.1 2,050,210 2,130,470

240 83,192.2 2,048,470 2,131,660

245 86,875.4 2,046,000 2,132,870

250 93,654.9 2,041,150 2,134,810

255 100,434 2,036,310 2,136,740

Documents

Improvement of the Model of Minimization of the Costs in a Time Overrun Context Case of Construction Projects