Improvement of the model of minimization of the costs in a time overrun context case of construction projects

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

114

IMPROVEMENT OF THE MODEL OF MINIMIZATION OF THE COSTS IN

A TIME-OVERRUN CONTEXT: CASE OF CONSTRUCTION PROJECTS

Paul Louzolo-Kimbembe1, BenoîtRomaric Mampika-Bathy

2

1Department of the Exact Sciences, Ecole Normale Supérieure (ENS),

Marien Ngouabi University, p.o. box 237, Brazzaville, Republic of Congo 2Department of Civil Engineering, École Nationale Supérieure 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 optimization model in time-overrun context (CCOMTOC) was developed to generate a new optimal schedule that could allow minimizing the total cost of a construction project subject to penalties for delay. The original CCOMTOC is based on the assumption that the delay on the whole project is envisaged before the beginning of the works. In practice, the delay can be noticed either before startup, or during the realization of a task. It is this reality that is reflected in the improvement of the original CCOMTOC. The comparison between the improved and the original model shows a greater reduction of the cost-overrun after skidding for the duration of the tasks. Keywords: Cost-Overrun, Time-Overrun, Delay Penalties, Optimization, Linear Programming, Construction Project. 1. INTRODUCTION

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

Numerous studies have been conducted to explain the causes of delay in the construction industry, particularly in Developing countries [Koushki et al, 2005; Singh, 2009; Assaf et al, 2006; Aibinu et al, 2002; Chalabi et al, 1984; Al-Momani, 2000; Al-Khalil, 1999]. It appears from these studies that the fact of not complying with the performance criteria of construction projectsdo not contributes to the reduction of additional costs.Mansfield et al (1994) attribute the problems to a poor practice of the management of the projects, economic factors and the natural environmental

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

Several authors have proposed different methods to analyze the impact of the factors causing the delay in construction. In this connection, an interesting review of literature was made by Shebob et al (2012) in an article where they develop a new methodology to analyze and quantify the impact of the delay factors affecting construction projects. However, the purpose of this study is not to deal with the actual causes of delay, but to take place in a context where we admit that delays in the completion of a construction project would become inevitable. If the execution of the works continued with the current pace, without acceleration of the tasks, the consequences will be non-compliance of the provisional deadline of the construction project and the additional costs related to the penalties for delay and the other induced charges.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 of a project, very often, three immediate consequences ensue from it:

- The change of the initial schedule, which entails ipso-facto an extension of the date of

completion of the works or the injection of new resources to catch up at best the delay [Tse et al, 2003];

- The increase in the total cost of the works, on the one hand, due to the injection of new

resources (or by the overtime work), and secondly by the weight of penalties and other charges that accumulate as the project is delayed within the new deadline;

- The prolonged or definitive abandonmentof the project. This is a very remarkable situation in Developing countries.

The optimal reduction of the additional costs incurred in this time-overrun context is a

difficult problem to solve for most companies, because many of them use only empirical, generally ineffective and inadequate methods in such situations. Also it is noticed dysfunctionswithin these entities, especially from the managerial point of view.

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

We note that in the specialized literature, very abundant, studies do focus on the compression of tasks in a project (project crashing),where the problem concerns especially the acceleration of anestablished program by advancing the initial date of completion of the project. We yet know that the biggest problem usually encountered in the conduct of construction projects lies just beyond the normal date of completion of the project.

The CCOMTOC was developed to take account of the perspective of passing of the deadline for completion of the construction project in order to anticipate the reorganization of the schedule of the work with the cost as low as possible. However, it appears that the CCOMTOC applies only for tasks that have not yet begun as we anticipate a possible delay in their execution. In reality, it happens that tasks already know a beginning of execution before falling through a situation of delay. It 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 a concrete case study. The objective is to demonstrate that with the new model the additional costs 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 of the construction. Where from it is required good coordination of tasks and regular monitoring of the project.

The CCOMTOC allows us to adjust certain parameters to minimize the additional costs induced by the exceeding of deadlines. This mathematical model is essentially based on linear programming. The decsion-making variable is the time parameter. The CCOMTOC is a tool that facilitates 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 additional cost that it will engender, we will have to reduce the foreseeable delay to lesser and reasonable proportions, with a fair knowledge of the possible lowest cost that this will bring. We will ensure that the operating time of the tasks (slabs, posts, beams, etc) that require special monitoring are not shortcuts despite the noticed skid.

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

- The penalties and the other charges that accumulate from the exceeding of deadlineplanned for the completion of the work. The corresponding expenses will be all thehigher as the delay will 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 their cost.

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



117

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

δij = skidded duration (maximum delay expected)

C1δij = maximum additional cost of the activityAij due to the penalties.

C2δij = 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]:

C2 (xij)

C1 (xij)

C2 ij

Pij

C 2 ij

C1 ij

0 Dij∆ijδijxij

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



118

∑∑

∈∈

+=Uji

ij

Uji

ijt xCxCCMinimize),(

2),(

1 )()( (1)

)()(1 ijijij DxWxC −= β (2)

)()1()( 22 ijij

ij

D

ij xD

CCxC

ij

ij−

−+= δα

δ (3)

Subject to the constraints:

iijij SjxTT ∈∀≥−− ,0 (4)

ijijij xD δ≤≤ (5)

n

ji

ij Tx∑∈

=µ),(

(6)

λ=nT (7)

nnD δλ ≤≤ (8)

niji TxT p+ (9)

Legend: (i, j) = arc from the summit i (step Ei) to the summit j (step Ej);

CDij = normal cost of the activity Aij

Dn = initial deadline of the project

δn = maximum delay for the whole project

λ = new deadline fixed for the completion of the construction project

µ = sub-setof the activities on the criticalpath

Si = set of the successors of the stageEi

Ti, Tj = the earliest dates of the start of the steps Ei and Ej 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

CW n= : daily cost of the construction project.

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

of the contract, with 0.01 ≤β ≤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 α (compression factor)designates a multiple of the initial resource reflecting the additional cost;

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

(I)



119

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

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

(7): constraints meaning that the date of completion of the project shall not exceed a clearly determined deadline. This date is imposed by the parameter λ;

(8): constraint meaning that the parameter λ must be limited between the normal deadlineDn and the skidded duration δn.

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

The decision variables are represented by xij and are non-negative (xij≥ 0). The CCOMTOC assumes that the parameters CDij and λ are constants. In reality, these are estimators based on predictions of future conditions. Therefore, the resulting calculations are generally used to starting point to support subsequent analyses of the problem [Djila, 2009]. 4. IMPROVEMENT OF THE CCOMTOC: INITIATING OF A TASK BEFORE THE

NORMAL DEADLINE If the delay in the progress of the work is envisaged after having realized a part of the task Aij in time σij<Dij (Figure 2), then this leads us to modify equation (2), which gives:

ijijij WxCxC σβ−=′ )()( 11

That is: ))(()(1 ijijijij DxWxC σβ +−=′ (10)

Also the equation (3) becomes:

ijijijij WxCxC σα )1()()( 22 −−=′

That is: ))(()1()( 22 ijijijijij xWCxC

ij−−−+=′ σδα

δ (11)

with: ij

Dij

ijD

CW = : daily cost of theAij. (12)

Note that ifσij = 0, this means that the task Aij has not been initiated before the prescribed deadline Dij. Then, we find the original model. The cost of the compression of a task is influenced by the coefficient α, multiplicative factor of compression, which reflects the importance of the additional resource compared to the initial resource (see equation (3)). In reality, the coefficient α is not constant; it depends on the considered task. Also in the equation (3), we will replace α byαij, corresponding to the task Aij. Similarly, in equation (2), the daily cost of the project W, which was considered to be uniform for all activities, will be replaced by Wij, meaning that the daily cost may be different for each activity Aij. So, we must have:

))(()(1 ijijijjiij DxWxC σβ +−=′ (13)

))(()1()( 22 ijijijijijij xWCxC

ij−−−+=′ σδα

δ (14)



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Legend:

σij = duration already carried out for the execution of the activity Aij

C’1(xij)= new penalties cost C’2(xij)= new cost resulting from the compression The improvement of CCOMTOC concerns essentially the coefficient αij,the daily cost Wij and the introduction of the duration of initiating σij relative to the task Aij. Also the improved CCOMTOCcan be written:

C'1 (xij)

C2 (xij)

C2 ij

Pij

C 2 ij

C1 ij

0 DijDij+σσσσij∆ijδij-σσσσijδijxij

C'2 (xij)

C1(xij

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



121

�� ′� ∑ ��

′ � �� ∑ ��′ � ��,��,�� (1)

��′ �� !�� (13)

�"′ �� "#�� $�� #�� !�� (14)

Subject to the constraints: iijij SjxTT ∈∀≥−− ,0 (4)

�� !�� % �� % #�� !�� (15)

& % !�� %�

"�#�� (16)

n

ji

ij Tx∑∈

=µ),(

(6)

λ=nT (7)

nnD δλ ≤≤ (8)

niji TxT p+ (9)

It should be noted that the original model (I) is replaced by the improved model (II). The modification of the original model concerns the equations (13) and (14), as well as the constraints (15) and (16). Thus, the reduction of the additional costs induced by the skid of the duration is possible with the CCOMTOC, starting from the following assumptions:

- The delay on the whole construction project is foreseen before the launch of the works, causing 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 the initiating 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 as illustration a project for the rehabilitation of thepremises of a site. 5. COMPARATIVE STUDY OF THE IMPROVED CCOMTOC AND THE ORIGINAL

CCOMTOC: APPLICATION TO THE CASE OF A PROJECT FOR THE

REHABILITATION OF THE PREMISES OF A SITE

The project which is the subject of our case study concerns the rehabilitation of the premises of 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 3 buildings of 2 bedrooms, living room, kitchen and a bathroom).

- A technical building (containing an electrical room, water room, and electric engineering local);

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

(II)



122

Criticalpath

The designation and allocation of cost by tasks are given in Appendix A. We determined the operating 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 exceeding of initial deadline. We assumed exceeded the cost and the deadline of the works, after starting up of the project. This skid suggests us to proceed to theoptimization of the total cost of the project through the improved CCOMTOC. The normal work schedule (Figure 3: PERT chart) indicates the initial date of completion of the 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 pessimistic estimation of the duration then allows us to assign to each operation a maximum delay that causes the skid of the normal operating duration of the activity Aij. This problem of skid will result ipso facto 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 initiated (original CCOMTOC) and the partial time-overrun contextwith tasks initiated (improved CCOMTOC). 5.1. ORIGINAL CCOMTOC: THE PARTIAL TIME-OVERRUN CONTEXT WITH NOT

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

1 1€ = 655.95 F FCA ; 1$ US = 500 F CFA



123

the tasks that will be performed after the whole construction project has fell overto a situation of delay. The start of works took place on the scheduled date. After the normal execution of the tasks A, B, C, D, E, F and J, and for any reasons (delay due to funding, the unavailability of materials, loss of the workforce or change of supervision, etc.), the remaining tasks of the project undergo a delay at the starting up causing a lengthening of their deadlines. In the present case, the optimization of the cost of the construction project is required to avoid significant cost-overrun due to the delay penalties and other charges (including rental charges). In our analysis, we consider firstly the tasks situatedon the critical path (Figure 3), those which 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. Anticipated skid is thus of 60 days over the initial deadline, that is an exceeding of time of 31%. The cost of the construction 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 of tasks amounts to 2,086,980,000 F CFA, while the optimized total cost of delay penalties is 102,301,000 F CFA (Appendix C, β = 0.70). The optimized total cost of the whole construction project 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 enormous financial losses within the company, because this has not been first expected in the planning of the project management structure in charge of the realization of the works. Under these conditions, it should be advisable to readjust this skid so that the total duration of the works is reduced to 215 days, while remaining rigorous in the performance of the works and the compliance with technical standards, as well as measures and safety instructions in the building and public works industry (construction). The simulation is performed thanks to the specialized language of linear programming software Visual Xpress-MP. An illustration of this simulation is presented in Appendix B, for a 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, the optimized total cost will then be 2,177,780,000F CFA (Appendix B, β = 0.70). It now represents a little lower overrun of the initial total cost, equal to 34.9%. This shortening of the deadline of completion, decided to minimize the total cost, led to a reduction of the additional cost of 0.7%, and therefore an apparent gain of 11,500,000 F CFA. This deadline fixed in 215 days gives us a new work schedule (Appendix B) fixing the optimal duration of each activity, as well as the corresponding optimal cost. We can notice that in the optimized schedule, the optimal duration of an activity is generally always chosen so as to impose the initial normal duration, except for the activities D1 and E1where the skidded duration is necessary, and especially the activity B1which takes a random duration generated by the calculation program and contained between D9,10 and δ9,10. The extension of the simulation to various deadlinesof completion of the construction project gave the results reported in Appendix C. The different values of costs, in relation to the deadlines of completion, allowed us to plot cost-time curves (TCT: Time-Cost-Trade-off) illustrated in figure 4.



124

The two curves of figure 4 have the same shape. They are characteristic of the TCT curves in a time-overrun context [Louzolo, 2005; Louzolo, 2014]. These curves are symmetrical to the TCT curves obtained in the usual context where the construction project must be delivered before the initial date of completion [Leu et al., 1999; Beasley, 2003]. Under normal circumstances, delay penalties are not taken into account. The TCT curve with β = 0.70 is above that with β = 0.60 (Figure 4). This shows that the penalties attenuation coefficient β 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 WITH

INITIATED TASKS We consider that our project is in situation of delay. Some tasks are already completed, while some of those that are initiated are delayed. In this case the delay will concern the begun tasks and those whose execution has not yet started. The starting up of the works took place on the scheduled date. But, for the same reasons as those pointed out in the first case, some tasks undergo an extension of the duration of execution. Note that tasks A, B, C, D, E, F and J were realized in due time, and that there was initiating of tasks G, 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 not completed to avoid significant financial losses. We illustrate in Appendix D (λ= 215 days, β = 0.70) the results of the simulation of a minimization of construction project cost in a partial time-overrun context with initiatedtasks. The optimal solution wishedfor λ = 215 days indicates a minimum cost of 2,128,180,000 F CFA (Appendix D, β = 0.70). This represents more than an exceedingof the initial total cost of 31.82%, while for λ = 255 days the cost-overrun is 32.35%. Thus the reduction of the cost-overrun will be 0.53% if we shorten the deadline of completion from 255 to 215 days that is a gain of about 8,560,000 F CFA.

2.167

2.170

2.173

2.176

2.179

2.182

2.185

2.188

2.191

215 220 225 230 235 240 245 250 255

Min

imu

m t

ota

l co

st (

x 1

06

F C

FA

)

Total duration of the construction project (day)

Ct _0.6

Ct_0.7

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



125

The calculation program generated values of operating durations other than Dij or δij for the tasks G, K, L, U, W and H1, thus offering a new optimized schedule for λ = 215 days. Note that these tasks are other than those who have been initiated. The optimal solutions of construction costs resulting from the simulation, with values of coefficients ofattenuationof penalties β 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 β = 0.60, while for β = 0.70 the cost varies slowly between 215 and 225 days. Beyond these deadlines, the cost varies very quickly that the delay increases. 5.3. COMPARISON OF THE IMPROVED CCOMTOCWITH THE ORIGINAL CCOMTOC We place two-two on the same graphic the curves TCT of figure 4 (original CCOMTOC) and those of figure 5 (improved CCOMTOC), respectively for β = 0.60 and β = 0.70.

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

2.117

2.120

2.123

2.126

2.129

2.132

2.135

2.138

215 220 225 230 235 240 245 250 255

Min

imu

m t

ota

l co

st (

x 1

06

F C

FA

)


C't _0.6

C't_0.7

2.115

2.125

2.135

2.145

2.155

2.165

2.175

215 220 225 230 235 240 245 250 255

Min

imu

m t

ota

l co

st (

x 1

06

F C

FA

)


Ct _0.6

C't _0.6

Figure (6): Comparison of curves Ct (original CCOMTOC) and C’t(improved CCOMTOC), for β = 0.60



126

We note that in both cases, β = 0.60 and β = 0.70, the curve corresponding to the improved CCOMTOC is below the curve Ctof the original CCOMTOC (Figures 6 and 7). This means that the cost-overrun caused by the delay is actually lower than planned by the original model. The results of the comparison between the two models are contained in table 1.

: Total cost of the construction project calculated with the original CCOMTOC : Total cost of the construction project calculated with the improved CCOMTOC

The difference of the total cost of the construction project calculated by using, respectively, the original CCOMTOC and the improvedCCOMTOC seems enough significant. It increases when we pass from 215 to 255 days. On figure 8 we represent the rate of variation of the cost, calculated

λ (day)

215 220 225 230 235 240 245 250 255

Ct

(106 F CFA) 2,177.78 2,178.14 2,178.99 2,180.03 2,181.22 2,182.43 2,184.37 2,186.31 2,189.28

(106 F CFA) 2,128.18 2,128.21 2,128.58 2,129.43 2,130.47 2,131.66 2,132.87 2,134.81 2,136.74 ∆Ct (106

F CFA) 49.6 49.93 50.41 50.6 50.75 50.77 51.5 51.5 52.54

(%) 2.28 2.29 2.31 2.32 2.33 2.33 2.36 2.36 2.40

Figure (7): Comparison of curves Ct (original CCOMTOC) and C’t (improved CCOMTOC), for β = 0.70

Table (1): Comparison between the improved CCOMTOC and the original CCOMTOC (β = 0.70)

2.125

2.135

2.145

2.155

2.165

2.175

2.185

2.195

215 220 225 230 235 240 245 250 255

Min

imu

m t

ota

l co

st (

x 1

06

F C

FA

)


Ct_0.7

C't_0.7



127

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

6. CONCLUSION The problem of time-overrun is a scourge that several companies knowall around the world. They are regularly victims by lack of effective managerialpractice, since the design phase of the project up to its implementation. For this purpose, the recourse of an optimal organization of projects becomes an essential factor for the success of the construction companies confronted with a situation of time-overrun. The improvement of the original CCOMTOC aims to approachat best of the practical realities for the treatment of this type of problem. The illustration through a case study allowed showing that the improved CCOMTOC provides a more significant reduction of the total cost of a construction project in situation of delay than does the original CCOMTOC. The difference is even greater that the delay becomes more important. The time-overrun context is actually only a consequence resulting from a violation of certain parameters of the project by the actors who are involved there. The improved CCOMTOCtries to give the best possible answers on how projects suffering from an exceeding of provisional deadline of execution must be planned and managed optimally to minimize the cost-overruns induced by the delay. Note, however, that the improved CCOMTOC is limited by the restriction placed upon the value of the duration of initiating of a task (σij), which may not exceed half of the difference betweenskidded duration and normal duration for a task, that is the quantity (δij - Dij) / 2.Thus, this model remains to perfect in order to take into account most important durations of initiating.

2.27

2.30

2.33

2.36

2.39

2.42

215 220 225 230 235 240 245 250 255

Ra

te o

f va

ria

tio

n o

f th

e c

on

stru

ctio

n c

ost

(%

)

Total duration of construction project (day)

DCt/Ct (%)

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

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



128

7. REFERENCES

[1] A. A. Aibinu, G. O. Jagboro, "The effects of construction delays on project delivery in

Nigeria construction industry ", International Journal of Project Management, vol. 20, no. 8, pp. 593-599, 2002.

[2] M. I. Al-Khalil, M. A. Al-Ghafly, "Delay in public utility projects in Saudi Arabia", International Journal of Project Management, vol. 17, no. 2, pp. 101-106, 1999.

[3] A. H. Al-Momami, "Construction delay: a quantitative analysis", International Journal of

Project Management, vol. 18, pp. 51-59, 2000. [4] H. Al-Tabtabai, N. Quadumi, H. Al-Khaiat, A. P. Alex, "Delay penalty formulation for

housing projects in Kuwait", International Journal of Housing Science and its Applications, vol. 22, no. 2, pp. 109-124, 1998.

[5] S. A. Assaf, S. Al-Hejji, “Causes of delay in large construction projects”, International

Journal of Project Management, vol. 24, pp. 349-357, 2006. [6] J. E. Beasley, "Operation Research Notes", Imperial College, 2003. Available on: http://mscmga.ms.ic.ac.uk/jeb/or/netcpm.html. (Accessed at April 2004). [7] F. A. Chalabi, D. Camp, "Causes of delays and overruns os construction projects in

Developing Countries", CIB Proceedings, W-65, vol. 2, pp. 723-734, 1984. [8] C. D'Alpaos, M. Moretto, P. Valbonesi, S. Vergalli, "It is never too late: Optimal penalty for

investment delay in Italian public procurement contracts", Nota di Lavoro 78.2009

dellaFodazioneEni Enrico Mattei, Institutions and markets series. Available on: http://www.feem.it/Feem/Pub/Publications/WPapersdefault.htm. (Accessed at

19 October 2010). [9] R. Djila, "Analyse de sensibilité dans le modèle d'optimisation du coût de la construction

dans un contexte hors délai (MO3CHD)", Mémoire d'Ingénieur de conception en Génie civil, Ecole Nationale Supérieure Polytechnique de Brazzaville, Université Marien Ngouabi, 80 p., 2009.

[10] Y. Frimpong, J. Oluwoye, L. Crawford, "Causes of delay and cost overruns in construction of groundwater projects in Developing Countries; Ghana as case study", International Journal

of Project Management, vol. 21, no. 5, pp. 321-326, 2003. [11] P. A. Koushki, K. Al-Rashid, N. Kartam, “Delays and cost increases in construction of

private residential projects in Kuwait”, Construction Management and Economics, vol. 23, pp. 285-294, March 2005.

[12] S.-S. Leu, C.-H. Yang, "GA-based multcriteria optimal model for construction scheduling", Journal of Construction Engineering and Management, ASCE, vol. 125, no. 6, pp. 420-427, 1999.

[13] P. Louzolo-Kimbembé, "Contribution aux méthodes de maîtrise du coût de la construction dans les pays en développement: estimation du coût et optimisation dans un contexte hors délai", thèse Ph. D, Ecole Nationale Supérieure Polytechnique de Yaoundé, Cameroun, 304 p., 2005.

[14] P. Louzolo-Kimbembé, C. Pettang, T. TamoTatiétsé, "Minimisation des surcoûts dans un contexte hors délai: cas des projets de construction dans les Pays en Développement", Canadian Journal of Civil Engineering, vol. 34, no. 9, pp. 1180-1191, 2007.

[15] P. Louzolo-Kimbembé, E. Mbani, "New approach of delay penalties formulation: Application to the case of construction projects in the Republic of Congo", Journal of Civil

Engineering and Construction Technology, vol. 4, no. 1, pp. 6-22, 2013. [16] P. Louzolo-Kimbembé, " Maîtrise du coût de la Construction dans les Pays en

développement: Estimation du Coût et Optimisation dans un Contexte Hors Délai", Editeur:



129

Presses Académiques Francophones (paf), imprimé par Schaltungsdienst Lange o.H.G., Berlin (Allemagne), 438 p., 2014.

[17] N. R. Mansfield, O. O. Ugwu, T. Dora, "Causes of delay and cost overruns in Nigeria construction projects", International Journal of Project Management, vol. 12, no. 1, pp. 254-260, 1994.

[18] A. Shebob, N. Dawood, R. K. Shah, "Development of a methodology for analyzing and quantiying the impact of delay factors affecting construction projects", Journal of

Construction Engineering and Project Management", vol. 2, no. 3, pp. 17-29, 2012. [19] Singh R., “Delays and cost overruns in infrastructure projects: an enquiry into extents, causes

and remedies”, Working paper no. 181, Centre for Development Economics, Department of Economics, Delhi School of Economics, 27 p., 2009.

Available on: http://www.econdse.org/faculty/ram/ram.htm (Accessed at October 2013). [20] R. Y. Tse, P. E. D. Love, "An economic analysis of the effect of delays on project costs",

Journal of Construction Research, vol. 4, no 2, pp. 155-160, 2003.

APPENDIX

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

Share

Code of tasks

Overview of tasks

Task durations Dij (day)

Costs of tasksCDij (F CFA)

N°1

: Pa

th a

nd V

ario

us n

etw

orks

–C

ivil

engi

neer

ig

A Installation construction site 06 4,220,000

B Removal of the openings of the ducts 08 100,000

C Trenchand the openings of the ducts 20 13,346,500

D Laying pipe 10 70,710,000

E Network adduction and networks

15 10,380,000

F Heavy work 25 22,745,250

G Roof 10 1,680,000

H Metalwork and painting 15 5,780,000

I Tiles 30 5,085,000

N

°2: R

evam

ping

-Kitc

hen

J Removal and modification kitchens 10 28,210,000

K Manufacturing 70 48,000,000

L Plumbing and electricity 35 90,792,000

M Tiles 30 36,960,000

N Laying and partition 45 23,400,000

O Painting/Coating 22 19,550,000

N°3

: C

arpe

nter

y P Carpenterywood and aluminium 30 156,900,000

Q Glaziery and mosquito nets 30 13,575,000

N°4

: Pl

umbi

ng

R Removal 15 9,000,000

S Network and equipment 35 20,400,000

T Suppressor 15 37,050,000



130

Share

Code

of tasks

Overview of tasks

Task duration

s Dij

(day)

Costs of tasksCDij (F CFA)

N°5

: Ele

ctri

cal c

ompl

ianc

e

U Removalelectrical installation 20 4,700,000

V Équipotential 20 1,900,000

W High-voltage transformer and celles 26 67,050,000

X Circuit breaker connectionand electrical 16 19,480,000

cupboards

Y Pathways 20 10,360,000

Z

Local equipments 17 17,890,000

A1 Connections and building equipments 20 38,740,000

B1 Électricity–Lowcurrents 15 600,000

C1 Firedetection

10 830,000

N°6

: Ele

ctri

cal

engi

neer

ing

– T

ank

dies

el f

uel

D1 Electrical engineering material removal and equipotential

08 8,530,000

E1 Generators 10 111,500,000

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

N°7

: Tel

ecom

net

wor

k an

d ho

useh

old

elec

tric

al a

pplia

nces

G1 Telecom network and television 35 162,560,500

H1

Household electrical appliances purchase and imported furnishingspurchase

79

420,000,500

I1 Localfurnishingspurchase 60 98,000,000

Total

1,614,449,750

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

Note that the compression factor of tasks is found by calculating the ratio'�� ()*/�,)*.



131

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

CCOMTOC

Tas

ks

Prev

ious

st

ages

Subs

eque

nt

stag

es

Nor

mal

du

rati

on

(day

) Sk

idde

d du

rati

on

(day

)

Nor

mal

cos

t (1

03 F

CFA

)

Skid

ded

cost

s w

ithou

t pe

nalt

ies

(103 F

CFA

)

Com

pres

sio

n fa

ctor

Optimal solution Earliest

new starting up date

Optimal duration

(day)

Optimal

cost (103 F CFA)

i j Dij δij CDij C2δij αij xij C(xij)

A 1 2 6 6 4,220 4,220.00 1.00 0 6 4,220 B 2 13 8 8 100 100.00 1.00 6e 8 100 C 2 3 20 20 13,346.5 13,346.50 1.00 6e 20 13,346.5 D 13 4 10 10 70,710 70,710.00 1.00 26e 10 91,923 E 3 4 15 15 10,380 10,380.00 1.00 26e 15 10,380 F 3 17 25 25 22,745.25 22,745.25 1.00 26e 25 22,745.3 G 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 9,016.8 I 19 20 30 38 5,085 6,441.00 1.28 76e 30 6,820.68 J 2 21 10 10 28,210 28,210.00 1.00 6e 10 28,210 K 21 23 70 75 48,000 51 ,428.57 1.07 16e 70 51,668.6 L 21 22 35 40 90,792 103,762.29 1.15 16e 35 105,708 M 22 23 30 40 36,960 49,280.00 1.34 51e 30 53,468.8 N 22 9 45 55 23,400 28,600.00 1.23 51e 45 29,796 O 23 20 22 27 19,550 23,993.18 1.23 86e 22 25,015.1 P 14 15 30 35 156,900 183,050.00 1.17 46e 30 187,496 Q 15 16 30 40 13,575 18,100.00 1.34 175e 30 19,638.5 R 8 24 15 19 9,000 11,400.00 1.27 120e 15 12,048 S 24 25 35 40 20,400 23,314.29 1.15 135e 35 23,751.4 T 25 27 15 20 37,050 49,400.00 1.34 170e 15 53,599 U 13 14 20 33 4,700 7,755.00 1.65 26e 20 47,470 V 14 5 20 33 1,900 3,135.00 1.65 46e 20 3,937.75 W 4 5 26 35 67,050 90,259.62 1.35 41e 26 98,383 X 5 6 16 25 19,480 30,437.50 1.56 67e 16 36,573.7 Y 6 7 20 25 10,360 12,950.00 1.25 83e 20 13,597.5 Z 7 8 17 25 17,890 26,308.82 1.47 103e 17 30,265.7 A1 8 9 20 30 38,740 58,110.00 1.50 120e 20 67,795 B1 9 10 15 23 600 920.00 1.53 140e 20 1,123.6 C1 16 27 10 11 830 913.00 1.10 205e 10 921.3 D1 10 11 8 15 8,530 15,993.75 1.88 160e 15 21,218.4 E1 11 12 10 18 111,500 200,700.00 1.80 175e 18 263,140 F1 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 35 177,888 H1 1 26 79 90 420,000.5 478 ,481.58 1.14 0 79 486,669 I1 26 27 60 75 98,000 122,500.00 1.25 79e 60 128,625

Dn

(day)

δn

(day)

Total

(103 F CFA)

Total

(103 F CFA)

Tn Imposed

total duration

(day)

Minimum total cost

(103 FCFA)

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



132

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

tasks; original CCOMTOC

Val

ue o

f th

e at

tenu

atio

n co

effi

cien

t β

Proj

ect i

niti

al

dead

line

(da

y)

Dn

Optimal solution

Impo

sed

dead

line

aft

er

skid

ding

(d

ay)

λ =

Tn

Opt

imiz

ed to

tal

cost

of

pena

lties

C

t1 (

103

F C

FA

)

Opt

imiz

ed to

tal

cost

fro

m

com

pres

sion

C

t2(1

03 F

CFA

)

Opt

imiz

ed to

tal

cost

of

the

proj

ect

Ct(1

03 F

CF

A)

0.60

195

215 60,938.3 2,106,920 2,167,860 220 62,471.3 2,105,490 2,167,960

225 66,123.8 2,102,080 2,168,210

230 69,479 2,099,230 2,168,710

235 72,636 2,096,760 2,169,400

240 74,190 2,096,110 2,170,300

245 80,001 2,091,270 2,171,270

250 85,812 2,086,430 2,172,240

255 107,649 2,066,640 2,174,290

0.70

195

215 67,804.6 2,109,970 2,177,780 220 69,593.1 2,108,550 2,178,140

225 73,854.4 2,105,140 2,178,990

230 76,646.7 2,103,380 2,180,030

235 79,581.8 2,101,640 2,181,220

240 83,265.1 2,099,170 2,182,430

245 90,044.6 2,094,330 2,184,370

250 96,824.1 2,089,480 2,186,310

255 102,301 2,086,980 2,189,280



133

Dn: Initial deadline; δn: Skidded total duration; Tn: Imposed total duration; '�� ()*/�,)*

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

CCOMTOC

Tas

ks

Prev

ious

st

ages

Subs

eque

nt

stag

es

Nor

mal

du

rati

on

(day

) Sk

idde

d du

rati

on

(day

)

Dur

atio

n of

in

itiat

ing

(day

)

Nor

mal

cos

t (1

03 F

CFA

)

Skid

ded

cost

s w

ithou

t pe

nalt

ies

(103 F

CFA

)

Com

pres

sion

fa

ctor

Optimal solution

Earliest new

starting up date

Optimal duration

(day)

Optimal cost (103 F CFA)

i j Dij δij σij CDij C2δij αij xij C'(xij)

A 1 2 6 6 0 4,220 4,220.00 1.00 0 6 4,220

B 2 13 8 8 0 100 100.00 1.00 6e 8 100 C 2 3 20 20 0 13,346.5 13,346.50 1.00 6e 20 13,346.5

D 13 4 10 10 0 70,710 70,710.00 1.00 26e 10 91,923

E 3 4 15 15 0 10,380 10,380.00 1.00 26e 15 10,380

F 3 17 25 25 0 22,745.25 22,745.25 1.00 26e 25 22,745.3

G 17 18 10 13 1 1,680 2,184.00 1.30 51e 11 2,234.4

H 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 6,820.68

J 2 21 10 10 0 28,210 28,210.00 1.00 6e 10 28,210 K 21 23 70 75 2 48,000 51,428.57 1.07 16e 72 51,476.6

L 21 22 35 40 2 90,792 103,762.29 1.15 16e 37 104,151

M 22 23 30 40 0 36,960 49,280.00 1.34 53e 30 53,468.8

N 22 9 45 55 0 23,400 28,600.00 1.23 53e 45 29,796 O 23 20 22 27 0 19,550 23,993.18 1.23 88e 22 25,015.1

P 14 15 30 35 0 156,900 183,050.00 1.17 52e 30 187,496

Q 15 16 30 40 0 13,575 18,100.00 1.34 175e 30 19,638.6

R 8 24 15 19 0 9,000 11,400.00 1.27 125e 15 12,048

S 24 25 35 40 0 20,400 23,314.29 1.15 140e 35 23,751.4

T 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 10,810 V 14 5 20 33 0 1,900 3,135.00 1.65 52e 20 3,937.75

W 4 5 26 35 3 67,050 90,259.62 1.35 41e 31 94,772.6

X 5 6 16 25 0 19,480 30,437.50 1.56 72e 16 36,573.7

Y 6 7 20 25 0 10,360 12,950.00 1.25 88e 20 13,597.5 Z 7 8 17 25 0 17,890 26,308.82 1.47 108e 17 30,265.7

A1 8 9 20 30 0 38,740 58,110.00 1.50 125e 20 67,795

B1 9 10 15 23 0 600 920.00 1.53 145e 15 1,089.6

C1 16 27 10 11 0 830 913.00 1.10 205e 10 921.3

D1 10 11 8 15 0 8,530 15,993.75 1.88 160e 15 21,218.4

E1 11 12 10 18 0 111,500 200,700.00 1.80 175e 18 263,140

F1 12 27 22 29 0 34,425 45,378.41 1.32 193e 22 48,883.5

G1 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 84 479,226

I1 26 27 60 75 0 98,000 122,500.00 1.25 84e 60 128,625

Dn

(jour)

δn

(jour)

Total

(103 F CFA)

Total

(103 F CFA)

Tn Imposed

total duration

(day)

Minimum total cost

(103 FCFA)

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



134

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

overrun context with initiated tasks; improvedCCOMTOC

Val

ue o

f th

e at

tenu

atio

n co

effi

cien

t β

Proj

ect i

nitia

l dea

dlin

e (d

ay)

D

n

Optimal solution

Impo

sed

dead

line

aft

er

skid

ding

(d

ay)

λ =

Tn

Opt

imiz

ed to

tal c

ost o

f pe

nalt

ies

C

t1 (

103 F

CF

A)

Opt

imiz

ed to

tal c

ost

from

com

pres

sion

C

t2(1

03 F

CFA

)

Opt

imiz

ed to

tal c

ost o

f th

e pr

ojec

t

Ct(1

03 F

CF

A)

0.60

195

215 61,092.9 2,056,910 2,118,000

220 61,212.9 2,056,800 2,118,010

225 62,745.9 2,055,370 2,118,120

230 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 2,128,180

220 71,415 2,056,800 2,128,210

225 73,203.5 2,055,370 2,128,580

230 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