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.

1. 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
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
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114
IJCIET
©IAEME
IMPROVEMENT OF THE MODEL OF MINIMIZATION OF THE COSTS IN
A TIME-OVERRUN CONTEXT: CASE OF CONSTRUCTION PROJECTS
Paul Louzolo-Kimbembe1, BenoîtRomaric Mampika-Bathy2
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

2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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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.
115
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.

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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The following methodology is adopted in this study:
116
2. METHODOLOGY
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.

4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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Pij
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
C2ij= maximum additional cost resulting from the acceleration of the activityAijto the catch up the
delay.
117
Legend:
Pij = cost of the activity Aij
xij = duration of the activity Aij
Dij = normal duration of the activity Aij
The mathematical formulation of the CCOMTOC is given by the linear program below
[Louzolo et al, 2007]:
C2 ij
C 2 ij
C1 ij
0 Dijijijxij
Figure (1): Curves representing the penalty costs (C1), and the costs resulting
fromthe compression (C2), for the activity Aij.

5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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t ij Minimize C C x C x
= + a − d d (3)
ij x
118
= +
Î Î
i j U
ij
i j U
( , )
2
( , )
1 ( ) ( ) (1)
( ) ( ) 1 ij ij ij C x = b W x − D (2)
D
( ) ( 1) ( ) 2 2 ij ij
D
ij
C
C x C ij
ij
−
Subject to the constraints:
j i ij i T −T − x ³ 0, j ÎS (4)
ij ij ij D £ x £d (5)
n
ij x T
i j
Î
=
( , ) μ
(6)
= l n T (7)
n n D £ l £ d (8)
i ij n T + x p T (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
n = maximum delay for the whole project
= 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).
D
D
n
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 the
initial resource reflecting the additional cost;
(4): constraints expressing the dependency relationships in the program, i.e. the link between tasks;

6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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(5): constraints indicating the limitation of the duration of each activity, in other words, they
¢ = + a − d −s − d (11)
¢ = + a − d −s − d (14)
119
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 ;
(8): constraint meaning that the parameter must be limited between the normal deadlineDn and the
skidded duration n.
(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 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 ijDij (Figure 2), then this leads us to modify equation (2), which gives:
ij ij ij C¢(x ) = C (x ) −b Ws 1 1
That is:
( ) ( ( )) 1 ij ij ij ij C¢ x = b W x − D +s (10)
Also the equation (3) becomes:
ij ij ij ij C ( x ) C ( x ) (a 1)W s 2¢ = 2 − −
That is:
( ) ( 1) (( ) ) 2 ij 2 ij ij ij ij C x C W x
ij
with:
Dij
ij D
ij
C
W = : daily cost of theAij. (12)
Note that ifsij = 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 , multiplicative factor
of compression, which reflects the importance of the additional resource compared to the initial
resource (see equation (3)). In reality, the coefficient is not constant; it depends on the considered
task. Also in the equation (3), we will replace byij, 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 ij i j ij ij ij C¢ x = b W x − D +s (13)
( ) ( 1) (( ) ) 2 ij 2 ij ij ij ij ij C x C W x
ij

7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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Pij
ij = 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
120
Legend:
The improvement of CCOMTOC concerns essentially the coefficient ij,the daily cost Wij and
the introduction of the duration of initiating ij relative to the task Aij.
Also the improved CCOMTOCcan be written:
C2 ij
C 2 ij
C1 ij
0 DijDij+sijijij-sijijxij
Figure (2): Consideration of the initiating of the task Aij before the exceeding
of the deadline Dij

8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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121

9. (1)

10. ! (13)
#

11. $

12. # ! (14)
Subject to the constraints:
j i ij i T −T − x ³ 0, jÎS (4)
! % % # ! (15)
% ! %

13. # (16)
n
ij x T
i j
Î
=
( , ) μ
(6)
= l n T (7)
n n D £ l £ d (8)
i ij n T + x p T (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.

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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
122
the project to the 195th day.
Criticalpath
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

15. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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the tasks that will be performed after the whole construction project has fell overto a situation of
delay.
123
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, = 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, = 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 9,10.
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.

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17. !# $%
!'(! )*+# $(# ,( -+#'!.
/
/
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
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 = 0.70 is above that with = 0.60 (Figure 4). This shows that the
penalties 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 WITH
124
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 (l= 215 days, = 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 = 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 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.

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The calculation program generated values of operating durations other than Dij or ij for the
tasks G, K, L, U, W and H1, thus offering a new optimized schedule for = 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 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 cost
varies very quickly that the delay increases.

19. Figure (5):Curves TCT ( = 0.60 and = 0.70) for the wholeconstruction project,
in a partial time-overrun context with initiated tasks; improvedCCOMTOC
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 = 0.60 and = 0.70.
125
!# $%
!'(! )*+# $(# ,( -+#'!.
0/
0/

20. /
0/
Figure (6): Comparison of curves Ct (original CCOMTOC) and C’t(improved CCOMTOC), for = 0.60

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22. /
0/
Figure (7): Comparison of curves Ct (original CCOMTOC) and C’t (improved CCOMTOC), for = 0.70
We note that in both cases, = 0.60 and = 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.
Table (1): Comparison between the improved CCOMTOC and the original CCOMTOC ( = 0.70)
: 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
126
l
(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

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with two models, according to the duration of the construction project. We note that this rate increase
strongly for a rising delay.
!'(! )# $(# ,( -+#'!.
Figure (8): Rate of variation of the construction cost ,
with , depending on the duration of the construction project ( = 0.70)
127

24. 1!+ )2!(! )*+# $(# # $3
6. CONCLUSION
453
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 (sij), which may not exceed half of the difference
betweenskidded duration and normal duration for a task, that is the quantity (ij - Dij) / 2.Thus, this
model remains to perfect in order to take into account most important durations of initiating.

25. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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7. REFERENCES
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ISSN 0976 – 6316(Online), Volume 5, Issue 9, September (2014), pp. 114-134 © IAEME
129
Presses Académiques Francophones (paf), imprimé par Schaltungsdienst Lange o.H.G.,
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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: Path and Various networks –
Civilengineerig
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: Revamping-Kitchen
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:
Carpentery
P Carpenterywood and aluminium 30 156,900,000
Q Glaziery and mosquito nets 30 13,575,000
N°4:
Plumbing
R Removal 15 9,000,000
S Network and equipment 35 20,400,000
T Suppressor 15 37,050,000

27. 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
130
Share
Code
of tasks
Overview of tasks
Task
duration
s
Dij
(day)
Costs of tasksCDij
(F CFA)
N°5: Electrical compliance
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: Electrical
engineering – Tank
diesel fuel
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: Telecom network
and household
electrical appliances
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; dn: Skidded total duration; Tn: Imposed total duration
Note that the compression factor of tasks is found by calculating the ratio' ()*+,)*.

28. 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
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 (l = 215 days; = 0.70); original
CCOMTOC
Tasks
Previous
stages
Subsequent
stages
Normal
duration
(day)
Skidded
duration
(day)
Normal cost
(103 F CFA)
Skidded
costs
without
penalties
(103 F CFA)
Compressio
n factor
Optimal solution
Earliest
new
starting
up date
Optimal
duration
(day)
Optimal
cost
(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 4,220
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)
dn
(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

29. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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132
Appendix - C: Synthetic results of the simulation for values of attenuationcoefficient of
penaltiesfixed to = 0.60 and = 0.70, case of the time-overrun context with not initiated
tasks; original CCOMTOC
Value of the
attenuation
coefficient
Project initial
deadline (day)
Dn
Optimal solution
Imposed
deadline after
skidding
(day)
l = Tn
Optimized total
cost of penalties
Ct1 (103 F CFA)
Optimized total
cost from
compression
Ct2(103 F CFA)
Optimized total
cost of the
Ct(103 F CFA)
project
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

30. 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
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 (l = 215 days; = 0.70); improved
CCOMTOC
i j Dij ij sij CDij C2ij ij 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
(103 F CFA)
195 255 1,614,449.75 1,967,142.97 215 2,128,180
133
Tasks
Previous
stages
Subsequent
stages
Normal
duration
(day)
Skidded
duration
(day)
Duration of
initiating (day)
Normal cost
(103 F CFA)
Skidded
costs without
penalties
(103 F CFA)
Compression
factor
Optimal solution
Earliest
new
starting
up date
Optimal
duration
(day)
Optimal cost
(103 F CFA)
Dn
(jour)
dn
(jour)
Total
(103 F CFA)
Total
Tn
Imposed
total
duration
(day)
Minimum total
cost
(103 FCFA)
Dn: Initial deadline; dn: Skidded total duration; Tn: Imposed total duration; ' ()*+,)*

31. 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
134
Appendix - E: Synthetic results of the simulation for values of penalties
coefficient of attenuation fixed to = 0.60 and = 0.70, case of the time-overrun
context with initiated tasks; improvedCCOMTOC
Value of the attenuation
coefficient
Project initial deadline (day)
Dn
Optimal solution
Imposed deadline after
skidding
(day)
l = Tn
Optimized total cost of
Ct1 (103 F CFA)
penalties
Optimized total cost
from compression
Ct2(103 F CFA)
Optimized total cost of
the project
Ct(103 F CFA)
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