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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 765
Planning and Optimization of Resource Constrained Project Scheduling
by Using Genetic Algorithm
Vineetha. S1 , Manjusha. M2
1Student, Dept. Of Civil Engineering, Sri Vellappally Natesan Collage of Engineering , Kerala, India
2Assistant Professor, Dept of Civil Engineering, Sri Vellappally Natesan Collage of Engineering, Kerala, India
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Abstract - Proper planning and scheduling are the top
challenges in project management. Traditionalanalytical and
heuristic approaches are inefficient and inflexible when
solving construction scheduling problems . The proposed
algorithm can effectively provide the optimal combination of
construction resources by the starting and finishing dates of
activities subjected to the objective of scheduling .The main
objective of this project is to optimize the schedule of
construction project activities in order to minimize the total
cost with resource constraints using Genetic Algorithm. This
project describes a genetic algorithm approach to project
scheduling problems in construction industry .Using
MatlabR2011 a genetic algorithm model is obtained by
providing a method for automatically creating a working
computer program from a high level problemstatementofthe
problem. The major advantage of the procedure is its simple
applicability within commercial project managementsystems
to improve the performance.
Key Words: Genetic algorithm, resource constraint
scheduling, critical path method, delay , construction
management.
1.INTRODUCTION
Project planning is one of the most important aspects
of construction project management in today’s
economy . In order to manage a construction project
effectively, we must havea plan which includeswhatis
to be accomplished , the technology involved and the
expected time for construction. The goal of planning is
to minimize resource expenditureswhilesatisfactorily
completing a given task.
In each project schedule has its own precedence
constraints, which means that each activity can be
processed when all its predecessors are finished. The
purpose of project scheduler is to minimize the
completiontimeandsubjecttoprecedenceconstraints.
So this paper brings out the drawback in existing
project scheduling methods. The representation show
that precedence constraints and the objective function
which measures overall performance of the project.
One of the main challenges of computer science is to
get a computer to do what needs to be done , without
telling it how to do it . Compared to the traditional
methods , the genetic algorithm has more advantages
as it can consider the objectives of project time and
cost minimization. So that the new approach,
employing the use of genetic algorithms has more
flexibility to solve construction scheduling problems .
1.1 Need for the Study
The traditional scheduling methods such as Critical Path
Method (CPM) are not enough for scheduling because they
cannot take resource constraints into account. In a resource
constrained project, the amount of resources needed during
one or more time periods is limited to less than required by
two or more activities occurring simultaneously. A need
arises for a new approach to optimize projects schedules
which take into consideration the shortage of resource.
1.2 Scope
This study aims is to develop a genetic algorithm
optimization model to schedule project activities in order to
minimize the total duration of the residential building
project, subjected to both precedence and resources
constraints by conducting a questionnaire survey among
various engineers and contractors.
1.3 Objectives
The various objectives include:
 To conduct a site visit to understand the property
and geography of site.
 To analyse and design a residential building in
STAAD Pro.
 Develop a computer model to automate the
schedule of construction projects.
 Develop Genetic Algorithm optimization model to
optimize the schedule of resource constrained
construction projects scheduling.
 Implement the model on a scheduling of a
residential building project
 Comparing the result of the model with result ofMS
project approaches.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 766
2. LITERATURE REVIEW
Shih and Liu [2] proposed a new scheduling model aiming
for the minimization of total project cost, including resource
usage and idle cost. But the model depends on providing
external resources to provide planners with additional
flexibility in arranging schedules and provide planners with
diversity of resource supply, and also the model needs in-
depth discussion on issues of determining the limit of
internal resource to minimize operational costs.
Senouci and Derham [2]presenteda genetic algorithm based
multi-objectives optimization model for the scheduling of
construction projects. But the model is valid for linear
construction projectsonly,whichcharacterized byrepetitive
activities.
Okada et .al [3] proposed a random key-based genetic
algorithm approach to solve optimization scheduling
problems, but they did not showcomputational experiments
to show the effectiveness of the proposed approach, and it
was recommended in their publication to do this in the
future research directions.
3. METHODOLOGY
The detailed methodology adopted in this study isexplained
below. The methodologyincludestheidentificationoffactors
affecting the delay in construction project and to conduct a
questionnaire survey . Further this data is used to develop
genetic algorithm models for optimizing construction
scheduling of a project.
3.1 Identification of Various Factors affecting
Delay
As the initial step previous research papers were reviewed
to investigate various factors causing delay in construction
building project . According the literature were studied and
45 major factors were identified which is listed in Annexure
A . Which include poor planning , shortage of technical
persons , poor coordination , strikes in construction etc.
3.2 Preparation of Questionnaire Survey and
Identification of Critical Factors
Various literature were studied and based on the
preliminary investigation conducted at the outset of the
study . A questionnaire was then drawn up and was divided
in to two sections . Section A sought to know the general
particulars of respondents while section B was focused on
the effect of delay in construction project . The respondents
were asked to rank the individual effect of delay based on
frequency of occurrence according to their own judgment
and local working experience . A four point scale is Adopted
to facilitate ranking exercise and to facilitate the analysis of
the responses , the following numerical values were
assigned to the respondent rating . They were no prominent
-0 , less prominent -1 , prominent -2 , highly prominent -3 ,
always prominent-4 .
After conducting the questionnaire survey the data was
analyzed and the critical factors affecting delay in
construction project were identified using Relative
Important Index (RII) method. A four point Likert scale of 0-
4 was adopted to assess the degree of agreement of each
cause or scale of impact. Each factor was given a scale of 0 to
4, so that person could easily express the severity range or
impact. i.e. 0 be the lowest and 4 be the highest. The scalefor
impact is categorized into 5 types Which are shown in Table
1.
Table -1: Assessment grades
Scale of impact
0 Not prominent
1 Less prominent
2 prominent
3 Highly prominent
4 Always prominent
The scale value for each factor was obtained and ranked
based on Relative Importance Index (RII) of the responses
are computed for their impact and significance. RII is
calculated using the equation
Where ΣW is the total weight given to each factor by the
respondents, which ranges from 0 to 4 was calculated by an
addition of the various weightings given to a factor by the
entire respondent , H is the highest ranking available (i.e, 4
in this case ) and N is the total number of respondents that
answered the question. Based on the RII value the factors
were ranked and identify the most critical factors.
3.3 Preparation of Program Schedule in Microsoft
Project Software
Microsoft project is a project management software
program, developed and sold by Microsoft , that is designed
to assist a project manager in developing a plan , assigning
resources to tasks, tracking progress , managing the budget
and analysing workloads. The activity schedule and time
duration in MS project of a residential building were
obtained is shown in Annexure C . Data will be used in
Genetic Algorithm model. The steps in MS Projects are first
to determine major tasks, enter them in Task Name column
(enter them in chronological order). Remember, these are
tasks and must contain a verb. Avoid the verb “design” since
this is ambiguous and is actually a process containing many
tasks (it is not a single task) then highlight rows just below
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 767
the major tasks and hit the “insert” key to insert blank rows.
Enter the subtasks for each major task (if there are any).
Remember to use verbs. Then highlight the subtasks (for a
given major task) and click on the “right arrow” key on the
toolbar (see last page for comments on toolbar icons) and
enter the duration for the subtasks.
3.4 Optimization of Scheduling by Genetic
Algoritham
A project such as a construction project consists of a
network of activities and a node in network corresponds to
an activity. Each activity in a project has corresponding
duration and also needs certain amount of resourcessuchas
labour material to execute itself with them.Activityduration
is usually measured in integral increments of time called
planning units. The normal duration of an activity refers to
the time required to complete that activity under normal
circumstances.
The GA begins like any other optimization algorithm, by
defining the optimization variables, the cost function, and
the cost. It ends like other optimization algorithms too, by
testing for convergence. In between,however,thisalgorithm
is quite different. A path through the components of the GA
is shown in the flowchart fig -1.
Fig-1: Flowchart showing Genetic Algorithm Process
4. RESULTS AND DISCUSSION
Questionnaire survey was conducted among 35 individuals,
based on the degree of assessment about 51.7 % were
responded as the shortage of skilled labour and poor
communication betweenconstructionpartieshadhigheffect
in construction projects whereas 33.28% people were
responded as medium effect. Mistakes in design had high
effect declared by 57.14% people whereas only 31.4 %
declared as have only medium effect. For the case of late
submission of nominated materials42.42%wereresponded
as medium effect and 45.7% were responded as high effect.
4.1 Critical Factors
Based on the degree of assessment the RII value was
calculated and ranking was carried out according to the
value. From the data obtained the value of RII varies from
37.14 to 81.90 for different factors. From the table4.1,it was
noted that poor communication between construction 23
parties and shortage of skilled labourshadgotanRIIvalueof
89.10% and was indicated as rank 1. The impact of poor
communication betweenindividualscausesvariousconflicts
and which delays the construction work. Mistakes in design
and poor workmanship . To overcome this problem proper
design according to specifications should adopt. Improper
planning, inadequate site investigation, misinterpretation of
data, unaware of future needs are some of the causes for
mistake in design. So proper planning, adequate
investigation of site and accurate design procedure are
needed to execute the project with high precession.
4.2 Microsoft Project Scheduling
The project manager is developing a plan , assigning
resources to task , tracking progress remanaging the budget
and analysing workloads . In this way the construction of a
residential building have 38 activity as per the planning,the
construction of the residential building by conventional
method can be completed by 185 days as shown in fig-2.
Fig-2: Planned Activities for Conventional Building
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 768
4.3 Genetic Algorithm Optimized Data
According to the scheduling data of the construction project
with the help of optimizing program should developed by
matrix manipulation , plotting of function and data ,
implementation of algorithm and creationofuserinterface .
Model verification and validation are essential parts of the
model development process if the model to be accepted and
used to support decision making.
Fig-3: Program Result for Optimized Schedule
The total duration of the project is 172 days in Genetic
Algorithm optimization program. No computational model
will ever be fully verified guaranteeing 100% error free
implementation. A high degree of statistical certainty is all
that can be realized for any model as more cases as tested.
The developed model was verified by more tests performed,
errors were identified, and corrections were made to
encountered errors. This took a long period of time, and a
huge effort by the researcher to get a high degree of
certainty about the model verification. Validation ensures
that the model meets its intended requirements in terms of
the methods employed and the results obtained. The
ultimate goal of the model validation is to make the model
useful in the sense that the model addresses the right
problem, provides accurate information about the system
being modeled, and finally to make the model accurately
used.
Table-2 Comparison between solution of the problem
Solution Total duration No of Iteration
CPM 136 ------
MS Project 185 ------
CPS Optimizer 172 10- 30
5. CONCLUSIONS
An implementation of the GA developed model for
residential building project scheduling has resulted in
optimized output with reduced cost . A real time project
solved using this optimization software shows that best
converging result can be obtained . develop a genetic
algorithm optimization model to schedule project activities
in order to minimize the total duration of the project,
subjected to precedence constraints. The problems are
applied and the results are studied and compared with the
results of previous studies and with the feature of “resource
leveling” in the commercial construction management
programs, which showed that the CPS Optimizer results
meet the intended goal of achieving the best schedule with
the minimum efforts. Crossover operator that suits the
studied problem and creates feasible solutions. The total
time duration of the project has 172 days in GA model but
for MS project scheduling it has 185 days in that way the
Genetic Algorithm method hasmoreeffectivetheMSProject.
REFERENCES
[1] K.C. Shin and S.S. Liu , Optimization model of external
Resource Allocation for Resource Constrained Project
Scheduling Problem . International Journal of Project
Management, vol.19, 2008, pp. 62-69.
[2] Senouci and H.R. Al- Derham , Genetic Algorithm Based
multi-objective model for Scheduling of linear
Construction Project. Advances in Engineering
Software, Vol. 39, 2008, pp. 1023-1028.
[3] S. Hartman , A competitive Genetic Algorithm for
resource constrained project Scheduling. Nava
Research logistics, vol.45, 1998, pp. 733-750.

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Genetic algorithm for resource constrained construction project scheduling

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 765 Planning and Optimization of Resource Constrained Project Scheduling by Using Genetic Algorithm Vineetha. S1 , Manjusha. M2 1Student, Dept. Of Civil Engineering, Sri Vellappally Natesan Collage of Engineering , Kerala, India 2Assistant Professor, Dept of Civil Engineering, Sri Vellappally Natesan Collage of Engineering, Kerala, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Proper planning and scheduling are the top challenges in project management. Traditionalanalytical and heuristic approaches are inefficient and inflexible when solving construction scheduling problems . The proposed algorithm can effectively provide the optimal combination of construction resources by the starting and finishing dates of activities subjected to the objective of scheduling .The main objective of this project is to optimize the schedule of construction project activities in order to minimize the total cost with resource constraints using Genetic Algorithm. This project describes a genetic algorithm approach to project scheduling problems in construction industry .Using MatlabR2011 a genetic algorithm model is obtained by providing a method for automatically creating a working computer program from a high level problemstatementofthe problem. The major advantage of the procedure is its simple applicability within commercial project managementsystems to improve the performance. Key Words: Genetic algorithm, resource constraint scheduling, critical path method, delay , construction management. 1.INTRODUCTION Project planning is one of the most important aspects of construction project management in today’s economy . In order to manage a construction project effectively, we must havea plan which includeswhatis to be accomplished , the technology involved and the expected time for construction. The goal of planning is to minimize resource expenditureswhilesatisfactorily completing a given task. In each project schedule has its own precedence constraints, which means that each activity can be processed when all its predecessors are finished. The purpose of project scheduler is to minimize the completiontimeandsubjecttoprecedenceconstraints. So this paper brings out the drawback in existing project scheduling methods. The representation show that precedence constraints and the objective function which measures overall performance of the project. One of the main challenges of computer science is to get a computer to do what needs to be done , without telling it how to do it . Compared to the traditional methods , the genetic algorithm has more advantages as it can consider the objectives of project time and cost minimization. So that the new approach, employing the use of genetic algorithms has more flexibility to solve construction scheduling problems . 1.1 Need for the Study The traditional scheduling methods such as Critical Path Method (CPM) are not enough for scheduling because they cannot take resource constraints into account. In a resource constrained project, the amount of resources needed during one or more time periods is limited to less than required by two or more activities occurring simultaneously. A need arises for a new approach to optimize projects schedules which take into consideration the shortage of resource. 1.2 Scope This study aims is to develop a genetic algorithm optimization model to schedule project activities in order to minimize the total duration of the residential building project, subjected to both precedence and resources constraints by conducting a questionnaire survey among various engineers and contractors. 1.3 Objectives The various objectives include:  To conduct a site visit to understand the property and geography of site.  To analyse and design a residential building in STAAD Pro.  Develop a computer model to automate the schedule of construction projects.  Develop Genetic Algorithm optimization model to optimize the schedule of resource constrained construction projects scheduling.  Implement the model on a scheduling of a residential building project  Comparing the result of the model with result ofMS project approaches.
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 766 2. LITERATURE REVIEW Shih and Liu [2] proposed a new scheduling model aiming for the minimization of total project cost, including resource usage and idle cost. But the model depends on providing external resources to provide planners with additional flexibility in arranging schedules and provide planners with diversity of resource supply, and also the model needs in- depth discussion on issues of determining the limit of internal resource to minimize operational costs. Senouci and Derham [2]presenteda genetic algorithm based multi-objectives optimization model for the scheduling of construction projects. But the model is valid for linear construction projectsonly,whichcharacterized byrepetitive activities. Okada et .al [3] proposed a random key-based genetic algorithm approach to solve optimization scheduling problems, but they did not showcomputational experiments to show the effectiveness of the proposed approach, and it was recommended in their publication to do this in the future research directions. 3. METHODOLOGY The detailed methodology adopted in this study isexplained below. The methodologyincludestheidentificationoffactors affecting the delay in construction project and to conduct a questionnaire survey . Further this data is used to develop genetic algorithm models for optimizing construction scheduling of a project. 3.1 Identification of Various Factors affecting Delay As the initial step previous research papers were reviewed to investigate various factors causing delay in construction building project . According the literature were studied and 45 major factors were identified which is listed in Annexure A . Which include poor planning , shortage of technical persons , poor coordination , strikes in construction etc. 3.2 Preparation of Questionnaire Survey and Identification of Critical Factors Various literature were studied and based on the preliminary investigation conducted at the outset of the study . A questionnaire was then drawn up and was divided in to two sections . Section A sought to know the general particulars of respondents while section B was focused on the effect of delay in construction project . The respondents were asked to rank the individual effect of delay based on frequency of occurrence according to their own judgment and local working experience . A four point scale is Adopted to facilitate ranking exercise and to facilitate the analysis of the responses , the following numerical values were assigned to the respondent rating . They were no prominent -0 , less prominent -1 , prominent -2 , highly prominent -3 , always prominent-4 . After conducting the questionnaire survey the data was analyzed and the critical factors affecting delay in construction project were identified using Relative Important Index (RII) method. A four point Likert scale of 0- 4 was adopted to assess the degree of agreement of each cause or scale of impact. Each factor was given a scale of 0 to 4, so that person could easily express the severity range or impact. i.e. 0 be the lowest and 4 be the highest. The scalefor impact is categorized into 5 types Which are shown in Table 1. Table -1: Assessment grades Scale of impact 0 Not prominent 1 Less prominent 2 prominent 3 Highly prominent 4 Always prominent The scale value for each factor was obtained and ranked based on Relative Importance Index (RII) of the responses are computed for their impact and significance. RII is calculated using the equation Where ΣW is the total weight given to each factor by the respondents, which ranges from 0 to 4 was calculated by an addition of the various weightings given to a factor by the entire respondent , H is the highest ranking available (i.e, 4 in this case ) and N is the total number of respondents that answered the question. Based on the RII value the factors were ranked and identify the most critical factors. 3.3 Preparation of Program Schedule in Microsoft Project Software Microsoft project is a project management software program, developed and sold by Microsoft , that is designed to assist a project manager in developing a plan , assigning resources to tasks, tracking progress , managing the budget and analysing workloads. The activity schedule and time duration in MS project of a residential building were obtained is shown in Annexure C . Data will be used in Genetic Algorithm model. The steps in MS Projects are first to determine major tasks, enter them in Task Name column (enter them in chronological order). Remember, these are tasks and must contain a verb. Avoid the verb “design” since this is ambiguous and is actually a process containing many tasks (it is not a single task) then highlight rows just below
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 767 the major tasks and hit the “insert” key to insert blank rows. Enter the subtasks for each major task (if there are any). Remember to use verbs. Then highlight the subtasks (for a given major task) and click on the “right arrow” key on the toolbar (see last page for comments on toolbar icons) and enter the duration for the subtasks. 3.4 Optimization of Scheduling by Genetic Algoritham A project such as a construction project consists of a network of activities and a node in network corresponds to an activity. Each activity in a project has corresponding duration and also needs certain amount of resourcessuchas labour material to execute itself with them.Activityduration is usually measured in integral increments of time called planning units. The normal duration of an activity refers to the time required to complete that activity under normal circumstances. The GA begins like any other optimization algorithm, by defining the optimization variables, the cost function, and the cost. It ends like other optimization algorithms too, by testing for convergence. In between,however,thisalgorithm is quite different. A path through the components of the GA is shown in the flowchart fig -1. Fig-1: Flowchart showing Genetic Algorithm Process 4. RESULTS AND DISCUSSION Questionnaire survey was conducted among 35 individuals, based on the degree of assessment about 51.7 % were responded as the shortage of skilled labour and poor communication betweenconstructionpartieshadhigheffect in construction projects whereas 33.28% people were responded as medium effect. Mistakes in design had high effect declared by 57.14% people whereas only 31.4 % declared as have only medium effect. For the case of late submission of nominated materials42.42%wereresponded as medium effect and 45.7% were responded as high effect. 4.1 Critical Factors Based on the degree of assessment the RII value was calculated and ranking was carried out according to the value. From the data obtained the value of RII varies from 37.14 to 81.90 for different factors. From the table4.1,it was noted that poor communication between construction 23 parties and shortage of skilled labourshadgotanRIIvalueof 89.10% and was indicated as rank 1. The impact of poor communication betweenindividualscausesvariousconflicts and which delays the construction work. Mistakes in design and poor workmanship . To overcome this problem proper design according to specifications should adopt. Improper planning, inadequate site investigation, misinterpretation of data, unaware of future needs are some of the causes for mistake in design. So proper planning, adequate investigation of site and accurate design procedure are needed to execute the project with high precession. 4.2 Microsoft Project Scheduling The project manager is developing a plan , assigning resources to task , tracking progress remanaging the budget and analysing workloads . In this way the construction of a residential building have 38 activity as per the planning,the construction of the residential building by conventional method can be completed by 185 days as shown in fig-2. Fig-2: Planned Activities for Conventional Building
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 768 4.3 Genetic Algorithm Optimized Data According to the scheduling data of the construction project with the help of optimizing program should developed by matrix manipulation , plotting of function and data , implementation of algorithm and creationofuserinterface . Model verification and validation are essential parts of the model development process if the model to be accepted and used to support decision making. Fig-3: Program Result for Optimized Schedule The total duration of the project is 172 days in Genetic Algorithm optimization program. No computational model will ever be fully verified guaranteeing 100% error free implementation. A high degree of statistical certainty is all that can be realized for any model as more cases as tested. The developed model was verified by more tests performed, errors were identified, and corrections were made to encountered errors. This took a long period of time, and a huge effort by the researcher to get a high degree of certainty about the model verification. Validation ensures that the model meets its intended requirements in terms of the methods employed and the results obtained. The ultimate goal of the model validation is to make the model useful in the sense that the model addresses the right problem, provides accurate information about the system being modeled, and finally to make the model accurately used. Table-2 Comparison between solution of the problem Solution Total duration No of Iteration CPM 136 ------ MS Project 185 ------ CPS Optimizer 172 10- 30 5. CONCLUSIONS An implementation of the GA developed model for residential building project scheduling has resulted in optimized output with reduced cost . A real time project solved using this optimization software shows that best converging result can be obtained . develop a genetic algorithm optimization model to schedule project activities in order to minimize the total duration of the project, subjected to precedence constraints. The problems are applied and the results are studied and compared with the results of previous studies and with the feature of “resource leveling” in the commercial construction management programs, which showed that the CPS Optimizer results meet the intended goal of achieving the best schedule with the minimum efforts. Crossover operator that suits the studied problem and creates feasible solutions. The total time duration of the project has 172 days in GA model but for MS project scheduling it has 185 days in that way the Genetic Algorithm method hasmoreeffectivetheMSProject. REFERENCES [1] K.C. Shin and S.S. Liu , Optimization model of external Resource Allocation for Resource Constrained Project Scheduling Problem . International Journal of Project Management, vol.19, 2008, pp. 62-69. [2] Senouci and H.R. Al- Derham , Genetic Algorithm Based multi-objective model for Scheduling of linear Construction Project. Advances in Engineering Software, Vol. 39, 2008, pp. 1023-1028. [3] S. Hartman , A competitive Genetic Algorithm for resource constrained project Scheduling. Nava Research logistics, vol.45, 1998, pp. 733-750.