Construction Scheduling Using Constraint Satisfaction Problem
MethodSeminar Report - 2014
CHAPTER 1INTRODUCTION1.1. GENERALConstruction projects are
characterized by their complexity, uniqueness, and the fact that
there are various types of constraints imposed by stakeholders.
This includes numerous constraints of various types, including
contractual due dates, resource limitations, safety, financial, and
managerial constraints. Satisfying project constraints is one of
the most challenging tasks in the construction scheduling process.
The practicality of a schedule depends considerably on the degree
to which these constraints are satisfied. Previous scheduling
systems primarily employed the critical path method to produce
schedules. CPM in its present form has proven inadequate for the
consideration of constraints in real-life construction projects.
This paper views construction scheduling as a constraint
satisfaction problem. CSP gradually generates valid schedules using
constraint propagation and constraint consistency checking
techniques. These techniques are useful for handling constraints
that are predetermined as well as those that become apparent during
schedule development. A CSP-based scheduling method has been
developed to facilitate expressive constraint representation and to
provide effective generation of practical, valid project schedules.
The nature of the constraints varies. The most commonly encountered
constraints in the case of high rise buildings includes time,
technological, managerial, logistic, resource and space
constraints. Technological constraints, such as the placement of
formwork and rebar must be completed before pouring concrete, are
rigid. Some constraints are imposed to ensure that certain
activities cannot be executed concurrently for safety reasons.
These constraints do not specifically dictate which activity is the
predecessor or successor. They can be classified as conditional
constraints. Organizational policies can be regarded as managerial
constraints. Some of them are rigid while others may be treated as
preferential (i.e., soft constraints). Constraints play an
important role in the scheduling generation process. Rigid
constraints impose a fixed logic, whereas conditional and
preferential ones signifies flexible and multiple logics in the
project network. The quality of schedules produced depends largely
on the degree to which project constraints are
satisfied.Construction scheduling has been an active research area
over the last five decades. Many of the previous efforts use the
critical path method (CPM) to determine the overall project
duration as well as the activity start and finish times. CPM is
based on the assumption that the duration and cost of activities in
a project network are deterministic. Traditional CPM scheduling
methods have proven to be helpful only when the project deadline is
not fixed and the resources are not constrained by either
availability or time. These methods have been widely criticized for
their inability to cope with non technological constraints. In
addition, CPM-based methods can primarily handle a predetermined
and rigid logic. In the later stage, Precedence Network Analysis
(PNA) framework is developed to manage constraints that arise from
static and dynamic construction requirements. This PNA technique is
commonly used for time planning of construction projects. They
introduce a concept called meta intervals to represent the complex
requirements that cause conditional relationships. The PNA
framework, however, does not address the treatment of constraints
in the situation in which they cannot be satisfied.In this study, a
new scheduling method called Constraint Satisfaction Problem (CSP)
method is discussed with the intent of overcoming this major
drawback inherent to most CPM-based methods. The proposed method
views construction scheduling as a constraint satisfaction problem
(CSP). CSP views this problem as a set of decision variables, each
having a set of possible values and a set of constraints
restricting the values to variables. The task of CSP is to
instantiate the variables with the values while satisfying all the
constraints. Efficient CSP formulation and solution generation
techniques are described. A practical case example that
incorporates both technological and non technological constraints
is used to demonstrate the practicality of the proposed method1.2.
OBJECTIVES To develop a comprehensive knowledge about the various
categories of constraints faced in a construction project. To know
about the various scheduling processes employed in construction
projects. To identify the inadequacies of construction scheduling
using Critical Path Method To develop a comprehensive knowledge
about the construction scheduling using the constraint satisfaction
problem. To compare the schedules developed using Critical Path
Method and Constraint Satisfaction problem Method.CHAPTER
2LITERATURE REVIEWConstruction projects are subjected to numerous
constraints of various types including contractual due dates,
resource limitations, safety, financial, and managerial
constraints. Satisfying project constraints is one of the most
challenging tasks in the construction scheduling process. The
practicality of a schedule depends considerably on the degree to
which these constraints are satisfied. For the literature review
related to the current study, articles from the following journals
were reviewed.According to Pasit Lorterapong and Mongkol
Ussavadilokrit (2013), Construction projects are characterized by
their complexity, uniqueness, and the fact that there are various
types of constraints imposed by stakeholders. The nature of these
constraints varies. They identified six types of constraints that
are commonly encountered in most high-rise building constructions,
including time, technological, managerial, logistic, resource, and
space constraints. Technological constraints, such as the placement
of formwork and rebar must be completed before pouring concrete,
are rigid. Some constraints are imposed to ensure that certain
activities cannot be executed concurrently for safety reasons.
These constraints do not specifically dictate which activity is the
predecessor or successor. They can be classified as conditional
constraints. Organizational policies can be regarded as managerial
constraints. Some of them are rigid while others may be treated as
preferential (i.e., soft constraints). Constraints play an
important role in the scheduling generation process. Rigid
constraints impose a fixed logic, whereas conditional and
preferential ones signify flexible (i.e., soft) and multiple logics
in the project network. The quality of schedules produced depends
largely on the degree to which project constraints are satisfied.
Claude Le Pape defined Constraint Satisfaction Problem as a
programming method based on three principles. The problem to be
solved is explicitly represented in terms of variables and
constraints on these variables. In a constraint-based program, this
explicit problem definition is clearly separated from the algorithm
used to solve the problem. Given a constraint-based definition of
the problem to be solved and a set of decisions, themselves
translated into constraints, a purely deductive process referred to
as constraint propagation is used to propagate the consequences of
the constraints. This process is applied each time a new decision
is made, and is clearly separated from the decision-making
algorithm. The overall constraint propagation process results from
the combination of several local and incremental processes, each of
which is associated with a particular constraint or a particular
constraint class. Construction scheduling has been an active
research area over the last five decades. Many of the previous
efforts use the critical path method (CPM) to determine the overall
project duration as well as the activity start and finish times.
CPM is based on the assumption that the duration and cost of
activities in a project network are deterministic (Sakka and
El-Sayegh 2007). Traditional CPM scheduling methods have proven to
be helpful only when the project deadline is not fixed and the
resources are not constrained by either availability or time
(Hegazy 1999). These methods have been widely criticized for their
inability to cope with nontechnological constraints (Jaafari 1984;
Pultar 1990; El-Bibany 1997; Choo et al. 1999). In addition,
CPM-based methods can primarily handle a predetermined and rigid
logic. Chua and Yeoh (2011) develop a PDM++ framework to manage
constraints that arise from static and dynamic construction
requirements. They introduce a concept called metaintervals to
represent the complex requirements that cause conditional
relationships. The PDM++ framework, however, does not address the
treatment of constraints in the situation in which they cannot be
satisfied.Pasit Lorterapong and Mongkol Ussavadilokrit (2013)
developed a new scheduling method with the intent of overcoming
this major drawback inherent to most CPM-based methods. The
proposed method views construction scheduling as a constraint
satisfaction problem (CSP). CSP views this problem as a set of
decision variables, each having a set of possible values and a set
of constraints restricting the values to variables. The task of CSP
is to instantiate the variables with the values while satisfying
all the constraints. Efficient CSP formulation and solution
generation techniques are described. A practical case example that
incorporates both technological and non technological constraints
is used to demonstrate the practicality of the proposed method.
CHAPTER 3CONSTRAINT SATISFACTION PROBLEM 3.1. CSP AN OVERVIEWIn
general, a Constraint Satisfaction Problem or CSP is defined by a
set of variables Xi = {x1, x2, x3,..........xn}, and a set of
constraints C1, C2, C3.........Cm. Each variable Xi has a non empty
domain Di of possible values. Each constraint is defined over a
subset of variables, and it restricts the combination of values
that these variables can assume. A CSP can be visualized as a
constraint graph consisting of nodes and arrows. A state of the
problem is defined by an assignment of values to some or all of the
variables, {Xi = vi, Xj = vj,.}. The nodes of the graph correspond
to variables, and the arcs correspond to project constraints.
Typical variables in the scheduling problem are the start and
finish times of project activities. Variables SA and FA represent
the start and finish times of activity A, respectively. Scheduling
constraints can be imposed on the scheduling variables introduced
in two formatsunary or non unary. The unary constraint is used to
restrain a set of possible values for each variable. The non unary
constraint, on the other hand, is applied between any two
scheduling variables. Interactions among scheduling variables and
constraints are modeled using a project graph. The figure given
below shows an example of a project constraint graph consisting of
four activities A, B, C, and D, and their representative scheduling
variables. The figure shows the way in which unary and non unary
constraints are imposed on the scheduling variables. For instance,
the unary constraint SA > 20 indicates that the domain of SA
must be greater than day 20.The non unary constraints SA + 2 = FA,
FB SC, and SB + 5 = FB, each represented by an arc, signify a
constraint from one variable to another. Conditional constraints,
such as activity C can be performed after A or B is finished, can
effectively be incorporated using a node OR in the constraint
graph.In some situations, it is possible that activities A and B
cannot be executed simultaneously. Their precedence relationships
are interchangeable. This situation generates a condition by which
A can precede B or vice versa.Logical operators such as , , =, and
are used to specify the relationships between variables. A solution
to the CSP problem is the assignment of a value from its domain to
every variable in such a way that all imposed constraints are
satisfied. Partial solutions are progressively generated and tested
through the use of CSP and search techniques. Two widely used CSP
techniques, node and arc consistency checking, are employed to
ensure that all imposed constraints are locally satisfied. In a
network-type problem, however, the assignment of a value to one
variable can affect the domain of the others. A technique called
constraint propagation is then used to disseminate the effect of
such an assignment to others. The effectiveness of any CSP depends
on how well constraints are represented and the techniques used to
propagate them.
Figure. 3.1. Project Constraint Graph (Pasit Lorterapong et.al
2013)3.2. DEVELOPMENT OF CSP BASED SCHEDULING METHODThis study
demonstrates a newly developed CSP-based scheduling method capable
of satisfying various types of constraints encountered in
construction projects. The proposed method utilizes Allens
constraint modeling techniques and employs widely used searching
techniques to produce schedules that satisfy project constraints.
Activity start (Si) and finish (Fi) times are set as scheduling
variables. Project constraints that are predetermined and rigid as
well as those conditional and situational in nature can be
incorporated. Tables 3.1 and 3.2 show the scheduling variables and
constraint representations utilized in the proposed method.Table
3.1. Scheduling Variables Representation (Pasit Lorterapong et.al
2013)Scheduling VariablesCSP ModelRemarks
Activity Start (Si)Si = [l , u]L, u are lower and upper bounds
of Si
Activity Finish (Fi)Fi = [l , u]L, u are lower and upper bounds
of Fi
Table. 3.2. Scheduling Constraint Representations (Pasit
Lorterapong et.al 2013)ConstraintExamplesUnary ConstraintNon unary
ConstraintConditional Constraint
TimeProject start and finish dates, activity duration,
milestonesXX
TechnologicalPrecedence relationships between activities exists
due to requirements for structural integrity, regulations, and
other technical requirements signifies that the activities must
take place in a particular sequenceX
ManagerialManagerial constraints are dependency relationships
emerged because of a decision by management. This often occurs in
the form of policy or preferences required by clients preferential
constraints allow multiple planning alternativesXX
LogisticLogistic constraints are numerous interferences between
configuration of construction site and construction work such as in
consequence disorganized material storage causes extra time for the
search of material or to rearrange storage areasXX
SafetySite safety rules: pipe welding activities must be
performed in isolation because it produces sparks, which might be
hazardous for othersXX
ResourceResource constraints relate to lack of needed resources,
which may force parallel activities to be performed in
sequenceXXX
SpaceSpace constraints are introduced to prevent any trade
interferenceXXX
Each variable is characterized by its domain interval (i.e., its
lower and upper bounds [l, u]). CSP scheduling involves modifying
the domains of all scheduling variables by successively imposing
project constraints in a stepwise manner. A CSP scheduling
procedure is generally performed in the five stages:
initialization, propagation, backtracking search, relaxation, and
realization.Stage 1: InitializationFormulate the problem by
identifying project constraints and activities. Scheduling
variables (i.e., Si and Fi) are generated. The overall project
duration specified in the contract is used to generate the initial
domain values [l, u] of Si and Fi.Stage 2: PropagationImpose
project constraints input in Stage 1 in a sequential manner. The
order in which those constraints are imposed is not restricted. To
facilitate faster schedule generation, however, it is recommended
that activity duration constraints are imposed first. Then, proceed
with rigid constraints (i.e., constraints that cannot be relaxed
such as technological, safety, and managerial), conditional, and
soft constraints, respectively. The widely known depth-first search
algorithm is employed to identify the relevant constraints. Each
constraint is checked to ensure its consistency. The successful
constraint is then propagated to the scheduling variables involved
where their domain values are updated (i.e., being reduced). Each
time a new domain value of any scheduling variable is obtained, the
related node and arc checks must be performed to ensure
consistency.Stage 3: Backtracking SearchIn the situation in which
no possible domain values can be found, a backtracking search is
performed to locate the decision point at which a non explored
alternative path exists (i.e., the OR gate in the project
constraint graph). Stage 2 is then repeated for the new path.Stage
4: RelaxationIn the situation in which a valid schedule cannot be
obtained, some constraints will have to be relaxed. This stage
allows planners to involve in the constraint relaxation process.
The newly relaxed constraint must then be re-propagated by
repeating Stage 2. The scheduling process ends when all project
constraints have been satisfied and Si and Fi have been assigned
valid domain intervals. Upon exhausting all paths in the constraint
graph, and still, some constraints are not satisfied, it can be
stated that the project is so constrained that no valid schedule
can be obtained.Stage 4: RealizationIf a solution exists, the next
step is to convert the final domains of each Si and Fi to the
common activity start and finish times, [ESi, EFi], respectively.
Accordingly, ESi takes the lower bound of Si, while EFi assumes the
lower bound of Fi. Similarly, the latest possible timeline of
activity i, [LSi, LFi], can be determined using the upper bounds of
Si and Fi.
Figure. 3.2. CSP based scheduling Algorithm (Pasit Lorterapong
et.al 2013)CHAPTER 4CASE STUDY4.1. DEFINITIONThe management of a
general hospital has decided to construct new buildings just
opposite to the old buildings. The figure given below shows the
site layout of this project. A solid line divides the existing
buildings from the new construction area. At present, the existing
road R1 and Gates G1 and G2 are used to serve the hospital, while
G3 is used as a spare gate. The scope of the work described in this
case study includes overhauling the existing road R1 (Sections 1-1,
1-2, 1-3) and constructing two new roads, R2 (Sections 2-1, 2-2,
2-3, 2-4) and R3 (Sections 3-1, 3-2, 3-3, 3-4, 3-5). The management
of this hospital demands that existing hospital buildings must be
fully accessible during the twenty-week construction period (i.e.,
time constraint). In other words, at least one road and one gate
must be available to serve the hospital at any time. Decisions
regarding which road and which gates be in-service at what time are
left to the authority at the project level. Such a policy can be
regarded as managerial constraints. These managerial constraints
have created several planning alternatives for this project.
Construction activities that take place in front of any gate
necessitates the closure of that gate. For demonstration purposes,
only the time, managerial, and the common technological constraints
are imposed on the case example.
Figure. 4.1. Project Site Layout (Pasit Lorterapong et.al
2013)
Table. 4.1. Technological Constraints among Project
Activities(Pasit Lorterapong et.al . 2013)Road SectionsDuration
(Di)(weeks)PredecessorsRemarks
R11 - 12-Overhaul the existing road
1 - 221 1
1 - 331 - 2
R22 12-Construct a new road
2 242 1
2 332 2
2 422 - 3
R33 142 1Construct a new road
3 253 1
3 333 2
3 423 3
3 513 - 4
4.2. SOLUTIONS GENERATED USING CPMThe CPM has been used to
generate project plans in this case example. The CPM allows
planners to explore one project plan at a time. To enable a
realistic schedule, however, the planner must generate a
comprehensive project network as input for CPM calculations. A
schedule is then generated and assessed for its practicality.
Alternative schedules necessitate various degrees of modifications
to the original project network. The previous process can be
repeated in a trial manner until acceptable schedules are obtained.
The CPM solutions for the case example are described
subsequentlyTrial 1: It is decided that G1 and G2 will be opened
such that construction can begin at R2 and R3. Upon completion of
R3, G1 and G3 will be in service and construction can begin on R1.
The calculated project duration is 24 weeks, 4 weeks greater than
the required 20 week project duration. Therefore, this alternative
is not acceptable.Trial 2: Similar to the first trial, construction
will start on R2 and R3 simultaneously. This time, R1 will start
once R2 is finished. The construction of section R3 (3-5) requires
the closing of G2. To maintain the given managerial constraints,
section R1 (1-3) can begin once section R3 (3-5) is completed. CPM
calculations yield 20 - week project duration. This alternative
satisfies the given project constraints. Actually, the planning
process can end once a satisfied schedule is discovered. More
alternatives can, however, be explored if desired.Trial 3: Suppose
that the planner would like to explore other planning option based
on Trial 2. This time, it is decided that R1 (1-3) is the
predecessor of R3 (3-5). The project duration is calculated to be
19 weeks (i.e., one week shorter than the required project
duration).
Figure 4.2. Project networks using the Critical Path Method :
(a) Project Network Trial 1; (b) Project Network Trial 2 ; (c)
Project Network Trial 3(Pasit Lorterapong et.al 2013)As
illustrated, the critical path method can be employed to calculate
project schedules. However, the challenging task of generating a
project network that satisfies all project constraints is still
borne by the planner. This task is very challenging, especially for
the projects that are complicated, subjecting it to numerous and a
variety of constraints.4.3. SOLUTIONS GENERATED USING CSPThe
proposed CSP-based scheduling procedure has been applied to the
case example. Technological constraints are also considered along
with the other constraints. The managerial constraints regarding
the accessible road and gates needed to maintain the hospitals
functionality are formulated, and their representations modeled in
the CSP format are illustrated in tables 4.2 & 4.3 shows the
CSP functions classified by the types of constraints.Table 4.2.
Managerial Constraints and their CSP representations(Pasit
Lorterapong et.al 2013)Managerial Constraint DescriptionResulting
Precedence RelationshipConstraint Function
At least one road (R1, R2 or R3) must be available to serve the
hospital during the construction period Section R1 ( 1 1)can start
after Section R2 (2 4) or Section R3 (3-5) has finished F2-4 S1-1 v
F3-5 S1-1
Due to physical constraint, the overhauling of R1 will always
begin at section R1 (1 1) and proceed toward section R1 ( 1 3) F1-1
S1-2 , F1-2 S1-3
At least one gate (G1 or G2) must be available at any time for
hospital entrance and exit Consequently, Section R1 (1 3) and
Section R3 (3 5) cannot be constructed simultaneously.
[Constructing Section R1 (1 3) caused G1 to be closed while
constructing Section R3 (3 5) causes G2 to be closed] F3-5 S1-3 v
F1-3 S3-5
Table 4.3. CSP Constraint functions of the Case Study (Pasit
Lorterapong et.al 2013)Constraint NumberConstraint FunctionType of
Constraint
1All Variables 20Time - related
2S2-1 + D2-1 = F2-1Time - related
3S2-2 + D2-2 = F2-2Time related
4S2-3 + D2-3 = F2-3Time related
5S2-4 + D2-4 = F2-4Time related
6S3-1 + D3-1 = F3-1Time related
7S3-2 + D3-2 = F3-2Time related
8S3-3 + D3-3 = F3-3Time related
9S3-4 + D3-4 = F3-4Time related
10S3-5 + D3-5 = F3-5Time related
11S1-1 + D1-1 = F1-1Time related
12S1-2 + D1-2 = F1-2Time related
13S1-3 + D1-3 = F1-3Time related
14F2-1 S2-2Technological
15F2-1 S3-1Technological
16F2-2 S2-3Technological
17F2-3 S2-4Technological
18F3-1 S3-4Technological
19F3-2 S3-3Technological
20F3-3 S3-4Technological
21F3-4 S3-5Technological
22F1-1 S1-2Technological
23F1-2 S1-3Technological
24F2-4 S1-1 v F3-5 S1-1Managerial
25F3-5 S1-3 v F1-3 S3-5Managerial
4.4. SCHEDULE DEVELOPMENT USING THE PROPOSED CSP METHODThe
schedule of the project is developed using the CSP method by
following the five procedural stages.Stage 1: Initialization1.
Initiate the domain of all activity start and finish times (i.e.,
Si and Fi) by imposing Constraint 1 (project duration constraint),
resulting in the initial domains of [0, 20] for all scheduling
variables.Stage 2: Propagation1. Impose the activity duration
constraints (i.e., Constraints 213) on all scheduling variables.
Constraint 2 (i.e., S2-1 + D2-1 = F2-1) is selected for
demonstration purposes. The initial domains of S2-1 and F2-1
obtained from step 1 are [0, 20]. Upon imposing Constraint 2, the
lower bound of S2-1 remains unchanged. The upper bound of S2-1,
however, must be reduced by 2 weeks (i.e., D2-1 = 2 weeks).
Consequently, the upper bound of S2-1 is reduced to week 18 after
constraint propagation, resulting in a newly reduced domain [0,
18]. Node and arc consistency are then checked to ensure that other
constraints associated with S2-1 are satisfied. Similarly, the
upper bound of F2-1 remains unchanged at week 20. The lower bound
of F2-1 is increased by the amount specified by D2-1, to week 2.
The resulting domains for F2-1 are [2, 20]. This process is
repeated for Constraints 313.2. Next, impose the technological
constraints (14 23). Considering, for example, Constraint 14 (i.e.,
F2-1 S2-2), the domains of F2-1 and S2-2 obtained from the previous
process are [2, 20] and [0, 16], respectively. By propagating
Constraint 14, the domains of F2-1 and S2-2 are further reduced to
weeks [2, 16]. Node and arc are checked and found to be consistent.
This propagation is considered to be successful. This process is
repeated for Constraints 1523
Figure 4.3. Satisfaction of Activity Duration Constraints
(Constraint 2)(Pasit Lorterapong et.al 2013)Figure 4.4.
Satisfaction of Technological Constraints (Constraint 14)(Pasit
Lorterapong et.al 2013)
3. Impose managerial constraint (i.e., 24, the service road
requirement). To maintain at least one accessible road during the
construction, R1(1 - 1) can start once R2(2 - 4) or R3(3 - 5) has
completed (i.e., F2-4 S1-1 or F3-5 S1-1). Take, for example, the
scenario in which R1 (1 - 1) can begin once R2 (2 - 4) has
finished. The figure given below illustrates the domains of F2-4
and S1-1 before and after Constraint 24 is propagated. Before
propagation, the domains of F2-4 and S1-1 were [11, 20] and [0,
13], respectively. Constraint 24 (i.e., F2-4 S1-1) indicates that
the domain of F2-4 must be smaller than or equal to that of S1-1.
As a result, the domains of both F2-4 and S1-1 are reduced to [11,
13]. Node and arc consistency is checked to ensure that these new
domains do not cause any violation to other constraints. This
process is repeated for Constraint 25.
Figure 4.5. Satisfaction of Managerial Constraints (Constraint
14)(Pasit Lorterapong et.al 2013)Stage 3: Backtracking Search and
Stage 4: Relaxation1. Backtracking search and relaxation are
required when any constraint is violated. For this case, no
violation has been encountered. As such, there is no need to
perform backtracking or relaxation.
Figure 4.6. Final Domains of all scheduling variables (Pasit
Lorterapong et.al 2013)Stage 5: Realization1. Finally, it is
necessary to convert the domain of all Si and Fi to their
respective start and finish times. As this figure demonstrates, the
final domains of S2-2 and F2-2 for this alternative are [2, 3] and
[6, 7], respectively. Thus, section 2-2 can start at any time
between the end of weeks 2 and 3, and it can finish at any time
between the end of weeks 6 and 7.2. Combine the domains of the
activity start and finish times into early or late Gantt charts.
Figure 4.7 illustrates the resulting early Gantt chart obtained
from the combination. As explained in Stage 5, the early start time
(ES) for R2 (2-2) assumes the lower bound of domains of S2-2 [2,3],
which is day 2. Similarly, the early finish time (EF) takes the
lower bound of F2-2 [6, 7], which is day 6. Figure 4.7 also
illustrates the earliest possible start and finish times of all
activities.
Figure 4.7. Resulting earliest possible times for all project
activities (Pasit Lorterapong et.al 2013)4.5.
DISCUSSIONSConstruction projects are well known for their
complexities, and they are subject to numerous constraints of
various types. The proposed CSP-based scheduling method focuses on
the satisfaction of project constraints, whereas most CPM-based
methods focus on scheduling activities according to a predefined
and fixed logic. As indicated in the case example, CPM generally
requires planners to comprehend all project constraints at the
outset of the scheduling process. These constraints are then used
to formulate a project network for forward and backward CPM
calculations. Conditional constraints, such as Road 1 can begin as
soon as Road 2 or Road 3 is finished, cannot be incorporated into
one network logic. Multiple logics will have to be modeled
separately in different networks. For large projects, this process
can be time consuming. More importantly, this drawback can limit
the opportunity to obtain schedules of better quality.The CSP-based
scheduling method, on the other hand, allows constraints to be
imposed in a more flexible and expressive manner. The conditional
constraints can be effectively incorporated. The less rigid
constraint such as G1 and G2 cannot be closed at the same time can
effectively be modeled. This type of constraint naturally causes
multiple logics that cannot be effectively modeled by CPM-based
methods. To produce schedules, the proposed CSP based method
propagates constraints and performs consistency checking to ensure
the production of a valid schedule. When inconsistencies are
detected, backtrack searching can be performed to find an
alternative logic
CHAPTER 6CONCLUSIONConstruction projects are subjected to
numerous constraints of various types including contractual due
dates, resource limitations, safety, financial, and managerial
constraints. Satisfying project constraints is one of the most
challenging tasks in the construction scheduling process. The
practicality of a schedule depends considerably on the degree to
which these constraints are satisfied. Most scheduling methods
based on Critical Path Method require that all projects constraints
should be arranged in to a single logical network for developing
project schedule. CPM in its present form has proven inadequate for
the consideration of constraints in real-life construction
projects. This study considered construction scheduling as a
constraint satisfaction problem. CSP gradually generates valid
schedules using constraint propagation and constraint consistency
checking techniques. These techniques are useful for handling
constraints that are predetermined as well as those that become
apparent during schedule development. A CSP-based scheduling method
has been developed to facilitate expressive constraint
representation and to provide effective generation of practical,
valid project schedules. CSP method can be performed in five stages
initialization, propagation, backtracking search, relaxation, and
realization. An application example is analyzed to illustrate the
use of the proposed method and to demonstrate its capability in
comparison to CPM. CSP exhibits a close resemblance to construction
scheduling problems; the variables of the CSP correspond directly
to the scheduling information related to project activities. In
addition, CSP allows constraints to be explicitly expressed and
satisfied. This process helps to facilitate the formulation of
solutions and the selection of search algorithms to guide the
solution. The present method is superior to CPM because of its more
expressive constraint representations and ability to handle multi
logic project networks. Alternative schedules can be obtained with
relative ease. Comparing with the traditional CPM-based methods,
the proposed method has the potential to transform the way
construction schedules are generated and managed. A computerized
CSP method supports humanmachine interactions in generating a more
realistic schedule.
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(2013), Construction Scheduling Using the Constraint Satisfaction
Problem Method Journal of Construction Engineering and Management,
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Dept. Of Civil Engineering19M.E.S.C.E, Kuttippuramthjkhj