Construction Scheduling Using Constraint Satisfaction Problem Method

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











14F2-1 S2-2Technological










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.

REFERENCES1. Pasit Lorterapong and Mongkol Ussavadilokrit (2013), Construction Scheduling Using the Constraint Satisfaction Problem Method Journal of Construction Engineering and Management, 2013.139 (ASCE), pp. 414 422 (9).2. Ioana Cobeanu, Vasile Comnac (2012), Multi-Agent Scheduling using Constraint Satisfaction Problem, 11th International Conference On Development And Application Systems, pp. 183 186 (4)3. Chan, W. T., and Hu, H. (2002), Constraint programming approach to precast production scheduling, Journal of Construction Engineering and Management, pp. 513521(9)4. Liliana Cucu - Grosjean & Olivier Buffet, Global Multiprocessor Real-Time Scheduling as a Constraint Satisfaction Problem, pp. 01 085. Claude Le Pape, Constraint-Based Scheduling: A Tutorial pp. 01 - 33

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Construction Scheduling Using Constraint Satisfaction Problem Method