The critical path method is one of the oldest and most important techniques used for planning and scheduling projects.The main objective of project management science is to determine the critical path through a networ...The critical path method is one of the oldest and most important techniques used for planning and scheduling projects.The main objective of project management science is to determine the critical path through a network representation of projects.The critical path through a network can be determined by many algorithms and is useful for managing,monitoring,and controlling the time and cost of an entire project.The essential problem in this case is that activity durations are uncertain;time presents considerable uncertainty because the time of an activity is not always easily or accurately estimated.This issue increases the need to use neutrosophic theory to solve the critical path problem.Real-world problems are characterized by a lack of precision,consistency,and completeness.The concept of neutrosophic sets has been introduced as a generalization of fuzzy,intuitionistic fuzzy,and crisp sets to overcome the ambiguity surrounding real-world problems.Truth-,falsity-,and indeterminacy-membership functions are used to express neutrosophic elements.This study was performed to examine a neutrosophic event-oriented algorithm for determining the critical path in activity-on-arc networks.The activity time estimates are presented as trapezoidal neutrosophic numbers,and score and accuracy functions are used to obtain a crisp model of the problem.An appropriate numerical example is then used to explain the proposed method.展开更多
Project scheduling is a key objective of many models and is the proposed method for project planning and management.Project scheduling problems depend on precedence relationships and resource constraints,in addition t...Project scheduling is a key objective of many models and is the proposed method for project planning and management.Project scheduling problems depend on precedence relationships and resource constraints,in addition to some other limitations for achieving a subset of goals.Project scheduling problems are dependent on many limitations,including limitations of precedence relationships,resource constraints,and some other limitations for achieving a subset of goals.Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required,which are known and stable during the implementation process.The concept of deterministic project scheduling conflicts with real situations,in which in many cases,some data on the activity’s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations.Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us.We use the multi-mode resource allocation and schedulingmodel that takes into account the dynamicity features of all parameters,that is,the scheduling process must be flexible to dynamic environment features.In this paper,we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations,in which we apply the proposed heuristic rules(PHR)for scheduling multi-mode resource-constrained projects.Five projects are considered test problems for the PHR.The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems.The results in many cases of the proposed priority rules are very promising,where they achieve better scheduling dates in many test case problems and the same results for the others.The proposed model is based on the dynamic features for project topography.展开更多
基金This work was supported by the Soonchunhyang University Research Fund.
文摘The critical path method is one of the oldest and most important techniques used for planning and scheduling projects.The main objective of project management science is to determine the critical path through a network representation of projects.The critical path through a network can be determined by many algorithms and is useful for managing,monitoring,and controlling the time and cost of an entire project.The essential problem in this case is that activity durations are uncertain;time presents considerable uncertainty because the time of an activity is not always easily or accurately estimated.This issue increases the need to use neutrosophic theory to solve the critical path problem.Real-world problems are characterized by a lack of precision,consistency,and completeness.The concept of neutrosophic sets has been introduced as a generalization of fuzzy,intuitionistic fuzzy,and crisp sets to overcome the ambiguity surrounding real-world problems.Truth-,falsity-,and indeterminacy-membership functions are used to express neutrosophic elements.This study was performed to examine a neutrosophic event-oriented algorithm for determining the critical path in activity-on-arc networks.The activity time estimates are presented as trapezoidal neutrosophic numbers,and score and accuracy functions are used to obtain a crisp model of the problem.An appropriate numerical example is then used to explain the proposed method.
文摘Project scheduling is a key objective of many models and is the proposed method for project planning and management.Project scheduling problems depend on precedence relationships and resource constraints,in addition to some other limitations for achieving a subset of goals.Project scheduling problems are dependent on many limitations,including limitations of precedence relationships,resource constraints,and some other limitations for achieving a subset of goals.Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required,which are known and stable during the implementation process.The concept of deterministic project scheduling conflicts with real situations,in which in many cases,some data on the activity’s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations.Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us.We use the multi-mode resource allocation and schedulingmodel that takes into account the dynamicity features of all parameters,that is,the scheduling process must be flexible to dynamic environment features.In this paper,we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations,in which we apply the proposed heuristic rules(PHR)for scheduling multi-mode resource-constrained projects.Five projects are considered test problems for the PHR.The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems.The results in many cases of the proposed priority rules are very promising,where they achieve better scheduling dates in many test case problems and the same results for the others.The proposed model is based on the dynamic features for project topography.
