In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related ...In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network （only consisting of all the related activities） is equal to the completion time of this path. We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process, the state space is related to the subnetwork structure. Then use the backward equation to compute the distribution of the sub-network＇s completion time, which is an important rule in project management and scheduling.展开更多
In the traditional methods of program evaluation and review technique （PERT） network optimization and compression of time limit for project, the uncertainty of free time difference and total time difference were not...In the traditional methods of program evaluation and review technique （PERT） network optimization and compression of time limit for project, the uncertainty of free time difference and total time difference were not considered as well as its time risk. The authors of this paper use the theory of dependent-chance programming to establish a new model about compression of time for project and multi-objective network optimization, which can overcome the shortages of traditional methods and realize the optimization of PERT network directly. By calculating an example with genetic algorithms, the following conclusions are drawn： （ 1 ） compression of time is restricted by cost ratio and completion probability of project; （2） activities with maximal standard difference of duration and minimal cost will be compressed in order of precedence; （3） there is no optimal solutions but noninferior solutions between chance and cost, and the most optimal node time depends on decision-maker＇s preference.展开更多
In this paper, we present a direct computing method of the Criticality Index (CI) of the activities in PERT networks. The method is no needed for determining CI of all the paths in a PERT network, and the CI of all th...In this paper, we present a direct computing method of the Criticality Index (CI) of the activities in PERT networks. The method is no needed for determining CI of all the paths in a PERT network, and the CI of all the activities can be estimated by computing CI of a small portion of the activities. We give the series of conclusions and computation formulas for computing the CI of activities, and the computing algorithm for the above mentioned conclusions has been applied to large size PERT network. The results are found to be very close to those obtained by extensive Monte Carlo sampling.展开更多
基金supported by the National Natural Science Foundation of China(10671212,10901164,90820302)the Graduate Research Innovation Projects in Hunan Province(CX2009B020)the Graduate Degree Thesis Innovation Foundation of Central Sourth University(2009ybfz11)
文摘In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network （only consisting of all the related activities） is equal to the completion time of this path. We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process, the state space is related to the subnetwork structure. Then use the backward equation to compute the distribution of the sub-network＇s completion time, which is an important rule in project management and scheduling.
文摘In the traditional methods of program evaluation and review technique （PERT） network optimization and compression of time limit for project, the uncertainty of free time difference and total time difference were not considered as well as its time risk. The authors of this paper use the theory of dependent-chance programming to establish a new model about compression of time for project and multi-objective network optimization, which can overcome the shortages of traditional methods and realize the optimization of PERT network directly. By calculating an example with genetic algorithms, the following conclusions are drawn： （ 1 ） compression of time is restricted by cost ratio and completion probability of project; （2） activities with maximal standard difference of duration and minimal cost will be compressed in order of precedence; （3） there is no optimal solutions but noninferior solutions between chance and cost, and the most optimal node time depends on decision-maker＇s preference.
文摘In this paper, we present a direct computing method of the Criticality Index (CI) of the activities in PERT networks. The method is no needed for determining CI of all the paths in a PERT network, and the CI of all the activities can be estimated by computing CI of a small portion of the activities. We give the series of conclusions and computation formulas for computing the CI of activities, and the computing algorithm for the above mentioned conclusions has been applied to large size PERT network. The results are found to be very close to those obtained by extensive Monte Carlo sampling.
