Approximating the Criticality Indices of the Activities in PERT Networks

Article Abstract:

A stochastic PERT network is a directed acyclic network in which the arc lengths are independent random variables with known distributions. A fundamental problem in PERT networks is to identify the activities which are critical to the achievement of the project objectives. In an activity network if the duration of each activity is not a random variable, then it is easy to identify the criticality of each activity represented by its float time. However, when the duration of any activity is a random variable, it is not easy to identify the criticality of each activity. In this case the criticality of an activity is known as the 'criticality index,' which is defined as the sum of the criticality indices of the paths containing it. The criticality index of a path is the probability that the duration of the path is greater than or equal to the duration of every other path in the network. Clearly, the criticality index of an activity can be obtained by determining the criticality indices of the paths, which requires identifying all the paths, determining their criticality indices, then identifying the paths containing the activity. In this paper we develop a theory which leads to a procedure to approximate the criticality indices of all the activities without going through the above three steps. The procedure has been applied to large size PERT networks generated at random, and the results are found to be very close to those obtained by extensive Monte Carlo sampling. (Reprinted by Permission of Publisher).

Management science, Project management software, Networks, Methods, Approximation, Monte Carlo Methods, Critical Path Method, PERT

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Approximating the criticality indices of the activities in PERT networks

Article Abstract:

PERT networks are defined as stochastic networks that are acyclic and directed, with arc lengths that reflect independently random variables for known distributions. Most PERT network analysis confines itself to an identification of the network activities required to meet the network's goals and objectives. The criticality of each activity may also be defined, according to the total of the criticality indices developed in this research. The criticality indices are themselves dependent upon the proper identification of all network paths, assignment of a criticality value to each path, and association of each path within the network to a network activity.

Models, Industrial project management, Network analysis (Planning), Program Evaluation and Review Technique, Critical path analysis

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The analysis of activity networks under generalized precedence relations (GPRs)

Article Abstract:

An expanded version of Kerbosch and Schell's model for network planning under generalized precedence relations (GPRs) that was first introduced in 1975 is presented. GPRs are relations between paired activities that do not adhere to the 'strict precedence' concept proposed in Kelley and Walker's CPM model, meaning that the completion of an activity need not be a condition for the commencement of another activity. Discussions on notation and terminology pertaining to activity networks with GPRs, on temporal analysis and feasibility issues, and on how GPRs may be transformed into more easily understandable relations are presented.

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