A New Approach to Determine the Critical Path in Stochastic Activity Network

Abstract

The determination of the critical path (CP) in stochastic networks is difficult. It is partly due to the randomness of path durations and partly due to the probability issue of the selection of the critical path in the network. What we are confronted with is not only the complexity among random variables but also the problem of path dependence of the network. Besides, we found that CP is not necessarily the longest (or shortest) path in the network, which was a conventional assumption in use. The Program Evaluation and Review Technique (PERT) and Critical Path Index (CPI) approaches are not able to deal with this problem efficiently. In this study, we give a new definition on the CP in stochastic network and propose a modified label-correcting tracing algorithm (M-LCTA) to solve it. Based on the numerical results, compared with Monte Carlo simulation (MCS), the proposed approach can accurately determine the CP in stochastic networks.

Assessing the Effectiveness of a Single Curriculum for a Group of Students with Different Mathematics Literacy

“…The enumeration of all the probable paths connecting the start and end node available in the project network is regarded as one of the most common approaches (Chu et. al., 2014a) [3]. Attempt to search for CP in stochastic network is something justified having its own reasons (Chu et.…”

On Determining the Critical Path of Activity Network with Normalized Heptagonal Fuzzy Data

“…Rautela et al [4] concluded that the CPM can be used by every department as a tool for meeting the commitment of the delivery to other related departments and thereby reducing the problem of internal delays which causes the delay in the delivery of the final product of the company where in this case the company being a shoe production plant. Chu et al [5] gave a new definition on the critical path in stochastic network and proposed a modified label-correcting tracing algorithm to solve it. Also, they compared the results with the Monte Carlo simulation, where the approach proposed can accurately determine the critical path in stochastic networks.…”